├── .gitignore ├── .nojekyll ├── .sandbox ├── Box.cpp ├── Poisson_layers.py ├── Rectangle.cpp ├── cbcpdesys │ ├── pdesys-sphinx │ │ ├── .buildinfo │ │ ├── _images │ │ │ ├── diffusor_F12.png │ │ │ ├── diffusor_R12.png │ │ │ ├── dolfin.gif │ │ │ ├── dolfin_temp.gif │ │ │ └── math │ │ │ │ ├── 07b7a448bfecd2f80c803ebf7fd4d0d3fac9036f.png │ │ │ │ ├── 0b2a51cd41243ff8b59ede0a9dccc538c08db0b2.png │ │ │ │ ├── 0e5c83cc0c639fc2ed843bbe2d3d209fb478b104.png │ │ │ │ ├── 15f4c9ff200fdbfde16109ecc1e017cae769f4db.png │ │ │ │ ├── 3372c1cb6d68cf97c2d231acc0b47b95a9ed04cc.png │ │ │ │ ├── 34aaaeb9473881f871555bc1355afd963410be9a.png │ │ │ │ ├── 3669b5db99224ebf0421c1a32dbe764c32c0bb2b.png │ │ │ │ ├── 36f73fc1312ee0349b3f3a0f3bd9eb5504339011.png │ │ │ │ ├── 428a9dc1d8e9806753dc4e8af5ccbac760b5d826.png │ │ │ │ ├── 4ea4839b68acd0e4233d3a4977b6ef432ae88096.png │ │ │ │ ├── 5134e1a5cbcb701ba41d11d3f29989450dcff82d.png │ │ │ │ ├── 52cb3f2ae29919e529bd2a0fd37a1d43f43f575b.png │ │ │ │ ├── 66464c07a6a700211159b4053873d23d58996a8e.png │ │ │ │ ├── 6c6b2103381c3afe56f678fb6598f5de4a1297b0.png │ │ │ │ ├── 8c325612684d41304b9751c175df7bcc0f61f64f.png │ │ │ │ ├── 9d7a0f503395c2eb4479b4eb37a16fe9e04732f6.png │ │ │ │ ├── abaaae67d0edc6cbfc16a2f7075c62a97a054774.png │ │ │ │ ├── bc2b87757d39785a57718562d1595e21fcf91b50.png │ │ │ │ ├── be298c21806debb3e79cdb3ab3386c57c2562998.png │ │ │ │ ├── c2a67e46b0ad4f3f21944eac231716dfd5457813.png │ │ │ │ ├── d9dcbe5ba2482e3a195875d5bd14530af9ea6b5e.png │ │ │ │ └── d9df74315a21f447e0a338c4c76dcd9880542eaf.png │ │ ├── _sources │ │ │ ├── index.txt │ │ │ └── pdesys.txt │ │ ├── _static │ │ │ ├── ajax-loader.gif │ │ │ ├── basic.css │ │ │ ├── comment-bright.png │ │ │ ├── comment-close.png │ │ │ ├── comment.png │ │ │ ├── dialog-note.png │ │ │ ├── dialog-seealso.png │ │ │ ├── dialog-topic.png │ │ │ ├── dialog-warning.png │ │ │ ├── doctools.js │ │ │ ├── dolfin.png │ │ │ ├── dorsal.png │ │ │ ├── down-pressed.png │ │ │ ├── down.png │ │ │ ├── download-button.png │ │ │ ├── epub.css │ │ │ ├── feature-item-1.png │ │ │ ├── featured.css │ │ │ ├── feed-icon-14x14.gif │ │ │ ├── fenics-news-icon.png │ │ │ ├── fenics-web.png │ │ │ ├── fenics.css │ │ │ ├── fenics.ico │ │ │ ├── fenics_banner.png │ │ │ ├── file.png │ │ │ ├── footerbg.png │ │ │ ├── headerbg.png │ │ │ ├── ie6.css │ │ │ ├── jquery.js │ │ │ ├── middlebg.png │ │ │ ├── minus.png │ │ │ ├── neuton-fontfacekit │ │ │ │ ├── Apache License Version 2.txt │ │ │ │ ├── Neuton-webfont.eot │ │ │ │ ├── Neuton-webfont.svg │ │ │ │ ├── Neuton-webfont.ttf │ │ │ │ ├── Neuton-webfont.woff │ │ │ │ ├── demo.html │ │ │ │ └── stylesheet.css │ │ │ ├── nobile-fontfacekit │ │ │ │ ├── SIL Open Font License 1.1.txt │ │ │ │ ├── demo.html │ │ │ │ ├── nobile-webfont.eot │ │ │ │ ├── nobile-webfont.svg │ │ │ │ ├── nobile-webfont.ttf │ │ │ │ ├── nobile-webfont.woff │ │ │ │ ├── nobile_bold-webfont.eot │ │ │ │ ├── nobile_bold-webfont.svg │ │ │ │ ├── nobile_bold-webfont.ttf │ │ │ │ ├── nobile_bold-webfont.woff │ │ │ │ ├── nobile_bold_italic-webfont.eot │ │ │ │ ├── nobile_bold_italic-webfont.svg │ │ │ │ ├── nobile_bold_italic-webfont.ttf │ │ │ │ ├── nobile_bold_italic-webfont.woff │ │ │ │ ├── nobile_italic-webfont.eot │ │ │ │ ├── nobile_italic-webfont.svg │ │ │ │ ├── nobile_italic-webfont.ttf │ │ │ │ ├── nobile_italic-webfont.woff │ │ │ │ └── stylesheet.css │ │ │ ├── plus.png │ │ │ ├── pygments.css │ │ │ ├── sample-news-image.png │ │ │ ├── searchtools.js │ │ │ ├── slides.min.jquery.js │ │ │ ├── transparent.gif │ │ │ ├── underscore.js │ │ │ ├── unknown.png │ │ │ ├── up-pressed.png │ │ │ ├── up.png │ │ │ └── websupport.js │ │ ├── cbc.rans-MekIT11.pdf │ │ ├── genindex.html │ │ ├── index.html │ │ ├── objects.inv │ │ ├── pdesys.html │ │ ├── search.html │ │ └── searchindex.js │ ├── pdesys.do.txt │ └── pdesys_latex2.pdf ├── chapter_1.py ├── comments.txt ├── da.py ├── da2.py ├── define_layers.py ├── dolfinprm2datapool.py ├── domain_hollow_circle.py ├── domain_types.py ├── extra │ ├── Kent_demo_subdomains.py │ ├── demo.py │ ├── dolfin_failed_trick.py │ ├── dolfin_parameters.xml │ ├── hpl2b.py │ ├── hpl3.py │ ├── hpl5.py │ └── hpl7.py ├── makebox.py ├── membrane2.py ├── membrane2_class.py ├── membrane2_experiment.py ├── nonlin_solver.py ├── sin__class_daD.py ├── test1.py └── triangle │ ├── 2DO │ ├── README │ ├── expre.py │ ├── gear.xml │ ├── gmsh.txt │ ├── makefile │ ├── plotmesh.py │ ├── prepro2D.py │ ├── showme.c │ ├── triangle.c │ ├── triangle.h │ ├── triangle.zip │ └── tricall.c ├── README.md ├── chinese ├── Makefile ├── README.md ├── anslistings.sty ├── bibliography.bib ├── chapters │ ├── chapter1.tex │ ├── chapter2.tex │ ├── chapter3.tex │ ├── chapter4.tex │ ├── chapter5.tex │ └── preface.tex ├── cover │ ├── cover.jpg │ └── cover.xcf ├── fenics-tutorial-chinese.tex ├── fig │ ├── elasticity.png │ ├── heat.png │ ├── magnetostatics_field.png │ ├── magnetostatics_geometry.pdf │ ├── magnetostatics_geometry.png │ ├── magnetostatics_geometry.svg │ ├── magnetostatics_mesh.png │ ├── magnetostatics_potential.png │ ├── navier_stokes_channel.png │ ├── navier_stokes_cylinder_geometry.pdf │ ├── navier_stokes_cylinder_geometry.png │ ├── navier_stokes_cylinder_geometry.svg │ ├── navier_stokes_cylinder_pressure.png │ ├── navier_stokes_cylinder_velocity.png │ ├── poisson_extended.pdf │ ├── poisson_extended.png │ ├── poisson_membrane_curves.png │ ├── poisson_membrane_deflection_load.png │ ├── poisson_paraview.png │ ├── poisson_plot.png │ ├── reaction_system.png │ ├── subdomains.pdf │ ├── subdomains.png │ ├── subdomains.svg │ └── vertex_numbering.png ├── images │ ├── background.jpg │ ├── cover.jpg │ ├── idea.pdf │ └── image-info ├── input │ ├── README.md │ ├── fenics-tutorial-vol1.pdf │ ├── ftut1.tex │ ├── ftut1_new.tex │ └── ftut1_original.tex ├── newcommands.tex └── tstextbook.cls ├── pub ├── README.md ├── html │ └── README.md ├── pdf │ └── README.md └── python │ └── vol1 │ ├── README.md │ ├── ft01_poisson.py │ ├── ft02_poisson_membrane.py │ ├── ft03_heat.py │ ├── ft04_heat_gaussian.py │ ├── ft05_poisson_nonlinear.py │ ├── ft06_elasticity.py │ ├── ft07_navier_stokes_channel.py │ ├── ft08_navier_stokes_cylinder.py │ ├── ft09_reaction_system.py │ ├── ft10_poisson_extended.py │ ├── ft11_magnetostatics.py │ └── ft12_poisson_solver.py ├── reviews ├── fenics_tutorial_review_2016_1.pdf ├── fenics_tutorial_review_2016_2.pdf ├── fenics_tutorial_review_2016_3.pdf ├── fenics_tutorial_review_2016_4.pdf └── fenics_tutorial_review_2016_4_new.pdf └── src ├── .dict4spell.txt ├── Makefile ├── README.md ├── TODO ├── bib ├── papers.pub └── venues.list ├── exer ├── clean.sh ├── p2D_flat_Neumann1.py ├── p2D_flat_Neumann2.py ├── poisson_3d_func.py └── vol1 │ ├── Expression_efficiency.py │ ├── membrane_func.py │ ├── navier_stokes_box.py │ ├── poisson_fsin_flat.py │ └── poisson_fsin_func.py ├── fig ├── elasticity.png ├── heat.png ├── magnetostatics_field.png ├── magnetostatics_geometry.pdf ├── magnetostatics_geometry.png ├── magnetostatics_geometry.svg ├── magnetostatics_mesh.png ├── magnetostatics_potential.png ├── navier_stokes_channel.png ├── navier_stokes_cylinder_geometry.pdf ├── navier_stokes_cylinder_geometry.png ├── navier_stokes_cylinder_geometry.svg ├── navier_stokes_cylinder_pressure.png ├── navier_stokes_cylinder_velocity.png ├── poisson_extended.pdf ├── poisson_extended.png ├── poisson_membrane_curves.png ├── poisson_membrane_deflection_load.png ├── poisson_paraview.png ├── poisson_plot.png ├── reaction_system.png ├── subdomains.pdf ├── subdomains.png ├── subdomains.svg └── vertex_numbering.png ├── ftut1.do.txt ├── ftut1.tex ├── ftut2.do.txt ├── mako_code.txt ├── mov ├── heat_gaussian.ogv ├── navier_stokes_cylinder.ogv └── reaction_system.ogv ├── newcommands.p.tex ├── notes.org ├── old ├── fig │ ├── Poisson2D_D1.pdf │ ├── Poisson2D_D1_mesh.pdf │ ├── Poisson2D_D1_wireframe.pdf │ ├── Poisson2D_Dvc.pdf │ ├── Poisson2D_Dvc.png │ ├── Poisson2D_Dvc_contour1.pdf │ ├── Poisson2D_Dvc_contour1.png │ ├── Poisson2D_Dvc_flux_x.pdf │ ├── Poisson2D_Dvc_flux_x.png │ ├── Poisson2D_Dvc_mesh1.pdf │ ├── Poisson2D_Dvc_mesh1.png │ ├── Poisson2D_Dvc_surf1.pdf │ ├── Poisson2D_Dvc_surf1.png │ ├── Poisson2D_Dvc_surfmesh1.pdf │ ├── Poisson2D_Dvc_surfmesh1.png │ ├── beam1.pdf │ ├── beam1.png │ ├── beam2.pdf │ ├── beam2.png │ ├── cube3D_quad_sol.pdf │ ├── cube3D_quad_sol.png │ ├── cube3D_quad_sol_contours.pdf │ ├── cube3D_quad_sol_contours.png │ ├── daynight.fig │ ├── daynight.pdf │ ├── daynight.png │ ├── daynight.pstex │ ├── daynight.pstex_t │ ├── daynight.tex │ ├── diffu_A_factors_BE.pdf │ ├── diffu_A_factors_BE.png │ ├── diffu_A_factors_CN.pdf │ ├── diffu_A_factors_CN.png │ ├── diffu_A_factors_fine_FE.pdf │ ├── diffu_A_factors_fine_FE.png │ ├── diffusion0_paraview_animation.png │ ├── ex1_gradu.pdf │ ├── ex1_gradu.png │ ├── ex1_mesh.pdf │ ├── ex1_mesh.png │ ├── ex1_u.pdf │ ├── ex1_u.png │ ├── gui_poisson1.png │ ├── gui_poisson2.png │ ├── guifig_view1.png │ ├── guifig_view1.tiff │ ├── guifig_view_dolfin_krylov_solver.png │ ├── guifig_view_dolfin_krylov_solver.tiff │ ├── guifig_view_results1.png │ ├── guifig_view_results1.tiff │ ├── guifig_view_results1_bootstrap.png │ ├── guifig_view_results1_bootstrap.tiff │ ├── hollow_cylinder.pdf │ ├── hollow_cylinder.png │ ├── layered_medium_2.py │ ├── layers.fig │ ├── layers.pdf │ ├── layers.pstex │ ├── layers.pstex_t │ ├── layers.sh │ ├── layers.tex │ ├── membrane_curveplot.pdf │ ├── membrane_curveplot.png │ ├── membrane_curveplot_new.pdf │ ├── membrane_curveplot_new.png │ ├── membrane_deflection.pdf │ ├── membrane_deflection.png │ ├── membrane_fenics_viz.pdf │ ├── membrane_fenics_viz.png │ ├── membrane_waxis.eps.Doug │ ├── membrane_waxis.eps.orig0 │ ├── membrane_waxis.pdf │ ├── membrane_waxis.png │ ├── paraview_animation_buttons.png │ ├── paraview_membrane.pdf │ ├── paraview_membrane.png │ ├── paraview_membrane2_3D.pdf │ ├── paraview_membrane2_3D.png │ ├── paraview_membrane3.pdf │ ├── paraview_membrane3.png │ ├── paraview_membrane3b.pdf │ ├── paraview_membrane3b.png │ ├── paraview_show_center_button.png │ ├── poisson0_paraview.pdf │ ├── poisson0_paraview.png │ ├── poisson_fsin.pdf │ ├── poisson_fsin.png │ ├── poisson_vc_structmesh.pdf │ ├── poisson_vc_structmesh.png │ ├── reaction_system_u1.png │ ├── reaction_system_u2.png │ ├── reaction_system_u3.png │ ├── thermal_layer1.pdf │ ├── thermal_layer1.png │ ├── thermal_layer1.py │ ├── thermal_layer1_BE20.pdf │ ├── thermal_layer1_BE20.png │ ├── thermal_layer1_CN20.pdf │ ├── thermal_layer1_CN20.png │ ├── thermal_layer1_sketch.pdf │ ├── thermal_layer1_sketch.png │ ├── thermal_layer2_CN20.pdf │ ├── thermal_layer2_CN20.png │ ├── thermal_layer2_sketch.pdf │ ├── thermal_layer2_sketch.png │ ├── thermal_layer3.py │ ├── thermal_layer3_CN20.pdf │ ├── thermal_layer3_CN20.png │ ├── thermal_layer3_scaling_sketch.pdf │ ├── thermal_layer3_scaling_sketch.png │ ├── thermal_layer3_sketch.pdf │ ├── thermal_layer3_sketch.png │ ├── thermal_layer4.pdf │ ├── thermal_layer4.png │ ├── two_domains.fig │ ├── two_domains.latex │ ├── welding3D.pdf │ ├── welding3D.png │ ├── welding_gamma2000_temp.pdf │ └── welding_gamma2000_temp.png └── mov │ ├── diffusion0.ogg │ ├── thermal_layer1 │ ├── movie.flv │ ├── movie.mp4 │ ├── movie.ogg │ └── movie.webm │ ├── thermal_layer2 │ ├── movie.flv │ ├── movie.mp4 │ ├── movie.ogg │ └── movie.webm │ ├── thermal_layer3 │ ├── movie.flv │ ├── movie.mp4 │ ├── movie.ogg │ ├── movie.webm │ └── paraview.ogg │ ├── thermal_layer4 │ ├── movie.flv │ ├── movie.mp4 │ ├── movie.ogg │ └── movie.webm │ └── welding │ ├── welding_gamma01_3D.ogg │ ├── welding_gamma1_2D.ogg │ ├── welding_gamma1_3D.ogg │ ├── welding_gamma2000_3D.ogg │ └── welding_gamma30_3D.ogg ├── scripts ├── clean.sh ├── install.sh ├── make.sh ├── make_notebooks.sh ├── make_simple.sh ├── number_src_files.py ├── publish.sh └── rsync_git.py ├── src ├── channel_flow.py ├── clean.sh ├── concentric_cylinders.py ├── convection_diffusion.py ├── gui │ ├── .tmp_pool.dat │ ├── clean.sh │ ├── noweb │ │ ├── .tmp_pool.dat │ │ ├── compute_noweb.py │ │ ├── controller_noweb.py │ │ ├── poisson_bcs.py │ │ ├── poisson_iterative.py │ │ ├── poisson_solver.py │ │ └── prm.xml │ └── web │ │ ├── BoxField.py │ │ ├── compute.py │ │ ├── controller.py │ │ ├── generate.py │ │ ├── model.py │ │ ├── poisson_bcs.py │ │ ├── poisson_iterative.py │ │ ├── poisson_solver.py │ │ ├── prm.xml │ │ └── static │ │ ├── dtree.css │ │ ├── dtree.js │ │ ├── img │ │ ├── base.gif │ │ ├── cd.gif │ │ ├── empty.gif │ │ ├── folder.gif │ │ ├── folderopen.gif │ │ ├── globe.gif │ │ ├── imgfolder.gif │ │ ├── join.gif │ │ ├── joinbottom.gif │ │ ├── line.gif │ │ ├── minus.gif │ │ ├── minusbottom.gif │ │ ├── musicfolder.gif │ │ ├── nolines_minus.gif │ │ ├── nolines_plus.gif │ │ ├── page.gif │ │ ├── plus.gif │ │ ├── plusbottom.gif │ │ ├── question.gif │ │ └── trash.gif │ │ └── latex │ │ └── Main_menu │ │ ├── Nx.png │ │ ├── Ny.png │ │ ├── dolfin │ │ ├── allow_extrapolation.png │ │ ├── dof_ordering_library.png │ │ ├── form_compiler │ │ │ ├── cache_dir.png │ │ │ ├── convert_exceptions_to_warnings.png │ │ │ ├── cpp_optimize.png │ │ │ ├── cpp_optimize_flags.png │ │ │ ├── epsilon.png │ │ │ ├── error_control.png │ │ │ ├── form_postfix.png │ │ │ ├── format.png │ │ │ ├── log_level.png │ │ │ ├── log_prefix.png │ │ │ ├── name.png │ │ │ ├── no-evaluate_basis_derivatives.png │ │ │ ├── optimize.png │ │ │ ├── output_dir.png │ │ │ ├── precision.png │ │ │ ├── quadrature_degree.png │ │ │ ├── quadrature_rule.png │ │ │ ├── representation.png │ │ │ ├── restrict_keyword.png │ │ │ └── split.png │ │ ├── ghost_mode.png │ │ ├── graph_coloring_library.png │ │ ├── krylov_solver │ │ │ ├── absolute_tolerance.png │ │ │ ├── divergence_limit.png │ │ │ ├── error_on_nonconvergence.png │ │ │ ├── gmres │ │ │ │ └── restart.png │ │ │ ├── maximum_iterations.png │ │ │ ├── monitor_convergence.png │ │ │ ├── nonzero_initial_guess.png │ │ │ ├── preconditioner │ │ │ │ ├── ilu │ │ │ │ │ └── fill_level.png │ │ │ │ ├── report.png │ │ │ │ ├── schwarz │ │ │ │ │ └── overlap.png │ │ │ │ ├── shift_nonzero.png │ │ │ │ └── structure.png │ │ │ ├── relative_tolerance.png │ │ │ └── report.png │ │ ├── linear_algebra_backend.png │ │ ├── lu_solver │ │ │ ├── report.png │ │ │ ├── reuse_factorization.png │ │ │ ├── same_nonzero_pattern.png │ │ │ ├── symmetric.png │ │ │ └── verbose.png │ │ ├── mesh_partitioner.png │ │ ├── num_threads.png │ │ ├── partitioning_approach.png │ │ ├── print_mpi_thread_support_level.png │ │ ├── refinement_algorithm.png │ │ ├── relative_line_width.png │ │ ├── reorder_cells_gps.png │ │ ├── reorder_dofs_serial.png │ │ ├── reorder_vertices_gps.png │ │ ├── std_out_all_processes.png │ │ ├── timer_prefix.png │ │ ├── use_petsc_signal_handler.png │ │ └── warn_on_xml_file_size.png │ │ ├── element_degree.png │ │ ├── f.png │ │ └── u0.png ├── heat2.py ├── heat_class.py ├── heat_func.py ├── make_moviefiles.sh ├── mat2_poisson.py ├── mat2x_poisson.py ├── modules │ ├── BoxField.py │ └── setup.py ├── nlpoisson_alg_newton.py ├── nlpoisson_class.py ├── nlpoisson_func.py ├── nlpoisson_pde_newton.py ├── nlpoisson_picard.py ├── numbering.py └── poisson_class.py ├── vol1 ├── extensions.do.txt ├── fundamentals.do.txt ├── fundamentals_membrane.do.txt ├── fundamentals_poisson.do.txt ├── gallery.do.txt ├── gallery_elasticity.do.txt ├── gallery_heat_equation.do.txt ├── gallery_navier_stokes.do.txt ├── gallery_nlpoisson.do.txt ├── gallery_reaction_system.do.txt ├── preface.do.txt ├── preliminaries.do.txt ├── python │ ├── boxfield.py │ ├── elasticity.py │ ├── heat.py │ ├── heat_gaussian.py │ ├── magnetostatics.py │ ├── navier_stokes_channel.py │ ├── navier_stokes_cylinder.py │ ├── poisson.py │ ├── poisson_extended.py │ ├── poisson_membrane.py │ ├── poisson_nonlinear.py │ ├── poisson_solver.py │ └── reaction_system.py └── subdomains.do.txt └── vol2 ├── gui.do.txt ├── handling_coefficient_on_subdomain.do.txt ├── heat.do.txt ├── heatlossproblem.do.txt ├── misc.do.txt ├── nlpoisson.do.txt ├── notes.txt ├── prepro.do.txt └── troubleshooting.do.txt /.gitignore: -------------------------------------------------------------------------------- 1 | # doconce files: 2 | *.rst 3 | *.ipynb 4 | *.gwiki 5 | *.cwiki 6 | *.mwiki 7 | automake_sphinx.py 8 | .*_html_file_collection 9 | .*.exerinfo 10 | .*.copyright 11 | sphinx-rootdir 12 | Trash 13 | papers.bib 14 | # compiled files: 15 | *.o 16 | *.so 17 | *.a 18 | # temporary files: 19 | *.pyc 20 | *.bak 21 | *.swp 22 | *~ 23 | .*~ 24 | *.old 25 | tmp* 26 | temp* 27 | .#* 28 | \#* 29 | # tex files: 30 | *.aux 31 | *.bbl 32 | *.blg 33 | *.log 34 | *.dvi 35 | *.idx 36 | *.ilg 37 | *.ind 38 | *.loe 39 | *.nav 40 | *.out 41 | *.toc 42 | *.snm 43 | *.vrb 44 | # 45 | # eclipse files: 46 | *.cproject 47 | *.project 48 | # misc: 49 | .DS_Store 50 | Trash 51 | *.pvd 52 | *.vtu 53 | *.tar.gz 54 | -------------------------------------------------------------------------------- /.nojekyll: 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Master file automatically created by doconce sphinx_dir 3 | 4 | Welcome to cbc.pde! 5 | ================================================================== 6 | 7 | Contents: 8 | 9 | .. toctree:: 10 | :maxdepth: 2 11 | 12 | pdesys 13 | 14 | 15 | Indices and tables 16 | ================== 17 | 18 | * :ref:`genindex` 19 | * :ref:`modindex` 20 | * :ref:`search` 21 | -------------------------------------------------------------------------------- /.sandbox/cbcpdesys/pdesys-sphinx/_static/ajax-loader.gif: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/hplgit/fenics-tutorial/bf8120cb448f244df18871ee305f4b9c463896cf/.sandbox/cbcpdesys/pdesys-sphinx/_static/ajax-loader.gif -------------------------------------------------------------------------------- /.sandbox/cbcpdesys/pdesys-sphinx/_static/comment-bright.png: -------------------------------------------------------------------------------- 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25 |

Font-face Demo for the Neuton Font

26 | 27 | 28 | 29 |

Neuton Regular - Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.

30 | 31 |
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format('woff'), 34 | url('nobile_bold-webfont.ttf') format('truetype'), 35 | url('nobile_bold-webfont.svg#NobileBold') format('svg'); 36 | font-weight: normal; 37 | font-style: normal; 38 | 39 | } 40 | 41 | @font-face { 42 | font-family: 'NobileBoldItalic'; 43 | src: url('nobile_bold_italic-webfont.eot'); 44 | src: url('nobile_bold_italic-webfont.eot?#iefix') format('embedded-opentype'), 45 | url('nobile_bold_italic-webfont.woff') format('woff'), 46 | url('nobile_bold_italic-webfont.ttf') format('truetype'), 47 | url('nobile_bold_italic-webfont.svg#NobileBoldItalic') format('svg'); 48 | font-weight: normal; 49 | font-style: normal; 50 | 51 | } 52 | 53 | -------------------------------------------------------------------------------- /.sandbox/cbcpdesys/pdesys-sphinx/_static/plus.png: -------------------------------------------------------------------------------- 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-------------------------------------------------------------------------------- https://raw.githubusercontent.com/hplgit/fenics-tutorial/bf8120cb448f244df18871ee305f4b9c463896cf/.sandbox/cbcpdesys/pdesys_latex2.pdf -------------------------------------------------------------------------------- /.sandbox/da.py: -------------------------------------------------------------------------------- 1 | """ 2 | Solve a Poisson equation and its adjoint. 3 | """ 4 | 5 | from dolfin import * 6 | 7 | # Create mesh and define function space 8 | mesh = UnitSquareMesh(6, 6) 9 | V = FunctionSpace(mesh, 'Lagrange', 1) 10 | 11 | # Define boundary conditions 12 | bc = DirichletBC(V, 0, "on_boundary") 13 | 14 | nu = 1 15 | 16 | # Define variational problem 17 | u = TrialFunction(V) 18 | v = TestFunction(V) 19 | f = Constant(-6) 20 | a = nu*inner(nabla_grad(u), nabla_grad(v))*dx 21 | L = f*v*dx 22 | 23 | # Compute solution 24 | u = Function(V) 25 | solve(a == L, u, bc) 26 | 27 | # Compute adjoint solution (when the adjoint PDE is derived by hand) 28 | lambda_ = TrialFunction(V) 29 | a = nu*inner(nabla_grad(v), nabla_grad(lambda_))*dx 30 | u_d = Expression('sin(pi*x[0])') 31 | L = -(u - u_d)*v*dx 32 | lambda_ = Function(V) 33 | solve(a == L, lambda_, bc) 34 | 35 | # Plot solution and mesh 36 | plot(u, interactive=True) 37 | plot(mesh, interactive=True) 38 | 39 | # Dump solution to file in VTK format 40 | file = File('poisson.pvd') 41 | file << u 42 | -------------------------------------------------------------------------------- /.sandbox/da2.py: -------------------------------------------------------------------------------- 1 | """ 2 | Solve a Poisson equation and its adjoint. 3 | """ 4 | 5 | from dolfin import * 6 | from dolfin_adjoint import * 7 | 8 | # Create mesh and define function space 9 | mesh = UnitSquareMesh(6, 6) 10 | V = FunctionSpace(mesh, 'Lagrange', 1) 11 | 12 | # Define boundary conditions 13 | bc = DirichletBC(V, 0.0, "on_boundary") 14 | 15 | # All parameters in dolfin-adjoint must be Constant or Function 16 | nu = Constant(1) 17 | 18 | # Define variational problem 19 | u = TrialFunction(V) 20 | v = TestFunction(V) 21 | f = Constant(1.0) 22 | f = interpolate(Constant(1.0), V) # Must be function for da to work 23 | a = nu*inner(nabla_grad(u), nabla_grad(v))*dx 24 | L = f*v*dx 25 | 26 | # Compute solution 27 | u = Function(V) 28 | solve(a == L, u, bc) 29 | 30 | # Compute adjoint solution 31 | u_d = Expression('sin(pi*x[0])') 32 | J = Functional(0.5*inner(u-u_d, u-u_d)*dx) 33 | m1 = SteadyParameter(f) 34 | m2 = ScalarParameter(nu) 35 | dJdm = compute_gradient(J, [m1, m2], project=True) 36 | print type(dJdm), dJdm.__class__.__name__, dJdm[0].__class__.__name__, dJdm[1].__class__.__name__ 37 | 38 | # Should compare with da.py 39 | 40 | # Plot solution and mesh 41 | plot(dJdm[0], interactive=True) 42 | print float(dJdm[1]) 43 | -------------------------------------------------------------------------------- /.sandbox/dolfinprm2datapool.py: -------------------------------------------------------------------------------- 1 | import sys, re 2 | from scitools.misc import str2obj, str2bool 3 | 4 | # NOTE: should first run the .h file through cpp with all the right 5 | # options to filter out all the right branches in #ifdef's! 6 | 7 | dolfin_addline_regex = re.compile(r'add\s*\("(.+?)"\s*,\s*(.+)\)\s*;') 8 | dolfin_heading_regex = re.compile(r'//\s*--+\s+(.+)\s+--+') 9 | 10 | def read_dolfin_prmfile(filename): 11 | f = open(filename, 'r') 12 | lines = f.readlines() 13 | f.close() 14 | 15 | menus = {} 16 | heading = None 17 | for line in lines: 18 | # check for heading (new submenu): 19 | m = dolfin_heading_regex.search(line) 20 | if m: 21 | heading = m.group(1) 22 | menus[heading] = [] 23 | # check for parameter definition: 24 | m = dolfin_addline_regex.search(line) 25 | if m: 26 | if not heading: 27 | print 'No heading before "add" call - error' 28 | sys.exit(1) 29 | name = m.group(1).strip() 30 | value = m.group(2).strip() 31 | if value[0] == '"' and value[-1] == '"': # C++ string, strip "" 32 | value = value[1:-1] 33 | #if value == 'true': value = True 34 | #if value == 'false': value = False 35 | # find out if value is float or int or string? 36 | value = str2obj(value) 37 | if isinstance(value, float): 38 | s2t = float 39 | elif isinstance(value, bool): 40 | s2t = str2bool 41 | elif isinstance(value, int): 42 | s2t = int 43 | elif isinstance(value, basestring): 44 | s2t = str 45 | menus[heading].append((name, value, s2t)) 46 | return menus 47 | 48 | import pprint 49 | pprint.pprint(read_dolfin_prmfile(sys.argv[1])) 50 | -------------------------------------------------------------------------------- /.sandbox/domain_hollow_circle.py: -------------------------------------------------------------------------------- 1 | """Transform rectangular mesh to a hollow circle.""" 2 | from dolfin import * 3 | import numpy 4 | 5 | # Hollow circle, Theta radians, 6 | # with inner radius a and outer radius b 7 | Theta = pi/2 8 | a, b = 1, 5.0 9 | nr = 10 # divisions in r direction 10 | nt = 20 # divisions in theta direction 11 | mesh = Rectangle(a, 0, b, 1, nr, nt, 'crossed') 12 | 13 | # First make a denser mesh towards r=a 14 | x = mesh.coordinates()[:,0] 15 | y = mesh.coordinates()[:,1] 16 | s = 1.3 17 | 18 | def denser(x, y): 19 | return [a + (b-a)*((x-a)/(b-a))**s, y] 20 | 21 | x_bar, y_bar = denser(x, y) 22 | xy_bar_coor = numpy.array([x_bar, y_bar]).transpose() 23 | mesh.coordinates()[:] = xy_bar_coor 24 | plot(mesh, title='stretched mesh') 25 | 26 | def cylinder(r, s): 27 | return [r*numpy.cos(Theta*s), r*numpy.sin(Theta*s)] 28 | 29 | x_hat, y_hat = cylinder(x_bar, y_bar) 30 | xy_hat_coor = numpy.array([x_hat, y_hat]).transpose() 31 | mesh.coordinates()[:] = xy_hat_coor 32 | plot(mesh, title='hollow cylinder') 33 | interactive() 34 | 35 | -------------------------------------------------------------------------------- /.sandbox/domain_types.py: -------------------------------------------------------------------------------- 1 | """Demonstrate mesh generating objects in DOLFIN.""" 2 | 3 | from dolfin import * 4 | 5 | mesh = UnitInterval(20) 6 | mesh = Interval(20, -1, 1) # domain [-1,1] 7 | print mesh 8 | 9 | mesh = UnitSquare(6, 10) # 'right' diagonal is default 10 | viz = plot(mesh, title='UnitSquare(6, 10)') 11 | #print 'Add labels:' 12 | #viz.add_point_labels() 13 | #viz.update(mesh) 14 | # The third argument governs directions of diagonals: 15 | mesh = UnitSquare(6, 10, 'left') 16 | plot(mesh, title='UnitSquare(6, 10, "left")') 17 | mesh = UnitSquare(6, 10, 'crossed') 18 | plot(mesh, title='UnitSquare(6, 10, "crossed")') 19 | 20 | print mesh 21 | 22 | # Domain [0,3]x[0,2] with 6x10 divisions and left diagonals 23 | mesh = Rectangle(0, 0, 3, 2, 6, 10, 'left') 24 | plot(mesh, title='Rectangle(0, 0, 3, 2, 6, 10, "left")') 25 | print mesh 26 | 27 | # 6x10x5 boxes in the unit cube, each box gets 6 tetrahedra: 28 | mesh = UnitCube(6, 10, 5) 29 | plot(mesh, title='UnitCube') 30 | print mesh 31 | 32 | # Domain [-1,1]x[-1,0]x[-1,2] with 6x10x5 divisions 33 | mesh = Box(-1, -1, -1, 1, 0, 2, 6, 10, 5) 34 | plot(mesh, title='Box(-1, -1, -1, 1, 0, 2, 6, 10, 5)') 35 | print mesh 36 | 37 | # 10 divisions in radial directions 38 | mesh = UnitCircle(10, 'crossed', 'maxn') 39 | plot(mesh, title='UnitCircle(10, "crossed", "maxn")') 40 | mesh = UnitCircle(10, 'right', 'maxn') 41 | plot(mesh, title='UnitCircle(10, "right", "maxn")') 42 | mesh = UnitCircle(10) 43 | plot(mesh, title='UnitCircle(10)') 44 | print mesh 45 | 46 | mesh = UnitSphere(10) # 10 divisions in radial directions 47 | plot(mesh, title='UnitSphere(10)') 48 | print mesh 49 | 50 | 51 | interactive() 52 | -------------------------------------------------------------------------------- /.sandbox/extra/Kent_demo_subdomains.py: -------------------------------------------------------------------------------- 1 | 2 | from dolfin import * 3 | import numpy 4 | 5 | class DirichletBoundary(SubDomain): 6 | def inside(self, x, on_boundary): 7 | return on_boundary 8 | 9 | class InnerStuff(SubDomain): 10 | def inside(self, x, on_boundary): 11 | if x[0]**2 + x[1]**2 < 0.1: 12 | return True 13 | return False 14 | 15 | mesh = Mesh("circle.xml.gz") 16 | 17 | W = FunctionSpace(mesh, "CG", 1) 18 | V = VectorFunctionSpace(mesh, "CG", 1) 19 | u = TrialFunction(V) 20 | v = TestFunction(V) 21 | 22 | bc_func = Function(V, ("0.01*x[0] + 0.01*x[1]", "0.01*x[1]" )) 23 | bc = DirichletBC(V, bc_func, DirichletBoundary()) 24 | 25 | subdomains = MeshFunction("uint", mesh, 0) 26 | 27 | innerstuff = InnerStuff() 28 | innerstuff.mark(subdomains, 1) 29 | 30 | #plot(subdomains) 31 | 32 | coeff_values = numpy.zeros(len(subdomains.values())) 33 | for i in range(len(subdomains.values())): 34 | val = subdomains.values()[i] 35 | print val 36 | if val == 1: 37 | coeff_values[i] = 1.0 38 | else: 39 | coeff_values[i] = 0.001 40 | 41 | coeff = Function(W) 42 | coeff.vector().set(coeff_values) 43 | 44 | plot(coeff) 45 | interactive() 46 | 47 | 48 | for i in range(0, 20): 49 | 50 | f = Function(V, ("0.0", "0.0" )) 51 | 52 | a = coeff*dot(grad(v), grad(u))*dx 53 | L = dot(v,f)*dx 54 | 55 | # Compute solution 56 | problem = VariationalProblem(a, L, bc) 57 | U = problem.solve() 58 | 59 | # Plot solution 60 | # plot(U) 61 | 62 | mesh.move(U) 63 | plot(mesh) 64 | 65 | 66 | interactive() 67 | 68 | 69 | 70 | -------------------------------------------------------------------------------- /.sandbox/extra/demo.py: -------------------------------------------------------------------------------- 1 | """This demo program solves Poisson's equation 2 | 3 | - div grad u(x, y) = f(x, y) 4 | 5 | on the unit square with source f given by 6 | 7 | f(x, y) = 500*exp(-((x-0.5)^2 + (y-0.5)^2)/0.02) 8 | 9 | and boundary conditions given by 10 | 11 | u(x, y) = 0 12 | du/dn(x, y) = 0 13 | 14 | using a discontinuous Galerkin formulation (interior penalty method). 15 | """ 16 | 17 | __author__ = "Kristian B. Oelgaard (k.b.oelgaard@tudelft.nl)" 18 | __date__ = "2007-10-02 -- 2008-12-19" 19 | __copyright__ = "Copyright (C) 2007 Kristian B. Oelgaard" 20 | __license__ = "GNU LGPL Version 2.1" 21 | 22 | # Modified by Anders Logg, 2008. 23 | 24 | from dolfin import * 25 | 26 | # Create mesh and define function space 27 | mesh = UnitSquare(24, 24) 28 | V = FunctionSpace(mesh, "DG", 1) 29 | 30 | # Define test and trial functions 31 | u = TrialFunction(V) 32 | v = TestFunction(V) 33 | 34 | # Define normal component, mesh size and right-hand side 35 | n = FacetNormal(mesh) 36 | h = CellSize(mesh) 37 | h_avg = (h('+') + h('-'))/2 38 | f = Expression("500.0*exp(-(pow(x[0] - 0.5, 2) + pow(x[1] - 0.5, 2)) / 0.02)", V = V) 39 | 40 | # Define parameters 41 | alpha = 4.0 42 | gamma = 8.0 43 | 44 | # Define bilinear form 45 | a = dot(grad(v), grad(u))*dx \ 46 | - dot(avg(grad(v)), jump(u, n))*dS \ 47 | - dot(jump(v, n), avg(grad(u)))*dS \ 48 | + alpha/h_avg*dot(jump(v, n), jump(u, n))*dS \ 49 | - dot(grad(v), u*n)*ds \ 50 | - dot(v*n, grad(u))*ds \ 51 | + gamma/h*v*u*ds 52 | 53 | # Define linear form 54 | L = v*f*dx 55 | 56 | # Compute solution 57 | problem = VariationalProblem(a, L) 58 | u = problem.solve() 59 | 60 | # Project solution to piecewise linears 61 | P1 = FunctionSpace(mesh, "CG", 1) 62 | u_proj = project(u, P1) 63 | 64 | # Save solution to file 65 | file = File("poisson.pvd") 66 | file << u_proj 67 | 68 | # Plot solution 69 | plot(u_proj, interactive=True) 70 | 71 | -------------------------------------------------------------------------------- /.sandbox/extra/dolfin_failed_trick.py: -------------------------------------------------------------------------------- 1 | # wrapper for with extensions to dolfin... 2 | import sys, os 3 | # make sure official dolfin is loaded before the present dolfin.py 4 | # module in os.curdir: 5 | print sys.prefix 6 | print sys.version 7 | dolfin_dir = os.path.join(sys.prefix, 'lib', 'python' + sys.version[:3], 8 | 'dist-packages') 9 | print dolfin_dir 10 | del sys.path[0] 11 | sys.path.insert(0, dolfin_dir) 12 | import pprint; pprint.pprint(sys.path) 13 | from dolfin import Mesh 14 | 15 | # add stuff here 16 | print dir() 17 | 18 | -------------------------------------------------------------------------------- /.sandbox/extra/hpl2b.py: -------------------------------------------------------------------------------- 1 | """ 2 | FEniCS tutorial demo program 2. -Laplace(u) = f, u = u0 on the boundary. 3 | u0 = u = 1 + x^2 + 2y^2, f = -6. 4 | """ 5 | 6 | from dolfin import * 7 | import numpy 8 | 9 | # Create mesh and define function space 10 | mesh = UnitSquare(2, 1) 11 | V = FunctionSpace(mesh, 'CG', 1) 12 | 13 | 14 | # Define boundary conditions 15 | u0 = Function(V, '1 + x[0]*x[0] + 2*x[1]*x[1]') 16 | 17 | class Boundary(SubDomain): # define the Dirichlet boundary 18 | def inside(self, x, on_boundary): 19 | return on_boundary 20 | 21 | u0_boundary = Boundary() 22 | bc = DirichletBC(V, u0, u0_boundary) 23 | 24 | # Define variational problem 25 | u = TrialFunction(V) 26 | v = TestFunction(V) 27 | f = Function(V, '-6') 28 | a = dot(grad(v), grad(u))*dx 29 | L = v*f*dx 30 | 31 | # Assemble and solve linear system 32 | A = assemble(a) 33 | b = assemble(L) 34 | bc.apply(A, b) 35 | u = Function(V) 36 | solve(A, u.vector(), b) 37 | 38 | 39 | #plot(u) 40 | #interactive() 41 | 42 | print """ 43 | Solution of the Poisson problem -Laplace(u) = f, 44 | with u = u0 on the boundary and a 45 | %s 46 | """ % mesh 47 | 48 | # Dump solution to the screen 49 | u_nodal_values = u.vector() 50 | u_array = u_nodal_values.array() 51 | coor = mesh.coordinates() 52 | for i in range(len(u_array)): 53 | print 'u(%8g,%8g) = %g' % (coor[i][0], coor[i][1], u_array[i]) 54 | 55 | 56 | # Verification 57 | tolerance = 1E-14 58 | u0.interpolate() 59 | u0_array = u0.vector().array() 60 | ok = numpy.allclose(u_array, u0_array, 61 | rtol=tolerance, atol=tolerance) 62 | print 'Solution is', 'ok' if ok else 'not correct' 63 | 64 | # Compare numerical and exact solution at (0.5, 0.5) 65 | center_point = numpy.array((0.5, 0.5)) 66 | u_value = numpy.zeros(1) 67 | u.eval(u_value, center_point) 68 | u0_value = numpy.zeros(1) 69 | u0.eval(u0_value, center_point) 70 | print 'numerical u at the center point:', u_value 71 | print 'exact u at the center point:', u0_value 72 | 73 | 74 | -------------------------------------------------------------------------------- /.sandbox/extra/hpl5.py: -------------------------------------------------------------------------------- 1 | """ 2 | ROBIN - does not work!!!! 3 | 4 | FEniCS tutorial demo program 1. -Laplace(u) = f on the unit square. 5 | u = u0 on x=0, 6 | u0 = u = 1 + x^2 + 2y^2, 7 | f = -6. 8 | """ 9 | 10 | from dolfin import * 11 | import numpy 12 | 13 | # Create mesh and define function space 14 | mesh = UnitSquare(3, 3) 15 | V = FunctionSpace(mesh, 'CG', 1) 16 | 17 | 18 | # Define boundary conditions 19 | u0 = Function(V, '1 + x[0]*x[0] + 2*x[1]*x[1]') 20 | 21 | class DirichletBoundary(SubDomain): 22 | def inside(self, x, on_boundary): 23 | if on_boundary and x[0] == 0: 24 | return True 25 | else: 26 | return False 27 | 28 | u0_boundary = DirichletBoundary() 29 | bc = DirichletBC(V, u0, u0_boundary) 30 | 31 | # Define variational problem 32 | u = TrialFunction(V) 33 | v = TestFunction(V) 34 | f = Function(V, '-6') 35 | g = Function(V, '-4*x[1]') 36 | S = Function(V, 'x[1]*x[1]') 37 | p = -1 38 | a = dot(grad(v), grad(u))*dx + p*(u-S)*ds 39 | L = v*f*dx - v*g*ds 40 | 41 | # Compute solution 42 | problem = VariationalProblem(a, L, bc) 43 | u = problem.solve() 44 | 45 | #plot(u) 46 | #interactive() 47 | 48 | print """ 49 | Solution of the Poisson problem -Laplace(u) = f, 50 | with u = u0 on the boundary and a 51 | %s 52 | """ % mesh 53 | 54 | # Dump solution to the screen 55 | u_nodal_values = u.vector() 56 | u_array = u_nodal_values.array() 57 | coor = mesh.coordinates() 58 | for i in range(len(u_array)): 59 | print 'u(%8g,%8g) = %g' % (coor[i][0], coor[i][1], u_array[i]) 60 | 61 | 62 | # Verification 63 | tolerance = 1E-14 64 | u0.interpolate() 65 | u0_array = u0.vector().array() 66 | ok = numpy.allclose(u_array, u0_array, 67 | rtol=tolerance, atol=tolerance) 68 | print 'Solution is', 'ok' if ok else 'not correct' 69 | 70 | # Compare numerical and exact solution at (0.5, 0.5) 71 | center_point = numpy.array((0.5, 0.5)) 72 | u_value = numpy.zeros(1) 73 | u.eval(u_value, center_point) 74 | u0_value = numpy.zeros(1) 75 | u0.eval(u0_value, center_point) 76 | print 'numerical u at the center point:', u_value 77 | print 'exact u at the center point:', u0_value 78 | 79 | 80 | -------------------------------------------------------------------------------- /.sandbox/extra/hpl7.py: -------------------------------------------------------------------------------- 1 | """ 2 | FEniCS tutorial demo program 1. -Laplace(u) = f on the unit square. 3 | u = u0 on x=0, 4 | u0 = u = 1 + x^2 + 2y^2, 5 | f = -6. 6 | """ 7 | 8 | from dolfin import * 9 | import numpy 10 | 11 | # Create mesh and define function space 12 | mesh = UnitSquare(4, 4) 13 | V = FunctionSpace(mesh, 'CG', 1) 14 | 15 | 16 | # Define boundary conditions 17 | u0 = Function(V, '1 + x[0]*x[0] + 2*x[1]*x[1]') 18 | 19 | class DirichletBoundary(SubDomain): 20 | def inside(self, x, on_boundary): 21 | tol = 1E-14 # tolerance for coordinate comparisons 22 | return on_boundary 23 | 24 | u0_boundary = DirichletBoundary() 25 | bc = DirichletBC(V, u0, u0_boundary) 26 | 27 | # Define variational problem 28 | u = TrialFunction(V) 29 | v = TestFunction(V) 30 | p = Function(V, 'x[0] + x[1]') 31 | f = Function(V, '-8*x[0] - 10*x[1]') 32 | a = p*dot(grad(v), grad(u))*dx 33 | L = v*f*dx 34 | 35 | # Compute solution 36 | problem = VariationalProblem(a, L, bc) 37 | u = problem.solve() 38 | 39 | #plot(u) 40 | #interactive() 41 | 42 | print """ 43 | Solution of the Poisson problem -Laplace(u) = f, 44 | with u = u0 on x=0,1 and -du/dn = g at y=0,1. 45 | %s 46 | """ % mesh 47 | 48 | # Dump solution to the screen 49 | u_nodal_values = u.vector() 50 | u_array = u_nodal_values.array() 51 | coor = mesh.coordinates() 52 | for i in range(len(u_array)): 53 | print 'u(%8g,%8g) = %g' % (coor[i][0], coor[i][1], u_array[i]) 54 | 55 | # Verification 56 | tolerance = 1E-14 57 | u0.interpolate() 58 | u0_array = u0.vector().array() 59 | ok = numpy.allclose(u_array, u0_array, 60 | rtol=tolerance, atol=tolerance) 61 | print 'Solution is', 'ok' if ok else 'not correct' 62 | 63 | # Compare numerical and exact solution at (0.5, 0.5) 64 | center_point = numpy.array((0.5, 0.5)) 65 | u_value = numpy.zeros(1) 66 | u.eval(u_value, center_point) 67 | u0_value = numpy.zeros(1) 68 | u0.eval(u0_value, center_point) 69 | print 'numerical u at the center point:', u_value 70 | print 'exact u at the center point:', u0_value 71 | 72 | 73 | -------------------------------------------------------------------------------- /.sandbox/membrane2.py: -------------------------------------------------------------------------------- 1 | """ 2 | FEniCS program for the deflection w(x,y) of a membrane: 3 | -Laplace(w) = p = Gaussian function, in a unit circle, 4 | with w = 0 on the boundary. 5 | As membrane1.py, but with computation of the energy (a 6 | quantity derived from the solution). 7 | """ 8 | 9 | from dolfin import * 10 | import numpy 11 | 12 | # Set pressure function: 13 | T = 10.0 # tension 14 | A = 1.0 # pressure amplitude 15 | R = 0.3 # radius of domain 16 | theta = 0.2 17 | x0 = 0.6*R*cos(theta) 18 | y0 = 0.6*R*sin(theta) 19 | sigma = 0.025 20 | n = 40 # approx no of elements in radial direction 21 | mesh = UnitCircle(n) 22 | V = FunctionSpace(mesh, 'Lagrange', 1) 23 | 24 | # Define boundary condition w=0 25 | 26 | def boundary(x, on_boundary): 27 | return on_boundary 28 | 29 | bc = DirichletBC(V, Constant(0.0), boundary) 30 | 31 | # Define variational problem 32 | w = TrialFunction(V) 33 | v = TestFunction(V) 34 | a = inner(nabla_grad(w), nabla_grad(v))*dx 35 | f = Expression('4*exp(-0.5*(pow((R*x[0] - x0)/sigma, 2)) ' 36 | ' - 0.5*(pow((R*x[1] - y0)/sigma, 2)))', 37 | R=R, x0=x0, y0=y0, sigma=sigma) 38 | L = f*v*dx 39 | 40 | # Compute solution 41 | w = Function(V) 42 | problem = LinearVariationalProblem(a, L, w, bc) 43 | solver = LinearVariationalSolver(problem) 44 | solver.parameters['linear_solver'] = 'cg' 45 | solver.parameters['preconditioner'] = 'ilu' 46 | solver.solve() 47 | 48 | # Plot solution and mesh 49 | plot(mesh, title='Mesh over scaled domain') 50 | plot(w, title='Scaled deflection') 51 | p = interpolate(f, V) 52 | plot(p, title='Scaled pressure') 53 | 54 | # Find maximum real deflection 55 | max_w = w.vector().array().max() 56 | max_D = A*max_w/(8*pi*sigma*T) 57 | print 'Maximum real deflection is', max_D 58 | 59 | # Compute elastic energy: integral of T*abs(grad(w))^2 60 | E_functional = 0.5*(A*R/(8*pi*sigma))**2*inner(nabla_grad(w), nabla_grad(w))*dx 61 | E = assemble(E_functional) 62 | #E = assemble(E_functional, mesh=mesh) 63 | print 'Elastic energy:', E 64 | 65 | # Should be at the end 66 | #interactive() 67 | -------------------------------------------------------------------------------- /.sandbox/membrane2_experiment.py: -------------------------------------------------------------------------------- 1 | from membrane2_class import Problem, Viz 2 | 3 | for sigma in 0.1, 1, 10: 4 | for A in 1, 100, 1000: 5 | print '\n\n ****************** sigma:', sigma 6 | dir = 'case-%g' % sigma 7 | os.mkdir(dir) 8 | os.chdir(dir) 9 | problem = Problem(sigma=sigma) 10 | problem.solve() 11 | visualizer = Viz(problem) 12 | visualizer.batch_viz() 13 | os.chdir(os.pardir) 14 | 15 | -------------------------------------------------------------------------------- /.sandbox/nonlin_solver.py: -------------------------------------------------------------------------------- 1 | """Rough code from Mikael. Develop this to a general class 2 | that can take a form (func or class) and run Newton or Picard 3 | on it. A first step toward pdesys. The nonline class has all 4 | necessary parameters in a parameters dict. 5 | """ 6 | 7 | 8 | import sys 9 | from dolfin import * 10 | mesh=UnitSquare(10, 10) 11 | V = FunctionSpace(mesh, 'CG', 1) 12 | u = TrialFunction(V) 13 | v = TestFunction(V) 14 | u_ = Function(V) 15 | bc = DirichletBC(V, Constant(0.), DomainBoundary()) 16 | x = u_.vector() 17 | bc.apply(x) 18 | omega = 1. 19 | error = 1. 20 | 21 | method = sys.argv[-1] 22 | 23 | def form(u, v, u_, **kwargs): 24 | return (1.-u_)*inner(grad(u), grad(v))*dx + Constant(1.)*v*dx 25 | 26 | if method == 'Newton': 27 | u_old = u 28 | u = u_ 29 | F_ = form(**vars()) 30 | u = u_old 31 | J = derivative(F_, u_, u) 32 | a, L = J, -F_ 33 | dx = Vector(x) 34 | i = 0 35 | while error > 1e-8: 36 | A = assemble(a) 37 | b = assemble(L) 38 | bc.apply(A, b, x) 39 | solve(A, dx, b) 40 | x.axpy(omega, dx) 41 | error = norm(dx) 42 | i+=1 43 | print i, 'error = ', error 44 | 45 | elif method == 'Picard': 46 | F = form(**vars()) 47 | a, L = lhs(F), rhs(F) 48 | x_star = Vector(x) 49 | i = 0 50 | while error > 1e-8: 51 | A = assemble(a) 52 | b = assemble(L) 53 | bc.apply(A, b) 54 | x_star[:] = x[:] 55 | solve(A, x_star, b) 56 | # x = (1-omega)*x + omega*x_star = x + omega*(x_star-x): 57 | x_star.axpy(-1., x); x.axpy(omega, x_star) 58 | error = norm(x_star) 59 | i+=1 60 | print i, 'error = ', error 61 | 62 | plot(u_) 63 | -------------------------------------------------------------------------------- /.sandbox/sin__class_daD.py: -------------------------------------------------------------------------------- 1 | """ 2 | Temperature variations in the ground. 3 | Class version of diffusion123D_sin.py. 4 | NOTE: go on with class Problem, but use the rest of the code 5 | from the newer sin_daD.py. 6 | """ 7 | 8 | class Problem: 9 | def __init__(self): 10 | """Set default values of problem parameters.""" 11 | self.d = 2 12 | self.degree = 1 13 | self.physics = dict(T_R = 0, T_A=0, omega=7.27E-5) 14 | self.numerics = dict(num_steps_per_period=14, num_periods=5) 15 | 16 | def update(self): 17 | """Update problem parameters that depend on others.""" 18 | omega = self.physics['omega'] 19 | period = 2*pi/omega 20 | self.numerics['dt'] = period/self.numerics['num_steps_per_period'] 21 | self.numerics['tstop'] = period*self.numerics['num_periods'] 22 | 23 | def T_0(self): 24 | return Expression( 25 | 'T_R + T_A*sin(omega*t)', 26 | 'T_R': self.physics['T_R'], 27 | 'T_A': self.physics['T_A'], 28 | 'omega': self.physics['omega']) 29 | 30 | def exact_solution(self, x, t): 31 | pass 32 | 33 | [[[[ not ready 34 | -------------------------------------------------------------------------------- /.sandbox/test1.py: -------------------------------------------------------------------------------- 1 | from dolfin import * 2 | import numpy 3 | 4 | mesh2D = UnitSquare(5, 4) 5 | V2D = FunctionSpace(mesh2D, 'Lagrange', 1) 6 | 7 | mesh1D = UnitInterval(4) 8 | V1D = FunctionSpace(mesh1D, 'Lagrange', 1) 9 | 10 | v_formula = Expression('4*x[0]*(1 - x[0])') 11 | 12 | v1D = project(v_formula, V1D) 13 | print 'v1D:', v1D.vector().array() 14 | 15 | # How to let v be a function of y and populate a Function u in V2D? 16 | # (channel flow) 17 | 18 | class v_interpolate2D(Expression): 19 | def eval(self, value, x): 20 | assert len(x) == 2 21 | point = [x[1]] 22 | value[0] = self.v(point) 23 | 24 | v2D_extension = v_interpolate2D() 25 | v2D_extension.v = v1D 26 | 27 | u = project(v2D_extension, V2D) 28 | print 'u:', u.vector().array() 29 | 30 | -------------------------------------------------------------------------------- /.sandbox/triangle/2DO: -------------------------------------------------------------------------------- 1 | Try new github version of meshpy: 2 | https://github.com/inducer/meshpy 3 | 4 | See also 5 | https://answers.launchpad.net/dolfin/+question/225893 6 | -------------------------------------------------------------------------------- /.sandbox/triangle/plotmesh.py: -------------------------------------------------------------------------------- 1 | from prepro2D import load_triangle_mesh, plot_mesh 2 | coordinates, connectivity, materials = load_triangle_mesh('tmp', '1') 3 | plot_mesh(coordinates, connectivity, materials) 4 | -------------------------------------------------------------------------------- /.sandbox/triangle/triangle.zip: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/hplgit/fenics-tutorial/bf8120cb448f244df18871ee305f4b9c463896cf/.sandbox/triangle/triangle.zip -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | The FEniCS Tutorial 2 | =================== 3 | 4 | By Hans Petter Langtangen and Anders Logg 5 | 6 | This repository contains all source files, published documents, and 7 | example programs for the FEniCS Tutorial. 8 | 9 | * `pub`: Published versions of all documents (book, online version, programs) 10 | * `src`: Sources for all documents (book, online version, programs) 11 | * `review`: Referee reports from Springer 12 | * `chinese`: Chinese version (does not use Doconce) 13 | -------------------------------------------------------------------------------- /chinese/Makefile: -------------------------------------------------------------------------------- 1 | BOOK=fenics-tutorial-chinese 2 | 3 | all: 4 | xelatex $(BOOK) 5 | 6 | final: 7 | xelatex $(BOOK) 8 | biber $(BOOK) 9 | makeindex $(BOOK) 10 | xelatex $(BOOK) 11 | xelatex $(BOOK) 12 | 13 | clean: 14 | rm -f *.aux *.mtc* *.out *.idx *.bcf *.log *~ *.ptc *.toc *.run.xml *.maf 15 | -------------------------------------------------------------------------------- /chinese/README.md: -------------------------------------------------------------------------------- 1 | This directory contains the Chinese edition of the book (volume I). 2 | Note that this version does not use Doconce bus instead manually 3 | translated from the generated LaTeX sources. 4 | 5 | To build the book, type `make`. 6 | -------------------------------------------------------------------------------- /chinese/chapters/preface.tex: -------------------------------------------------------------------------------- 1 | \chapter*{前言} 2 | \addcontentsline{toc}{chapter}{前言} 3 | 4 | 本书简要介绍了有限元素 5 | 基于流行的FEniCS软件库在Python中进行编程。 6 | FEniCS可以在C++和Python中编程，但本教程 7 | 专注于Python编程，因为这是最简单的 8 | 并为初学者提供最有效的方法。 消化过后 9 | 本教程中的示例，读者应该能够了解更多 10 | 从FEniCS文档中可以看到众多演示程序 11 | 与软件和综合FEniCS书 \emph{Automated 12 | Solution of Differential Equations by the Finite Element Method} 13 | \cite{FEniCS}。 本教程是开幕式的进一步发展 14 | \cite{FEniCS}中的章节。 15 | 16 | 我们感谢Johan Hake，Kent-Andre Mardal和Kristian Valen-Sendstad 17 | 在准备第一个时候进行许多有益的讨论 18 | 本教程的版本为FEniCS书\cite{FEniCS}。 我们是 19 | 特别感谢Douglas Arnold非常有价值 20 | 对文本早期版本的反馈。 Øystein Sørensen指出 21 | 许多打字错误，并提供了许多有用的意见。 许多错误 22 | 还有Mauricio Angeles，IdaDrøsdal， 23 | Miroslav Kuchta，Hans Ekkehard Plesser，Marie Rognes，Hans Joachim 24 | Scroll，Glenn Terje Lines，Simon Funke，Matthew Moelter和Magne 25 | Nordaas。 Ekkehard Ellmann以及两位匿名评审员 26 | 一系列建议和改进。 特别感谢 27 | Benjamin Kehlet为他所有的工作与\texttt{mshr}工具和快速 28 | 实施我们对本教程的要求。 29 | 30 | 注释和更正可以报告为本书Git存储库的\ emph {issue}： 31 | \begin{center} 32 | \url{https://github.com/hplgit/fenics-tutorial} 33 | \end{center} 34 | 35 | \vspace{1cm} 36 | 37 | \noindent 38 | {\it Oslo and Smögen, November 2016} \hfill {\it Hans Petter Langtangen, Anders Logg} 39 | -------------------------------------------------------------------------------- /chinese/cover/cover.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/hplgit/fenics-tutorial/bf8120cb448f244df18871ee305f4b9c463896cf/chinese/cover/cover.jpg -------------------------------------------------------------------------------- /chinese/cover/cover.xcf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/hplgit/fenics-tutorial/bf8120cb448f244df18871ee305f4b9c463896cf/chinese/cover/cover.xcf -------------------------------------------------------------------------------- /chinese/fenics-tutorial-chinese.tex: -------------------------------------------------------------------------------- 1 | \documentclass{tstextbook} 2 | 3 | \begin{document} 4 | 5 | \tsbook{在Python中解决PDE \\ 6 | FEniCS教程} 7 | {Hans Petter Langtangen \& Anders Logg} 8 | {} 9 | {2017} 10 | {xxxxx}{xxx--xx--xxxx--xx--x}{0.0} 11 | {Chinese translation by Jiping Xin} 12 | {Wuxi, China} 13 | 14 | \input{newcommands} 15 | 16 | %--------------------------------------------------------------------------- 17 | % Chapters 18 | %--------------------------------------------------------------------------- 19 | 20 | \input{chapters/preface} 21 | \input{chapters/chapter1} 22 | \input{chapters/chapter2} 23 | \input{chapters/chapter3} 24 | \input{chapters/chapter4} 25 | \input{chapters/chapter5} 26 | 27 | %--------------------------------------------------------------------------- 28 | % Bibliography 29 | %--------------------------------------------------------------------------- 30 | 31 | \addcontentsline{toc}{chapter}{\textcolor{tssteelblue}{参考书目}} 32 | \printbibliography[title=参考书目]{} 33 | 34 | %--------------------------------------------------------------------------- 35 | % Index 36 | %--------------------------------------------------------------------------- 37 | 38 | \printindex 39 | 40 | \end{document} 41 | -------------------------------------------------------------------------------- /chinese/fig/elasticity.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/hplgit/fenics-tutorial/bf8120cb448f244df18871ee305f4b9c463896cf/chinese/fig/elasticity.png 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https://raw.githubusercontent.com/hplgit/fenics-tutorial/bf8120cb448f244df18871ee305f4b9c463896cf/chinese/images/cover.jpg -------------------------------------------------------------------------------- /chinese/images/idea.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/hplgit/fenics-tutorial/bf8120cb448f244df18871ee305f4b9c463896cf/chinese/images/idea.pdf -------------------------------------------------------------------------------- /chinese/images/image-info: -------------------------------------------------------------------------------- 1 | The background picture with clouds were aquired from: 2 | https://pixabay.com/en/lake-water-brightness-reflection-430508/ 3 | 4 | Free for commercial use 5 | No attribution required 6 | 7 | Free download 8 | -------------------------------------------------------------------------------- /chinese/input/README.md: -------------------------------------------------------------------------------- 1 | This file contains the original version of the Tutorial (2017-06-01) 2 | as well as a modified version used as basis for the Chinese translation. 3 | -------------------------------------------------------------------------------- /chinese/input/fenics-tutorial-vol1.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/hplgit/fenics-tutorial/bf8120cb448f244df18871ee305f4b9c463896cf/chinese/input/fenics-tutorial-vol1.pdf -------------------------------------------------------------------------------- /pub/README.md: -------------------------------------------------------------------------------- 1 | This directory contains the generated FEniCS Tutorial in various formats. 2 | -------------------------------------------------------------------------------- /pub/html/README.md: -------------------------------------------------------------------------------- 1 | This directory contains the generated FEniCS Tutorial in HTML format. 2 | -------------------------------------------------------------------------------- /pub/pdf/README.md: -------------------------------------------------------------------------------- 1 | This directory contains the generated FEniCS Tutorial in PDF format. 2 | -------------------------------------------------------------------------------- /pub/python/vol1/README.md: -------------------------------------------------------------------------------- 1 | This directory contains the example programs generated from the FEniCS Tutorial Vol 1. 2 | -------------------------------------------------------------------------------- /pub/python/vol1/ft01_poisson.py: -------------------------------------------------------------------------------- 1 | """ 2 | FEniCS tutorial demo program: Poisson equation with Dirichlet conditions. 3 | Test problem is chosen to give an exact solution at all nodes of the mesh. 4 | 5 | -Laplace(u) = f in the unit square 6 | u = u_D on the boundary 7 | 8 | u_D = 1 + x^2 + 2y^2 9 | f = -6 10 | """ 11 | 12 | from __future__ import print_function 13 | from fenics import * 14 | import matplotlib.pyplot as plt 15 | 16 | # Create mesh and define function space 17 | mesh = UnitSquareMesh(8, 8) 18 | V = FunctionSpace(mesh, 'P', 1) 19 | 20 | # Define boundary condition 21 | u_D = Expression('1 + x[0]*x[0] + 2*x[1]*x[1]', degree=2) 22 | 23 | def boundary(x, on_boundary): 24 | return on_boundary 25 | 26 | bc = DirichletBC(V, u_D, boundary) 27 | 28 | # Define variational problem 29 | u = TrialFunction(V) 30 | v = TestFunction(V) 31 | f = Constant(-6.0) 32 | a = dot(grad(u), grad(v))*dx 33 | L = f*v*dx 34 | 35 | # Compute solution 36 | u = Function(V) 37 | solve(a == L, u, bc) 38 | 39 | # Plot solution and mesh 40 | plot(u) 41 | plot(mesh) 42 | 43 | # Save solution to file in VTK format 44 | vtkfile = File('poisson/solution.pvd') 45 | vtkfile << u 46 | 47 | # Compute error in L2 norm 48 | error_L2 = errornorm(u_D, u, 'L2') 49 | 50 | # Compute maximum error at vertices 51 | vertex_values_u_D = u_D.compute_vertex_values(mesh) 52 | vertex_values_u = u.compute_vertex_values(mesh) 53 | import numpy as np 54 | error_max = np.max(np.abs(vertex_values_u_D - vertex_values_u)) 55 | 56 | # Print errors 57 | print('error_L2 =', error_L2) 58 | print('error_max =', error_max) 59 | 60 | # Hold plot 61 | plt.show() 62 | -------------------------------------------------------------------------------- /pub/python/vol1/ft02_poisson_membrane.py: -------------------------------------------------------------------------------- 1 | """ 2 | FEniCS tutorial demo program: Deflection of a membrane. 3 | 4 | -Laplace(w) = p in the unit circle 5 | w = 0 on the boundary 6 | 7 | The load p is a Gaussian function centered at (0, 0.6). 8 | """ 9 | 10 | from __future__ import print_function 11 | from fenics import * 12 | from mshr import * 13 | import numpy as np 14 | 15 | # Create mesh and define function space 16 | domain = Circle(Point(0, 0), 1) 17 | mesh = generate_mesh(domain, 64) 18 | V = FunctionSpace(mesh, 'P', 2) 19 | 20 | # Define boundary condition 21 | w_D = Constant(0) 22 | 23 | def boundary(x, on_boundary): 24 | return on_boundary 25 | 26 | bc = DirichletBC(V, w_D, boundary) 27 | 28 | # Define load 29 | beta = 8 30 | R0 = 0.6 31 | p = Expression('4*exp(-pow(beta, 2)*(pow(x[0], 2) + pow(x[1] - R0, 2)))', 32 | degree=1, beta=beta, R0=R0) 33 | 34 | # Define variational problem 35 | w = TrialFunction(V) 36 | v = TestFunction(V) 37 | a = dot(grad(w), grad(v))*dx 38 | L = p*v*dx 39 | 40 | # Compute solution 41 | w = Function(V) 42 | solve(a == L, w, bc) 43 | 44 | # Plot solution 45 | p = interpolate(p, V) 46 | plot(w, title='Deflection') 47 | plot(p, title='Load') 48 | 49 | # Save solution to file in VTK format 50 | vtkfile_w = File('poisson_membrane/deflection.pvd') 51 | vtkfile_w << w 52 | vtkfile_p = File('poisson_membrane/load.pvd') 53 | vtkfile_p << p 54 | 55 | # Curve plot along x = 0 comparing p and w 56 | import numpy as np 57 | import matplotlib.pyplot as plt 58 | tol = 0.001 # avoid hitting points outside the domain 59 | y = np.linspace(-1 + tol, 1 - tol, 101) 60 | points = [(0, y_) for y_ in y] # 2D points 61 | w_line = np.array([w(point) for point in points]) 62 | p_line = np.array([p(point) for point in points]) 63 | plt.plot(y, 50*w_line, 'k', linewidth=2) # magnify w 64 | plt.plot(y, p_line, 'b--', linewidth=2) 65 | plt.grid(True) 66 | plt.xlabel('$y$') 67 | plt.legend(['Deflection ($\\times 50$)', 'Load'], loc='upper left') 68 | plt.savefig('poisson_membrane/curves.pdf') 69 | plt.savefig('poisson_membrane/curves.png') 70 | 71 | # Hold plots 72 | interactive() 73 | plt.show() 74 | -------------------------------------------------------------------------------- /pub/python/vol1/ft03_heat.py: -------------------------------------------------------------------------------- 1 | """ 2 | FEniCS tutorial demo program: Heat equation with Dirichlet conditions. 3 | Test problem is chosen to give an exact solution at all nodes of the mesh. 4 | 5 | u'= Laplace(u) + f in the unit square 6 | u = u_D on the boundary 7 | u = u_0 at t = 0 8 | 9 | u = 1 + x^2 + alpha*y^2 + \beta*t 10 | f = beta - 2 - 2*alpha 11 | """ 12 | 13 | from __future__ import print_function 14 | from fenics import * 15 | import numpy as np 16 | 17 | T = 2.0 # final time 18 | num_steps = 10 # number of time steps 19 | dt = T / num_steps # time step size 20 | alpha = 3 # parameter alpha 21 | beta = 1.2 # parameter beta 22 | 23 | # Create mesh and define function space 24 | nx = ny = 8 25 | mesh = UnitSquareMesh(nx, ny) 26 | V = FunctionSpace(mesh, 'P', 1) 27 | 28 | # Define boundary condition 29 | u_D = Expression('1 + x[0]*x[0] + alpha*x[1]*x[1] + beta*t', 30 | degree=2, alpha=alpha, beta=beta, t=0) 31 | 32 | def boundary(x, on_boundary): 33 | return on_boundary 34 | 35 | bc = DirichletBC(V, u_D, boundary) 36 | 37 | # Define initial value 38 | u_n = interpolate(u_D, V) 39 | #u_n = project(u_D, V) 40 | 41 | # Define variational problem 42 | u = TrialFunction(V) 43 | v = TestFunction(V) 44 | f = Constant(beta - 2 - 2*alpha) 45 | 46 | F = u*v*dx + dt*dot(grad(u), grad(v))*dx - (u_n + dt*f)*v*dx 47 | a, L = lhs(F), rhs(F) 48 | 49 | # Time-stepping 50 | u = Function(V) 51 | t = 0 52 | for n in range(num_steps): 53 | 54 | # Update current time 55 | t += dt 56 | u_D.t = t 57 | 58 | # Compute solution 59 | solve(a == L, u, bc) 60 | 61 | # Plot solution 62 | plot(u) 63 | 64 | # Compute error at vertices 65 | u_e = interpolate(u_D, V) 66 | error = np.abs(u_e.vector().array() - u.vector().array()).max() 67 | print('t = %.2f: error = %.3g' % (t, error)) 68 | 69 | # Update previous solution 70 | u_n.assign(u) 71 | 72 | # Hold plot 73 | interactive() 74 | -------------------------------------------------------------------------------- /pub/python/vol1/ft04_heat_gaussian.py: -------------------------------------------------------------------------------- 1 | """ 2 | FEniCS tutorial demo program: Diffusion of a Gaussian hill. 3 | 4 | u'= Laplace(u) + f in a square domain 5 | u = u_D on the boundary 6 | u = u_0 at t = 0 7 | 8 | u_D = f = 0 9 | 10 | The initial condition u_0 is chosen as a Gaussian hill. 11 | """ 12 | 13 | from __future__ import print_function 14 | from fenics import * 15 | import time 16 | 17 | T = 2.0 # final time 18 | num_steps = 50 # number of time steps 19 | dt = T / num_steps # time step size 20 | 21 | # Create mesh and define function space 22 | nx = ny = 30 23 | mesh = RectangleMesh(Point(-2, -2), Point(2, 2), nx, ny) 24 | V = FunctionSpace(mesh, 'P', 1) 25 | 26 | # Define boundary condition 27 | def boundary(x, on_boundary): 28 | return on_boundary 29 | 30 | bc = DirichletBC(V, Constant(0), boundary) 31 | 32 | # Define initial value 33 | u_0 = Expression('exp(-a*pow(x[0], 2) - a*pow(x[1], 2))', 34 | degree=2, a=5) 35 | u_n = interpolate(u_0, V) 36 | 37 | # Define variational problem 38 | u = TrialFunction(V) 39 | v = TestFunction(V) 40 | f = Constant(0) 41 | 42 | F = u*v*dx + dt*dot(grad(u), grad(v))*dx - (u_n + dt*f)*v*dx 43 | a, L = lhs(F), rhs(F) 44 | 45 | # Create VTK file for saving solution 46 | vtkfile = File('heat_gaussian/solution.pvd') 47 | 48 | # Time-stepping 49 | u = Function(V) 50 | t = 0 51 | for n in range(num_steps): 52 | 53 | # Update current time 54 | t += dt 55 | 56 | # Compute solution 57 | solve(a == L, u, bc) 58 | 59 | # Save to file and plot solution 60 | vtkfile << (u, t) 61 | plot(u) 62 | 63 | # Update previous solution 64 | u_n.assign(u) 65 | 66 | # Hold plot 67 | interactive() 68 | -------------------------------------------------------------------------------- /pub/python/vol1/ft05_poisson_nonlinear.py: -------------------------------------------------------------------------------- 1 | """ 2 | FEniCS tutorial demo program: Nonlinear Poisson equation. 3 | 4 | -div(q(u)*grad(u)) = f in the unit square. 5 | u = u_D on the boundary. 6 | """ 7 | 8 | from __future__ import print_function 9 | 10 | # Warning: from fenics import * will import both `sym` and 11 | # `q` from FEniCS. We therefore import FEniCS first and then 12 | # overwrite these objects. 13 | from fenics import * 14 | 15 | def q(u): 16 | "Return nonlinear coefficient" 17 | return 1 + u**2 18 | 19 | # Use SymPy to compute f from the manufactured solution u 20 | import sympy as sym 21 | x, y = sym.symbols('x[0], x[1]') 22 | u = 1 + x + 2*y 23 | f = - sym.diff(q(u)*sym.diff(u, x), x) - sym.diff(q(u)*sym.diff(u, y), y) 24 | f = sym.simplify(f) 25 | u_code = sym.printing.ccode(u) 26 | f_code = sym.printing.ccode(f) 27 | print('u =', u_code) 28 | print('f =', f_code) 29 | 30 | # Create mesh and define function space 31 | mesh = UnitSquareMesh(8, 8) 32 | V = FunctionSpace(mesh, 'P', 1) 33 | 34 | # Define boundary condition 35 | u_D = Expression(u_code, degree=2) 36 | 37 | def boundary(x, on_boundary): 38 | return on_boundary 39 | 40 | bc = DirichletBC(V, u_D, boundary) 41 | 42 | # Define variational problem 43 | u = Function(V) # Note: not TrialFunction! 44 | v = TestFunction(V) 45 | f = Expression(f_code, degree=2) 46 | F = q(u)*dot(grad(u), grad(v))*dx - f*v*dx 47 | 48 | # Compute solution 49 | solve(F == 0, u, bc) 50 | 51 | # Plot solution 52 | plot(u) 53 | 54 | # Compute maximum error at vertices. This computation illustrates 55 | # an alternative to using compute_vertex_values as in poisson.py. 56 | u_e = interpolate(u_D, V) 57 | import numpy as np 58 | error_max = np.abs(u_e.vector().array() - u.vector().array()).max() 59 | print('error_max = ', error_max) 60 | 61 | # Hold plot 62 | interactive() 63 | -------------------------------------------------------------------------------- /pub/python/vol1/ft06_elasticity.py: -------------------------------------------------------------------------------- 1 | """ 2 | FEniCS tutorial demo program: Linear elastic problem. 3 | 4 | -div(sigma(u)) = f 5 | 6 | The model is used to simulate an elastic beam clamped at 7 | its left end and deformed under its own weight. 8 | """ 9 | 10 | from __future__ import print_function 11 | from fenics import * 12 | 13 | # Scaled variables 14 | L = 1; W = 0.2 15 | mu = 1 16 | rho = 1 17 | delta = W/L 18 | gamma = 0.4*delta**2 19 | beta = 1.25 20 | lambda_ = beta 21 | g = gamma 22 | 23 | # Create mesh and define function space 24 | mesh = BoxMesh(Point(0, 0, 0), Point(L, W, W), 10, 3, 3) 25 | V = VectorFunctionSpace(mesh, 'P', 1) 26 | 27 | # Define boundary condition 28 | tol = 1E-14 29 | 30 | def clamped_boundary(x, on_boundary): 31 | return on_boundary and x[0] < tol 32 | 33 | bc = DirichletBC(V, Constant((0, 0, 0)), clamped_boundary) 34 | 35 | # Define strain and stress 36 | 37 | def epsilon(u): 38 | return 0.5*(nabla_grad(u) + nabla_grad(u).T) 39 | #return sym(nabla_grad(u)) 40 | 41 | def sigma(u): 42 | return lambda_*nabla_div(u)*Identity(d) + 2*mu*epsilon(u) 43 | 44 | # Define variational problem 45 | u = TrialFunction(V) 46 | d = u.geometric_dimension() # space dimension 47 | v = TestFunction(V) 48 | f = Constant((0, 0, -rho*g)) 49 | T = Constant((0, 0, 0)) 50 | a = inner(sigma(u), epsilon(v))*dx 51 | L = dot(f, v)*dx + dot(T, v)*ds 52 | 53 | # Compute solution 54 | u = Function(V) 55 | solve(a == L, u, bc) 56 | 57 | # Plot solution 58 | plot(u, title='Displacement', mode='displacement') 59 | 60 | # Plot stress 61 | s = sigma(u) - (1./3)*tr(sigma(u))*Identity(d) # deviatoric stress 62 | von_Mises = sqrt(3./2*inner(s, s)) 63 | V = FunctionSpace(mesh, 'P', 1) 64 | von_Mises = project(von_Mises, V) 65 | plot(von_Mises, title='Stress intensity') 66 | 67 | # Compute magnitude of displacement 68 | u_magnitude = sqrt(dot(u, u)) 69 | u_magnitude = project(u_magnitude, V) 70 | plot(u_magnitude, 'Displacement magnitude') 71 | print('min/max u:', 72 | u_magnitude.vector().array().min(), 73 | u_magnitude.vector().array().max()) 74 | 75 | # Save solution to file in VTK format 76 | File('elasticity/displacement.pvd') << u 77 | File('elasticity/von_mises.pvd') << von_Mises 78 | File('elasticity/magnitude.pvd') << u_magnitude 79 | 80 | # Hold plot 81 | interactive() 82 | -------------------------------------------------------------------------------- /reviews/fenics_tutorial_review_2016_1.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/hplgit/fenics-tutorial/bf8120cb448f244df18871ee305f4b9c463896cf/reviews/fenics_tutorial_review_2016_1.pdf -------------------------------------------------------------------------------- /reviews/fenics_tutorial_review_2016_2.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/hplgit/fenics-tutorial/bf8120cb448f244df18871ee305f4b9c463896cf/reviews/fenics_tutorial_review_2016_2.pdf -------------------------------------------------------------------------------- /reviews/fenics_tutorial_review_2016_3.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/hplgit/fenics-tutorial/bf8120cb448f244df18871ee305f4b9c463896cf/reviews/fenics_tutorial_review_2016_3.pdf -------------------------------------------------------------------------------- /reviews/fenics_tutorial_review_2016_4.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/hplgit/fenics-tutorial/bf8120cb448f244df18871ee305f4b9c463896cf/reviews/fenics_tutorial_review_2016_4.pdf -------------------------------------------------------------------------------- /reviews/fenics_tutorial_review_2016_4_new.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/hplgit/fenics-tutorial/bf8120cb448f244df18871ee305f4b9c463896cf/reviews/fenics_tutorial_review_2016_4_new.pdf -------------------------------------------------------------------------------- /src/Makefile: -------------------------------------------------------------------------------- 1 | all: 2 | bash scripts/make.sh 3 | 4 | 1: 5 | bash scripts/make.sh 1 6 | 7 | 2: 8 | bash scripts/make.sh 2 9 | 10 | simple: 11 | bash scripts/make_simple.sh 12 | 13 | publish: 14 | bash scripts/publish.sh 15 | -------------------------------------------------------------------------------- /src/README.md: -------------------------------------------------------------------------------- 1 | This directory contains the source code for the FEniCS Tutorial. 2 | 3 | The tutorial is written in DocOnce and compiled to LaTeX PDF, Sphinx 4 | (FEniCS style), and Bootstrap HTML. 5 | 6 | The parent documents are: 7 | 8 | * `ftut1.do.txt` (FEniCS Tutorial Volume 1 9 | * `ftut2.do.txt` (FEniCS Tutorial Volume 2, in preparation) 10 | 11 | The directories `vol1` and `vol2` contain the sources for chapters 12 | and code for the two volumes. 13 | 14 | To build the book (in all formats), type `make` or run `scripts/make.sh`. 15 | 16 | Building the book requires a relatively long list of packages, most notably 17 | `doconce`, `preprocess`, `publish`, and `sphinx`. The easiest way to install 18 | these packages is via the script `install_rich.sh` which can be found in 19 | the subdirectory `scripts`. If running on Ubuntu, the script should just 20 | work and install all required packages. 21 | 22 | If running on another operating system, the easiest solution is to 23 | create a FEniCS Docker image and run the script from within that 24 | directory. Make sure you have installed Docker and the FEniCS Docker 25 | scripts; see `http://fenicsproject.org/download for instructions`. 26 | The position yourself in the top level directory of this repository 27 | and then run the following commands: 28 | 29 | fenicsproject create fenics-tutorial stable 30 | fenicsproject start fenics-tutorial 31 | 32 | Then run the install script inside the container: 33 | 34 | src/scripts/install.sh 35 | -------------------------------------------------------------------------------- /src/bib/venues.list: -------------------------------------------------------------------------------- 1 | publisher: Prentice-Hall 2 | publisher: O'Reilly 3 | publisher: APress 4 | publisher: Irwin 5 | -------------------------------------------------------------------------------- /src/exer/clean.sh: -------------------------------------------------------------------------------- 1 | #!/bin/sh 2 | rm -rf *~ *.vtu *.pvd dolfin_plot* __pychache__ tmp* 3 | -------------------------------------------------------------------------------- /src/exer/p2D_flat_Neumann1.py: -------------------------------------------------------------------------------- 1 | """ 2 | FEniCS tutorial demo program: 3 | Poisson equation with Dirichlet and Neumann conditions. 4 | The solution is checked to coincide with the exact solution at all nodes. 5 | 6 | -Laplace(u) = f on the unit square. 7 | u = u0 on x=0 and x=1. 8 | -du/dn = g on y=0 and y=1. 9 | u0 = u = 1 + x^2 + 2y^2, f = -6, g = -4y. 10 | """ 11 | 12 | from __future__ import print_function 13 | from fenics import * 14 | import numpy 15 | 16 | # Create mesh and define function space 17 | mesh = UnitSquareMesh(3, 2) 18 | V = FunctionSpace(mesh, 'Lagrange', 1) 19 | 20 | # Define Dirichlet boundary conditions 21 | u0 = Expression('1 + x[0]*x[0] + 2*x[1]*x[1]') 22 | 23 | def Dirichlet_boundary(x, on_boundary): 24 | tol = 1E-14 # tolerance for coordinate comparisons 25 | return on_boundary and \ 26 | (abs(x[0]) < tol or abs(x[0] - 1) < tol) 27 | 28 | bc = DirichletBC(V, u0, Dirichlet_boundary) 29 | 30 | # Define variational problem 31 | u = TrialFunction(V) 32 | v = TestFunction(V) 33 | f = Constant(-6.0) 34 | g = Expression('-4*x[1]') 35 | a = inner(grad(u), grad(v))*dx 36 | L = f*v*dx - g*v*ds 37 | 38 | # Compute solution 39 | u = Function(V) 40 | solve(a == L, u, bc) 41 | 42 | #plot(u) 43 | 44 | print(""" 45 | Solution of the Poisson problem -Laplace(u) = f, 46 | with u = u0 on x=0,1 and -du/dn = g at y=0,1. 47 | %s 48 | """ % mesh) 49 | 50 | # Verification 51 | u_e = interpolate(u0, V) 52 | u_e_array = u_e.vector().array() 53 | u_array = u.vector().array() 54 | print('Max error:', numpy.abs(u_e_array - u_array).max()) 55 | 56 | # Compare numerical and exact solution 57 | center = (0.5, 0.5) 58 | print('numerical u at the center point:', u(center)) 59 | print('exact u at the center point:', u0(center)) 60 | 61 | #interactive() 62 | -------------------------------------------------------------------------------- /src/exer/vol1/Expression_efficiency.py: -------------------------------------------------------------------------------- 1 | from __future__ import print_function 2 | from fenics import * 3 | import time 4 | 5 | def make_sine_Function(N, method): 6 | """Fill a Function with sin(x*y*z) values.""" 7 | mesh = UnitCubeMesh(N, N, N) 8 | V = FunctionSpace(mesh, 'Lagrange', 2) 9 | 10 | if method.startswith('Python'): 11 | if method.endswith('fenics.sin'): 12 | # Need sin as local variable in this function 13 | from fenics import sin 14 | elif method.endswith('math.sin'): 15 | from math import sin 16 | elif method.endswith('numpy.sin'): 17 | from numpy import sin 18 | elif method.endswith('sympy.sin'): 19 | from sympy import sin 20 | else: 21 | raise NotImplementedError('method=%s' % method) 22 | print('sin:', sin, type(sin)) 23 | 24 | class SineXYZ(Expression): 25 | def __init__(self, a, b): 26 | self.a, self.b = a, b 27 | 28 | def eval(self, value, x): 29 | value[0] = self.a*sin(self.b*x[0]*x[1]*x[2]) 30 | 31 | expr = SineXYZ(a=1, b=2) 32 | 33 | elif method == 'C++': 34 | expr = Expression('a*sin(b*x[0]*x[1]*x[2])', a=1, b=2) 35 | 36 | t0 = time.clock() 37 | u = interpolate(expr, V) 38 | t1 = time.clock() 39 | return u, t1-t0 40 | 41 | def main(N): 42 | u, cpu_py_fenics = make_sine_Function(N, 'Python-fenics.sin') 43 | u, cpu_py_math = make_sine_Function(N, 'Python-math.sin') 44 | u, cpu_py_numpy = make_sine_Function(N, 'Python-numpy.sin') 45 | u, cpu_py_sympy = make_sine_Function(N, 'Python-sympy.sin') 46 | u, cpu_cpp = make_sine_Function(N, 'C++') 47 | print("""DOFs: %d 48 | Python: 49 | fenics.sin: %.2f 50 | math.sin: %.2f 51 | numpy.sin: %.2f 52 | sympy.sin: %.2f 53 | C++: %.2f 54 | Speed-up: math: %.2f sympy: %.2f""" % 55 | (u.function_space().dim(), 56 | cpu_py_fenics, cpu_py_math, 57 | cpu_py_numpy, cpu_py_sympy, 58 | cpu_cpp, 59 | cpu_py_math/float(cpu_cpp), 60 | cpu_py_sympy/float(cpu_cpp))) 61 | 62 | def profile(): 63 | import cProfile 64 | prof = cProfile.Profile() 65 | prof.runcall(main) 66 | prof.dump_stats("tmp.profile") 67 | # http://docs.python.org/2/library/profile.html 68 | 69 | main(20) 70 | #profile() 71 | -------------------------------------------------------------------------------- /src/exer/vol1/poisson_fsin_flat.py: -------------------------------------------------------------------------------- 1 | from __future__ import print_function 2 | from fenics import * 3 | 4 | Nx = Ny = 20 5 | error = [] 6 | for i in range(2): 7 | Nx *= (i+1) 8 | Ny *= (i+1) 9 | 10 | # Create mesh and define function space 11 | mesh = UnitSquareMesh(Nx, Ny) 12 | V = FunctionSpace(mesh, 'Lagrange', 1) 13 | 14 | # Define boundary conditions 15 | u0 = Constant(0) 16 | 17 | def u0_boundary(x, on_boundary): 18 | return on_boundary 19 | 20 | bc = DirichletBC(V, u0, u0_boundary) 21 | 22 | # Define variational problem 23 | u = TrialFunction(V) 24 | v = TestFunction(V) 25 | f = Expression('-2*exp(-2*x[0])*sin(pi*x[1])*(' 26 | '(4-5*pow(pi,2))*sin(2*pi*x[0]) ' 27 | ' - 8*pi*cos(2*pi*x[0]))') 28 | # Note: no need for pi=DOLFIN_PI in f, pi is valid variable 29 | a = inner(nabla_grad(u), nabla_grad(v))*dx 30 | L = f*v*dx 31 | 32 | # Compute solution 33 | u = Function(V) 34 | solve(a == L, u, bc) 35 | 36 | u_e = Expression( 37 | '2*exp(-2*x[0])*sin(2*pi*x[0])*sin(pi*x[1])') 38 | 39 | u_e_Function = interpolate(u_e, V) # exact solution 40 | u_e_array = u_e_Function.vector().array() # dof values 41 | max_error = (u_e_array - u.vector().array()).max() 42 | print('max error:', max_error, '%dx%d mesh' % (Nx, Ny)) 43 | error.append(max_error) 44 | 45 | print('Error reduction:', error[1]/error[0]) 46 | 47 | # Plot solution and mesh 48 | plot(u) 49 | 50 | # Dump solution to file in VTK format 51 | file = File("poisson.pvd") 52 | file << u 53 | 54 | # Hold plot 55 | interactive() 56 | -------------------------------------------------------------------------------- /src/exer/vol1/poisson_fsin_func.py: -------------------------------------------------------------------------------- 1 | from __future__ import print_function 2 | #from fenics import * # not necessary, need only a few 3 | import os, sys 4 | path = os.path.join(os.pardir, os.pardir, os.pardir, 5 | 'src', 'stationary', 'poisson') 6 | sys.path.insert(0, path) 7 | from poisson_solver import ( 8 | solver, Expression, Constant, interpolate, File, plot, 9 | interactive) 10 | 11 | def data(): 12 | """Return data for this Poisson problem.""" 13 | u0 = Constant(0) 14 | u_e = Expression( 15 | '2*exp(-2*x[0])*sin(2*pi*x[0])*sin(pi*x[1])') 16 | f = Expression('-2*exp(-2*x[0])*sin(pi*x[1])*(' 17 | '(4-5*pow(pi,2))*sin(2*pi*x[0]) ' 18 | ' - 8*pi*cos(2*pi*x[0]))') 19 | return u0, f, u_e 20 | 21 | def test_solver(): 22 | """Check convergence rate of solver.""" 23 | u0, f, u_e = data() 24 | Nx = 20 25 | Ny = Nx 26 | error = [] 27 | # Loop over refined meshes 28 | for i in range(2): 29 | Nx *= i+1 30 | Ny *= i+1 31 | print('solving on 2(%dx%d) mesh' % (Nx, Ny)) 32 | u = solver(f, u0, Nx, Ny, degree=1) 33 | # Make a finite element function of the exact u_e 34 | V = u.function_space() 35 | u_e_array = interpolate(u_e, V).vector().array() 36 | max_error = (u_e_array - u.vector().array()).max() # Linf norm 37 | error.append(max_error) 38 | print('max error:', max_error) 39 | for i in range(1, len(error)): 40 | error_reduction = error[i]/error[i-1] 41 | print('error reduction:', error_reduction) 42 | assert abs(error_reduction - 0.25) < 0.1 43 | 44 | def application(): 45 | """Plot the solution.""" 46 | u0, f, u_e = data() 47 | Nx = 40 48 | Ny = Nx 49 | u = solver(f, u0, Nx, Ny, 1) 50 | # Dump solution to file in VTK format 51 | file = File("poisson.pvd") 52 | file << u 53 | # Plot solution and mesh 54 | plot(u) 55 | 56 | if __name__ == '__main__': 57 | test_solver() 58 | application() 59 | # Hold plot 60 | 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Volume II 8 | % elif FORMAT == "pdflatex": 9 | # Get newlines right 10 | #TITLE: More Advanced FEniCS Finite Element Programming 11 | TITLE: Solving PDEs in Hours - \\ The FEniCS Tutorial Volume II 12 | % else: 13 | #TITLE: More Advanced FEniCS Finite Element Programming 14 | TITLE: Solving PDEs in Hours -
The FEniCS Tutorial Volume II 15 | #- Writing Advanced State-of-the-Art Finite Element Solvers in Hours 16 | % endif 17 | AUTHOR: Hans Petter Langtangen {copyright|CC BY} Email: hpl@simula.no at Center for Biomedical Computing, Simula Research Laboratory & Department of Informatics, University of Oslo 18 | AUTHOR: Anders Logg {copyright|CC BY} Email: logg@chalmers.se at Department of Mathematics, Chalmers University of Technology & Center for Biomedical Computing, Simula Research Laboratory & Computational Engineeing and Design, Fraunhofer-Chalmers Centre 19 | 20 | # Can refer to ftut1 as with the xr package in latex (just use ref{} and cite{}) 21 | # Externaldocuments: ftut1 22 | 23 | __Preface.__ 24 | This book addresses... 25 | 26 | DATE: today 27 | 28 | !split 29 | TOC: on 30 | 31 | !split 32 | # #include "vol2/heat.do.txt" 33 | 34 | !split 35 | # #include "vol2/nlpoisson.do.txt" 36 | 37 | !split 38 | ========= Mixed finite element programming ========= 39 | label{ch:mixedFEM} 40 | 41 | ========= High-performance computing ========= 42 | label{ch:HPC} 43 | 44 | How to take an ordinary FEniCS program, profile it, optimize the code, 45 | and turn into an HPC application for parallel platforms. 46 | 47 | ========= Multi-physics in multi-domains ========= 48 | label{ch:multiphys} 49 | 50 | Systems of PDEs, coupling of domains, typically elasticity with a 51 | larger domain for heat transfer, simple fluid-structure interaction? 52 | 53 | ========= Vol II ends here now ========= 54 | 55 | ========= More old stuff ========= 56 | 57 | # #include "vol2/misc.do.txt" 58 | 59 | # #include "vol2/troubleshooting.do.txt" 60 | 61 | !split 62 | ======= Bibliography ======= 63 | 64 | BIBFILE: bib/papers.pub 65 | -------------------------------------------------------------------------------- /src/mako_code.txt: -------------------------------------------------------------------------------- 1 | ## Mako variables and functions 2 | <% 3 | src_url = 'https://fenicsproject.org/pub/tutorial/python/vol1' 4 | pub_url = 'https://fenicsproject.org/pub/tutorial' 5 | fenics_version = '2016.2' 6 | 7 | # AL: Stuff at the bottom added manually for now to get vol2 to compile. 8 | 9 | # Automatically computed by number_src_files.py 10 | prog = { 11 | 'poisson': 'ft01_poisson', 12 | 'poisson_membrane': 'ft02_poisson_membrane', 13 | 'heat': 'ft03_heat', 14 | 'heat_gaussian': 'ft04_heat_gaussian', 15 | 'poisson_nonlinear': 'ft05_poisson_nonlinear', 16 | 'elasticity': 'ft06_elasticity', 17 | 'navier_stokes_channel': 'ft07_navier_stokes_channel', 18 | 'navier_stokes_cylinder': 'ft08_navier_stokes_cylinder', 19 | 'reaction_system': 'ft09_reaction_system', 20 | 'poisson_extended': 'ft10_poisson_extended', 21 | 'magnetostatics': 'ft11_magnetostatics', 22 | 'poisson_solver': 'ft12_poisson_solver' 23 | } 24 | 25 | %> 26 | -------------------------------------------------------------------------------- /src/mov/heat_gaussian.ogv: 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-------------------------------------------------------------------------------- 1 | * Ideas for volume 2 2 | Parallel computing 3 | Periodic table of finite elements 4 | Pictures of elements and numbering 5 | Mesh generation: mshr and MeshEditor 6 | Troubleshooting: pick most common problems from Q&A 7 | DirichletBC: pointwise, topological, geometric 8 | PDE-constrained optimization? 9 | Adaptivity and mesh refinement 10 | Higher-order time-stepping schemes 11 | Programming FEniCS in C++ 12 | 13 | -------------------------------------------------------------------------------- /src/old/fig/Poisson2D_D1.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/hplgit/fenics-tutorial/bf8120cb448f244df18871ee305f4b9c463896cf/src/old/fig/Poisson2D_D1.pdf -------------------------------------------------------------------------------- /src/old/fig/Poisson2D_D1_mesh.pdf: 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\put(7381,-1636){\makebox(0,0)[lb]{\smash{{\SetFigFontNFSS{12}{14.4}{\familydefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}$x$}% 20 | }}}} 21 | \put(4366,-1276){\makebox(0,0)[lb]{\smash{{\SetFigFontNFSS{12}{14.4}{\familydefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}$T_0(t)= T_R + T_A\sin(\omega t)$}% 22 | }}}} 23 | \put(8146,-2716){\makebox(0,0)[lb]{\smash{{\SetFigFontNFSS{12}{14.4}{\familydefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}$D$}% 24 | }}}} 25 | \put(4186,-6586){\makebox(0,0)[lb]{\smash{{\SetFigFontNFSS{12}{14.4}{\familydefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}$W$}% 26 | }}}} 27 | \put(4006,-3031){\makebox(0,0)[lb]{\smash{{\SetFigFontNFSS{12}{14.4}{\familydefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}$\kappa\ll \kappa_0$}% 28 | }}}} 29 | \put(4051,-4381){\makebox(0,0)[lb]{\smash{{\SetFigFontNFSS{12}{14.4}{\familydefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}$\varrho, c, \kappa_0$}% 30 | }}}} 31 | 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(W/2,0.5*(a[i]+a[i+1]))) 18 | for i in range(len(a)-1)} 19 | 20 | sides ={'left': Line((0,0), (0,H)), 'right': Line((W,0), (W,H))} 21 | d = sides.copy() 22 | d.update(layers) 23 | d.update(symbols_q) 24 | fig = Composition(d) 25 | 26 | fig.draw() 27 | drawing_tool.display() 28 | drawing_tool.savefig('tmp2') 29 | 30 | raw_input() 31 | -------------------------------------------------------------------------------- /src/old/fig/layers.fig: -------------------------------------------------------------------------------- 1 | #FIG 3.2 Produced by xfig version 3.2.5b 2 | Landscape 3 | Center 4 | Metric 5 | A4 6 | 100.00 7 | Single 8 | -2 9 | 1200 2 10 | 2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2 11 | 0 0 1.00 60.00 120.00 12 | 900 6750 6525 6750 13 | 2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 3 14 | 900 2925 4725 2925 4725 6750 15 | 2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2 16 | 2340 6750 2340 2925 17 | 2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2 18 | 1755 6750 1755 2925 19 | 2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2 20 | 4005 6750 4005 2925 21 | 2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2 22 | 0 0 1.00 60.00 120.00 23 | 900 6795 900 1350 24 | 4 0 0 50 -1 0 12 0.0000 2 195 2040 2160 2565 $\\partial u/\\partial n = 0$\001 25 | 4 0 0 50 -1 0 12 0.0000 2 195 2040 2160 7155 $\\partial u/\\partial n = 0$\001 26 | 4 0 0 50 -1 0 12 0.0000 2 165 525 180 4770 $u=0$\001 27 | 4 0 0 50 -1 0 12 0.0000 2 165 525 4905 4770 $u=1$\001 28 | 4 0 0 50 -1 0 12 0.0000 2 195 1050 4185 3735 $\\Omega_3$\001 29 | 4 0 0 50 -1 0 12 0.0000 2 195 1050 3015 3735 $\\Omega_2$\001 30 | 4 0 0 50 -1 0 12 0.0000 2 195 1050 1935 3735 $\\Omega_1$\001 31 | 4 0 0 50 -1 0 12 0.0000 2 180 525 1935 4140 $k_1$\001 32 | 4 0 0 50 -1 0 12 0.0000 2 195 1050 1170 3735 $\\Omega_0$\001 33 | 4 0 0 50 -1 0 12 0.0000 2 180 525 6210 6975 $x_0$\001 34 | 4 0 0 50 -1 0 12 0.0000 2 180 525 1170 4140 $k_0$\001 35 | 4 0 0 50 -1 0 12 0.0000 2 180 525 3015 4140 $k_2$\001 36 | 4 0 0 50 -1 0 12 0.0000 2 180 525 4185 4140 $k_3$\001 37 | 4 0 0 50 -1 0 12 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dvips -E layers.dvi -o layers.eps 12 | # check layers.eps - you probably need to adjust the placement of $...$ text 13 | # include layers.eps in the latex document 14 | 15 | 16 | 17 | -------------------------------------------------------------------------------- /src/old/fig/layers.tex: -------------------------------------------------------------------------------- 1 | \documentclass{article} 2 | \usepackage{epsfig} 3 | \usepackage{color} 4 | \setlength{\textwidth}{100cm} 5 | \setlength{\textheight}{100cm} 6 | \begin{document} 7 | \pagestyle{empty} 8 | \input{layers.pstex_t} 9 | \end{document} 10 | -------------------------------------------------------------------------------- /src/old/fig/membrane_curveplot.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/hplgit/fenics-tutorial/bf8120cb448f244df18871ee305f4b9c463896cf/src/old/fig/membrane_curveplot.pdf 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Rectangle((0.3, 0.3), 0.4, 0.4) 12 | text1 = Text('$u=1$', (-0.2,0.5), alignment='left') 13 | text2 = Text('$u=0$', (1.2,0.5), alignment='right') 14 | text3 = Text(r'$\partial u/\partial n=0$', (0.5, 1.05), alignment='center') 15 | text4 = Text(r'$\partial u/\partial n=0$', (0.5, -0.1), alignment='center') 16 | 17 | fig1 = Composition({ 18 | 'domain': domain, 19 | 'x=0': text1, 'x=1': text2, 'y=1': text3, 'y=0': text4, 20 | }) 21 | 22 | fig1.draw() 23 | drawing_tool.display() 24 | drawing_tool.savefig('tmp1') 25 | 26 | drawing_tool.erase() 27 | fig1['subdomain'] = subdomain 28 | fig1['x=1'] = Text(r'$\partial u/\partial n = 0$', 29 | (1.3,0.5), alignment='right') 30 | 31 | fig1.draw() 32 | drawing_tool.savefig('tmp2') 33 | 34 | raw_input() 35 | -------------------------------------------------------------------------------- /src/old/fig/thermal_layer1_BE20.pdf: -------------------------------------------------------------------------------- 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| text4 = Text(r'$\frac{\partial u}{\partial n}=0$', (0.5, -0.1), alignment='center') 14 | 15 | import numpy as np 16 | x = np.linspace(-0.1, 1.1, 101) 17 | y = 1.15 + 0.025*np.sin(2*np.pi/0.2*x) 18 | 19 | fig1 = Composition({ 20 | 'domain': Rectangle((0,0), 1, 1), 21 | 'subdomain': Rectangle((0.3, 0.3), 0.4, 0.4), 22 | 'y=1': text1, 'x=0': text2, 'x=1': text3, 'y=0': text4, 23 | 'sine': Curve(x,y), 24 | }) 25 | 26 | fig1.draw() 27 | drawing_tool.savefig('tmp3') 28 | 29 | fig1['subdomain'] = Rectangle((0.3,0.5), 0.4, 0.4) 30 | fig1['y=1'] = Text(r'$u= \sin 2t$', (0.5,1.05), alignment='center') 31 | drawing_tool.erase() 32 | fig1.draw() 33 | drawing_tool.savefig('tmp4') 34 | 35 | 36 | """ 37 | text1 = Text(r'$u= \sin 2t$', (0.08,1.05), alignment='center') 38 | text2 = Text(r'$\frac{\partial u}{\partial n}=0$', (-0.2, 0.5), alignment='left') 39 | text3 = Text(r'$\frac{\partial u}{\partial n}=0$', (0.2, 0.5), alignment='left') 40 | text4 = Text(r'$\frac{\partial u}{\partial n}=0$', (0.08, -0.1), alignment='center') 41 | 42 | x = np.linspace(-0.1, 0.167+0.1, 101) 43 | y = 1.15 + 0.025*np.sin(2*np.pi/0.1*x) 44 | 45 | fig2 = Composition({ 46 | 'domain': Rectangle((0,0), 0.167, 1), 47 | 'subdomain': Rectangle((0.3*0.167, 0.3), 0.4*0.167, 0.4), 48 | 'x=0': text1, 'x=1': text2, 'y=1': text3, 'y=0': text4, 49 | 'sine': Curve(x,y), 50 | }) 51 | """ 52 | 53 | raw_input() 54 | -------------------------------------------------------------------------------- /src/old/fig/thermal_layer3_CN20.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/hplgit/fenics-tutorial/bf8120cb448f244df18871ee305f4b9c463896cf/src/old/fig/thermal_layer3_CN20.pdf -------------------------------------------------------------------------------- /src/old/fig/thermal_layer3_CN20.png: -------------------------------------------------------------------------------- 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-------------------------------------------------------------------------------- /src/scripts/clean.sh: -------------------------------------------------------------------------------- 1 | #!/bin/sh 2 | #rm -f automake_sphinx.py # not used here, see make.sh 3 | doconce clean 4 | rm -rf ftut*.pdf fenics_tutorial*.pdf automake* papers.bib newcommands.tex 5 | -------------------------------------------------------------------------------- /src/scripts/install.sh: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env bash 2 | # 3 | # This script installs all required packages for building the book. 4 | 5 | sudo apt-get update 6 | 7 | # Install basic packages 8 | sudo apt-get install \ 9 | git mercurial texlive texlive-latex-extra ispell 10 | 11 | # Install Chinese LaTeX 12 | sudo apt-get install texlive-lang-chinese 13 | 14 | # Install standard Python packages 15 | sudo apt-get install \ 16 | python-future python-mako python-lxml python-sphinx python-pip ipython 17 | 18 | # Install extra Python packages 19 | sudo pip2 install git+https://github.com/hplgit/doconce.git 20 | sudo pip2 install git+https://github.com/hplgit/preprocess.git 21 | sudo pip2 install hg+https://bitbucket.org/logg/publish 22 | sudo pip2 install python-Levenshtein 23 | -------------------------------------------------------------------------------- /src/scripts/make_notebooks.sh: -------------------------------------------------------------------------------- 1 | #!/bin/bash 2 | set -x 3 | 4 | function system { 5 | "$@" 6 | if [ $? -ne 0 ]; then 7 | echo "make.sh: unsuccessful command $@" 8 | echo "abort!" 9 | exit 1 10 | fi 11 | } 12 | 13 | EXV=True 14 | 15 | system preprocess -DFORMAT=html newcommands.p.tex > newcommands.tex 16 | filenames='poisson0 membrane0 diffusion0' 17 | for filename in $filenames; do 18 | doconce format ipynb $filename --encoding=utf-8 EXV=$EXV 19 | done 20 | 21 | # Publish in doc/pub 22 | dest=../pub 23 | cp *.ipynb $dest 24 | -------------------------------------------------------------------------------- /src/scripts/number_src_files.py: -------------------------------------------------------------------------------- 1 | """Copy src files with logical names to numbered src files. 2 | The files are published in the directory ../pub/python. 3 | """ 4 | 5 | # Note the following issues: 6 | # 7 | # 1. Running this script requires tmp_preprocess__ftut1.do.txt, which 8 | # in turn requires building the book, which in turn requires 9 | # mako_code.txt, which should be generated by this script... :-) 10 | # So some bootstrapping is needed. Add lines 'foo': 'bar') manually 11 | # to make_code.txt, then build the book, then run this script and 12 | # udpate mako_code.txt. 13 | # 14 | # 2. The source files are only copied to pub when running this script 15 | # and it is not integrated with the build system. 16 | 17 | import commands, re 18 | 19 | # Find all references to Python programs 20 | cmd = r"""grep -o -h -E 'prog\[".*?"\]' tmp_preprocess__ftut1.do.txt""" 21 | status, output = commands.getstatusoutput(cmd) 22 | 23 | # Extract filenames from references 24 | filenames = [] 25 | for line in output.splitlines(): 26 | names = re.findall(r'prog\["(.*?)"\]', line) 27 | print names 28 | [filenames.append(f) for f in names if f not in filenames] 29 | 30 | print filenames 31 | 32 | # Generate mapping from logical to numbered filenames 33 | counter = 1 34 | prog = [] 35 | for filename in filenames: 36 | new_filename = 'ft%02d_%s' % (counter, filename) 37 | print filename, '-->', new_filename 38 | counter += 1 39 | prog.append((filename, new_filename)) 40 | 41 | # Copy source files 42 | for filename, new_filename in prog: 43 | cmd = 'cp vol1/python/%s.py ../pub/python/vol1/%s.py' % (filename, new_filename) 44 | status, output = commands.getstatusoutput(cmd) 45 | 46 | # Write prog to mako_code.txt 47 | print 48 | print 'Stick this into mako_code.txt:' 49 | print 50 | rows = [] 51 | for (filename, new_filename) in prog: 52 | rows.append("'%s': '%s'" % (filename, new_filename)) 53 | print 'prog = {' 54 | print ',\n'.join(rows) 55 | print '}' 56 | -------------------------------------------------------------------------------- /src/scripts/publish.sh: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env sh 2 | 3 | rsync -avz --delete ../pub/ fenics-web@fenicsproject.org:/home/fenics-web/pub/tutorial/ 4 | -------------------------------------------------------------------------------- /src/scripts/rsync_git.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python 2 | """ 3 | Sync two directory trees with rsync and perform corresponding 4 | git operations (add or rm). 5 | Skip files listed in $HOME/1/.rsyncexclude. 6 | 7 | Usage: rsync_git.py from-dir to-dir 8 | Example: rsync_git.py src-mychap $HOME/repos/pub/mybook/src/mychap 9 | 10 | The from-dir is the source and the to-dir is the destination 11 | (e.g. a public directory where resources are exposed). 12 | The script must be run from a dir within the repo of to-dir. 13 | """ 14 | 15 | # Typical rsync output: 16 | """ 17 | sending incremental file list 18 | deleting decay7.py 19 | decay_TULL.py 20 | 21 | sent 675 bytes received 34 bytes 1418.00 bytes/sec 22 | total size is 94788 speedup is 133.69 23 | """ 24 | 25 | import commands, os, sys 26 | 27 | from_ = sys.argv[1] 28 | to_ = sys.argv[2] 29 | cmd = 'rsync -rtDvz -u -e ssh -b --exclude-from=$HOME/1/.rsyncexclude --suffix=.rsync~ --delete --force %s/ %s' % (from_, to_) 30 | print cmd 31 | failure, output = commands.getstatusoutput(cmd) 32 | print output 33 | 34 | delete = [] 35 | add = [] 36 | for line in output.splitlines(): 37 | relevant_line = True 38 | for text in 'sending incremental file list', \ 39 | 'sent ', 'total size is': 40 | if line.startswith(text): 41 | relevant_line = False 42 | if relevant_line and line != '': 43 | if line.startswith('deleting'): 44 | delete.append(line.split()[1]) 45 | else: 46 | add.append(line.strip()) 47 | 48 | print delete 49 | print add 50 | 51 | for filename in delete: 52 | option = '-rf' if os.path.isdir('%s/%s' % (to_, filename)) else '-f' 53 | cmd = 'git rm %s %s/%s' % (option, to_, filename) 54 | print cmd 55 | os.system(cmd) 56 | for filename in add: 57 | cmd = 'git add %s/%s' % (to_, filename) 58 | print cmd 59 | os.system(cmd) 60 | -------------------------------------------------------------------------------- /src/src/clean.sh: -------------------------------------------------------------------------------- 1 | #!/bin/sh 2 | rm -rf *.vtu *.pvd *.pdf *.png *.pyc __pycache__ tmp* *~ *.mat Results* 3 | -------------------------------------------------------------------------------- /src/src/concentric_cylinders.py: -------------------------------------------------------------------------------- 1 | from dolfin import * 2 | import mshr 3 | 4 | # Parameters for geometry 5 | a = 0.04 6 | b = a + 0.004 7 | c = a + 0.01 8 | L = 0.5 9 | 10 | # Define cylinders 11 | inner = mshr.CSGCGALDomain3D(mshr.Cylinder(Point(0, 0, 0), Point(0, 0, L), a, a)) 12 | mid = mshr.CSGCGALDomain3D(mshr.Cylinder(Point(0, 0, 0), Point(0, 0, L), b, b)) 13 | outer = mshr.CSGCGALDomain3D(mshr.Cylinder(Point(0, 0, 0), Point(0, 0, L), c, c)) 14 | 15 | generator = mshr.TetgenMeshGenerator3D() 16 | generator.parameters["preserve_surface"] = True 17 | generator.parameters["mesh_resolution"] = 16. 18 | 19 | # Mesh inner cylinder 20 | inner_mesh = generator.generate(inner) 21 | 22 | 23 | # Mesh mid part 24 | mid_mesh = generator.generate(mshr.CSGCGALDomain3D(mid-inner)) 25 | 26 | # Mesh outer part 27 | outer_mesh = generator.generate(mshr.CSGCGALDomain3D(outer-mid)) 28 | 29 | # Glue together inner and mid mesh 30 | inner_mid_mesh = mshr.DolfinMeshUtils.merge_meshes(inner_mesh, mid_mesh) 31 | 32 | # Glue outer and inner/mid 33 | the_entire_domain = mshr.DolfinMeshUtils.merge_meshes(inner_mid_mesh, outer_mesh) 34 | 35 | # Save to file 36 | File('pipe_mesh.pvd') << the_entire_domain 37 | 38 | plot(the_entire_domain, interactive=True) 39 | -------------------------------------------------------------------------------- /src/src/convection_diffusion.py: -------------------------------------------------------------------------------- 1 | """ 2 | FEniCS tutorial demo program: Convection-diffusion in a cylinder 3 | with particular focus on mesh generation, subdomains and boundary 4 | conditions. 5 | 6 | -div(lmbda*grad(u)) + div(c*beta*u) = f 7 | """ 8 | 9 | from __future__ import print_function 10 | from fenics import * 11 | from mshr import * 12 | 13 | # Parameters for geometry 14 | a = 0.04 15 | b = a + 0.004 16 | c = a + 0.01 17 | L = 0.5 18 | 19 | # Define cylinders 20 | cylinder_a = Cylinder(Point(0, 0, 0), Point(0, 0, L), a, a) 21 | cylinder_b = Cylinder(Point(0, 0, 0), Point(0, 0, L), b, b) 22 | cylinder_c = Cylinder(Point(0, 0, 0), Point(0, 0, L), c, c) 23 | 24 | # Define domain and set subdomains 25 | domain = cylinder_c 26 | domain.set_subdomain(1, cylinder_b) 27 | domain.set_subdomain(2, cylinder_a) 28 | 29 | # Generate mesh 30 | mesh = generate_mesh(domain, 16) 31 | 32 | xmlfile = File('pipe.xml') 33 | xmlfile << mesh 34 | 35 | vtkfile = File('pipe.pvd') 36 | vtkfile << mesh 37 | -------------------------------------------------------------------------------- /src/src/gui/clean.sh: -------------------------------------------------------------------------------- 1 | #!/bin/sh 2 | # Clean up files that can be regenerated 3 | rm -rf uploads/ templates/ static/ controller.py model.py *.pyc *~ clean.sh -------------------------------------------------------------------------------- /src/src/gui/noweb/controller_noweb.py: -------------------------------------------------------------------------------- 1 | import os 2 | from compute_noweb import compute_noweb as compute_function # changed 3 | 4 | # Pool object (must be imported before model) 5 | from compute_noweb import define_pool as pool_function 6 | pool = pool_function() 7 | 8 | # Can define other default values in a file: --poolfile name 9 | from parampool.pool.UI import set_defaults_from_file 10 | pool = set_defaults_from_file(pool) 11 | # Can override default values on the command line 12 | from parampool.pool.UI import set_values_from_command_line 13 | pool = set_values_from_command_line(pool) 14 | 15 | # Removed everything with Flask 16 | 17 | def compute(pool): 18 | """ 19 | Generic function for calling compute_function with values 20 | taken from the pool object. 21 | Return the output from the compute_function. 22 | """ 23 | 24 | # compute_function must have only one positional argument 25 | # named pool 26 | import inspect 27 | arg_names = inspect.getargspec(compute_function).args 28 | if len(arg_names) == 1 and arg_names[0] == "pool": 29 | result = compute_function(pool) 30 | else: 31 | raise TypeError('%s(%s) can only have one argument named "pool"' 32 | % (compute_function.__name__, ', '.join(arg_names))) 33 | return result 34 | 35 | if __name__ == '__main__': 36 | result = compute_function(pool) # Add 37 | 38 | # Dump pool to file for use with --poolfile .tmp_pool.dat 39 | from parampool.pool.UI import write_poolfile 40 | write_poolfile(pool, '.tmp_pool.dat') 41 | -------------------------------------------------------------------------------- /src/src/gui/web/controller.py: -------------------------------------------------------------------------------- 1 | import os 2 | from compute import compute as compute_function 3 | 4 | # Pool object (must be imported before model) 5 | from compute import define_pool as pool_function 6 | pool = pool_function() 7 | 8 | # Can define other default values in a file: --poolfile name 9 | from parampool.pool.UI import set_defaults_from_file 10 | pool = set_defaults_from_file(pool) 11 | # Can override default values on the command line 12 | from parampool.pool.UI import set_values_from_command_line 13 | pool = set_values_from_command_line(pool) 14 | 15 | from flask import Flask, render_template, request 16 | from model import Compute 17 | 18 | # Application object 19 | app = Flask(__name__) 20 | 21 | # Path to the web application 22 | @app.route('/', methods=['GET', 'POST']) 23 | def index(): 24 | form = Compute(request.form) 25 | if request.method == 'POST': # and form.validate(): 26 | 27 | # Send data to Pool object 28 | for field in form: 29 | if field.name not in request.files: 30 | name = field.description 31 | value = field.data 32 | data_item = pool.set_value(name, value) 33 | 34 | result = compute(pool) 35 | 36 | else: 37 | result = None 38 | 39 | return render_template("view.html", form=form, result=result) 40 | 41 | 42 | def compute(pool): 43 | """ 44 | Generic function for calling compute_function with values 45 | taken from the pool object. 46 | Return the output from the compute_function. 47 | """ 48 | 49 | # compute_function must have only one positional argument 50 | # named pool 51 | import inspect 52 | arg_names = inspect.getargspec(compute_function).args 53 | if len(arg_names) == 1 and arg_names[0] == "pool": 54 | result = compute_function(pool) 55 | else: 56 | raise TypeError('%s(%s) can only have one argument named "pool"' 57 | % (compute_function.__name__, ', '.join(arg_names))) 58 | return result 59 | 60 | if __name__ == '__main__': 61 | app.run(debug=True) 62 | 63 | # Dump pool to file for use with --poolfile .tmp_pool.dat 64 | from parampool.pool.UI import write_poolfile 65 | write_poolfile(pool, '.tmp_pool.dat') 66 | -------------------------------------------------------------------------------- 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-------------------------------------------------------------------------------- 1 | """ 2 | FEniCS tutorial demo program: Diffusion equation with Dirichlet 3 | conditions and a solution that will be exact at all nodes on 4 | a uniform mesh. 5 | Difference from heat.py: A (coeff.matrix) is assembled 6 | only once. 7 | """ 8 | 9 | from __future__ import print_function 10 | from fenics import * 11 | import numpy as np 12 | 13 | # Create mesh and define function space 14 | nx = ny = 4 15 | mesh = UnitSquareMesh(nx, ny) 16 | V = FunctionSpace(mesh, 'P', 1) 17 | 18 | # Define boundary conditions 19 | alpha = 3; beta = 1.2 20 | u0 = Expression('1 + x[0]*x[0] + alpha*x[1]*x[1] + beta*t', 21 | alpha=alpha, beta=beta, t=0) 22 | 23 | def boundary(x, on_boundary): 24 | return on_boundary 25 | 26 | bc = DirichletBC(V, u0, boundary) 27 | 28 | # Initial condition 29 | u_1 = interpolate(u0, V) 30 | #project(u0, V) # will not result in exact solution at the nodes! 31 | 32 | dt = 0.3 # time step 33 | 34 | # Define variational problem 35 | u = TrialFunction(V) 36 | v = TestFunction(V) 37 | f = Constant(beta - 2 - 2*alpha) 38 | a = u*v*dx + dt*dot(grad(u), grad(v))*dx 39 | L = (u_1 + dt*f)*v*dx 40 | 41 | A = assemble(a) # assemble only once, before the time stepping 42 | b = None # necessary for memory saving assemeble call 43 | 44 | # Compute solution 45 | u = Function(V) # the unknown at a new time level 46 | T = 1.9 # total simulation time 47 | t = dt 48 | while t <= T: 49 | print('time =', t) 50 | b = assemble(L, tensor=b) 51 | u0.t = t 52 | bc.apply(A, b) 53 | solve(A, u.vector(), b) 54 | 55 | # Verify 56 | u_e = interpolate(u0, V) 57 | error = np.abs(u_e.vector().array() - 58 | u.vector().array()).max() 59 | print('error, t=%.2f: %-10.3g' % (t, error)) 60 | 61 | t += dt 62 | u_1.assign(u) 63 | -------------------------------------------------------------------------------- /src/src/make_moviefiles.sh: -------------------------------------------------------------------------------- 1 | #!/bin/sh 2 | set -x 3 | if [ $# -ge 1 ]; then 4 | name=$1 5 | else 6 | name="tmp_%04d.png" 7 | fi 8 | if [ $# -ge 2 ]; then 9 | fps=$2 10 | else 11 | fps=25 12 | fi 13 | prog=ffmpeg 14 | 15 | # Make movies in modern web friendly formats 16 | rm -f movie.flv movie.mp4 movie.webm movie.ogg 17 | $prog -i $name -r $fps -vcodec flv movie.flv 18 | $prog -i $name -r $fps -vcodec libx264 movie.mp4 19 | $prog -i $name -r $fps -vcodec libvpx movie.webm 20 | $prog -i $name -r $fps -vcodec libtheora movie.ogg 21 | -------------------------------------------------------------------------------- /src/src/modules/setup.py: -------------------------------------------------------------------------------- 1 | from distutils.core import setup 2 | name = 'BoxField' 3 | setup(name=name, 4 | version='1.0', 5 | author='Hans Petter Langtangen ', 6 | py_modules=[name], 7 | #scripts=[name + '.py'], 8 | ) 9 | -------------------------------------------------------------------------------- /src/vol1/fundamentals.do.txt: -------------------------------------------------------------------------------- 1 | ========= Fundamentals: Solving the Poisson equation ========= 2 | label{ch:fundamentals} 3 | 4 | !bquote 5 | The goal of this chapter is to show how the Poisson equation, the 6 | most basic of all PDEs, can be quickly solved with a few lines 7 | of FEniCS code. We introduce the most 8 | fundamental FEniCS objects such as `Mesh`, `Function`, 9 | `FunctionSpace`, `TrialFunction`, 10 | and `TestFunction`, and learn how to write a basic PDE solver, 11 | including how to formulate the mathematical variational problem, 12 | apply boundary conditions, call the FEniCS solver, and plot 13 | the solution. 14 | !equote 15 | 16 | # #include "fundamentals_poisson.do.txt" 17 | 18 | !split 19 | # #include "fundamentals_membrane.do.txt" 20 | -------------------------------------------------------------------------------- /src/vol1/gallery.do.txt: -------------------------------------------------------------------------------- 1 | ========= A Gallery of finite element solvers ========= 2 | label{ch:gallery} 3 | 4 | !bquote 5 | The goal of this chapter is to demonstrate how a range of important 6 | PDEs from science and engineering can be quickly solved with a few 7 | lines of FEniCS code. We start with the heat equation and continue 8 | with a nonlinear Poisson equation, the equations for linear 9 | elasticity, the Navier--Stokes equations, and finally look at how to 10 | solve systems of nonlinear advection--diffusion--reaction 11 | equations. These problems illustrate how to solve time-dependent 12 | problems, nonlinear problems, vector-valued problems, and systems of 13 | PDEs. For each problem, we derive the variational formulation and 14 | express the problem in Python in a way that closely resembles the 15 | mathematics. 16 | !equote 17 | 18 | # #include "gallery_heat_equation.do.txt" 19 | 20 | !split 21 | # #include "gallery_nlpoisson.do.txt" 22 | 23 | !split 24 | # #include "gallery_elasticity.do.txt" 25 | 26 | !split 27 | # #include "gallery_navier_stokes.do.txt" 28 | 29 | !split 30 | # #include "gallery_reaction_system.do.txt" 31 | -------------------------------------------------------------------------------- /src/vol1/preface.do.txt: -------------------------------------------------------------------------------- 1 | ========= Preface ========= 2 | 3 | This book gives a concise and gentle introduction to finite element 4 | programming in Python based on the popular FEniCS software library. 5 | FEniCS can be programmed in both C++ and Python, but this tutorial 6 | focuses exclusively on Python programming, since this is the simplest 7 | and most effective approach for beginners. After having digested the 8 | examples in this tutorial, the reader should be able to learn more 9 | from the FEniCS documentation, the numerous demo programs that come 10 | with the software, and the comprehensive FEniCS book *Automated 11 | Solution of Differential Equations by the Finite Element Method* 12 | cite{FEniCS}. This tutorial is a further development of the opening 13 | chapter in cite{FEniCS}. 14 | 15 | We thank Johan Hake, Kent-Andre Mardal, and Kristian Valen-Sendstad 16 | for many helpful discussions during the preparation of the first 17 | version of this tutorial for the FEniCS book cite{FEniCS}. We are 18 | particularly thankful to Professor Douglas Arnold for very valuable 19 | feedback on early versions of the text. Øystein Sørensen pointed out 20 | numerous typos and contributed with many helpful comments. Many errors 21 | and typos were also reported by Mauricio Angeles, Ida Drøsdal, 22 | Miroslav Kuchta, Hans Ekkehard Plesser, Marie Rognes, Hans Joachim 23 | Scroll, Glenn Terje Lines, Simon Funke, Matthew Moelter, and Magne 24 | Nordaas. Ekkehard Ellmann as well as two anonymous reviewers provided 25 | a series of suggestions and improvements. Special thanks go to 26 | Benjamin Kehlet for all his work with the `mshr` tool and for quickly 27 | implementing our requests for this tutorial. 28 | 29 | Comments and corrections can be reported as *issues* for the 30 | "Git repository of this book": 31 | "https://github.com/hplgit/fenics-tutorial/", 32 | or via email 33 | to `logg@chalmers.se`. 34 | 35 | # #if FORMAT in ("latex", "pdflatex") 36 | \vspace{1cm} 37 | 38 | \noindent 39 | {\it Oslo and Smögen, November 2016} \hfill {\it Hans Petter Langtangen, Anders Logg} 40 | # #endif 41 | -------------------------------------------------------------------------------- /src/vol1/python/elasticity.py: -------------------------------------------------------------------------------- 1 | """ 2 | FEniCS tutorial demo program: Linear elastic problem. 3 | 4 | -div(sigma(u)) = f 5 | 6 | The model is used to simulate an elastic beam clamped at 7 | its left end and deformed under its own weight. 8 | """ 9 | 10 | from __future__ import print_function 11 | from fenics import * 12 | 13 | # Scaled variables 14 | L = 1; W = 0.2 15 | mu = 1 16 | rho = 1 17 | delta = W/L 18 | gamma = 0.4*delta**2 19 | beta = 1.25 20 | lambda_ = beta 21 | g = gamma 22 | 23 | # Create mesh and define function space 24 | mesh = BoxMesh(Point(0, 0, 0), Point(L, W, W), 10, 3, 3) 25 | V = VectorFunctionSpace(mesh, 'P', 1) 26 | 27 | # Define boundary condition 28 | tol = 1E-14 29 | 30 | def clamped_boundary(x, on_boundary): 31 | return on_boundary and x[0] < tol 32 | 33 | bc = DirichletBC(V, Constant((0, 0, 0)), clamped_boundary) 34 | 35 | # Define strain and stress 36 | 37 | def epsilon(u): 38 | return 0.5*(nabla_grad(u) + nabla_grad(u).T) 39 | #return sym(nabla_grad(u)) 40 | 41 | def sigma(u): 42 | return lambda_*nabla_div(u)*Identity(d) + 2*mu*epsilon(u) 43 | 44 | # Define variational problem 45 | u = TrialFunction(V) 46 | d = u.geometric_dimension() # space dimension 47 | v = TestFunction(V) 48 | f = Constant((0, 0, -rho*g)) 49 | T = Constant((0, 0, 0)) 50 | a = inner(sigma(u), epsilon(v))*dx 51 | L = dot(f, v)*dx + dot(T, v)*ds 52 | 53 | # Compute solution 54 | u = Function(V) 55 | solve(a == L, u, bc) 56 | 57 | # Plot solution 58 | plot(u, title='Displacement', mode='displacement') 59 | 60 | # Plot stress 61 | s = sigma(u) - (1./3)*tr(sigma(u))*Identity(d) # deviatoric stress 62 | von_Mises = sqrt(3./2*inner(s, s)) 63 | V = FunctionSpace(mesh, 'P', 1) 64 | von_Mises = project(von_Mises, V) 65 | plot(von_Mises, title='Stress intensity') 66 | 67 | # Compute magnitude of displacement 68 | u_magnitude = sqrt(dot(u, u)) 69 | u_magnitude = project(u_magnitude, V) 70 | plot(u_magnitude, 'Displacement magnitude') 71 | print('min/max u:', 72 | u_magnitude.vector().array().min(), 73 | u_magnitude.vector().array().max()) 74 | 75 | # Save solution to file in VTK format 76 | File('elasticity/displacement.pvd') << u 77 | File('elasticity/von_mises.pvd') << von_Mises 78 | File('elasticity/magnitude.pvd') << u_magnitude 79 | 80 | # Hold plot 81 | interactive() 82 | -------------------------------------------------------------------------------- /src/vol1/python/heat.py: -------------------------------------------------------------------------------- 1 | """ 2 | FEniCS tutorial demo program: Heat equation with Dirichlet conditions. 3 | Test problem is chosen to give an exact solution at all nodes of the mesh. 4 | 5 | u'= Laplace(u) + f in the unit square 6 | u = u_D on the boundary 7 | u = u_0 at t = 0 8 | 9 | u = 1 + x^2 + alpha*y^2 + \beta*t 10 | f = beta - 2 - 2*alpha 11 | """ 12 | 13 | from __future__ import print_function 14 | from fenics import * 15 | import numpy as np 16 | 17 | T = 2.0 # final time 18 | num_steps = 10 # number of time steps 19 | dt = T / num_steps # time step size 20 | alpha = 3 # parameter alpha 21 | beta = 1.2 # parameter beta 22 | 23 | # Create mesh and define function space 24 | nx = ny = 8 25 | mesh = UnitSquareMesh(nx, ny) 26 | V = FunctionSpace(mesh, 'P', 1) 27 | 28 | # Define boundary condition 29 | u_D = Expression('1 + x[0]*x[0] + alpha*x[1]*x[1] + beta*t', 30 | degree=2, alpha=alpha, beta=beta, t=0) 31 | 32 | def boundary(x, on_boundary): 33 | return on_boundary 34 | 35 | bc = DirichletBC(V, u_D, boundary) 36 | 37 | # Define initial value 38 | u_n = interpolate(u_D, V) 39 | #u_n = project(u_D, V) 40 | 41 | # Define variational problem 42 | u = TrialFunction(V) 43 | v = TestFunction(V) 44 | f = Constant(beta - 2 - 2*alpha) 45 | 46 | F = u*v*dx + dt*dot(grad(u), grad(v))*dx - (u_n + dt*f)*v*dx 47 | a, L = lhs(F), rhs(F) 48 | 49 | # Time-stepping 50 | u = Function(V) 51 | t = 0 52 | for n in range(num_steps): 53 | 54 | # Update current time 55 | t += dt 56 | u_D.t = t 57 | 58 | # Compute solution 59 | solve(a == L, u, bc) 60 | 61 | # Plot solution 62 | plot(u) 63 | 64 | # Compute error at vertices 65 | u_e = interpolate(u_D, V) 66 | error = np.abs(u_e.vector().array() - u.vector().array()).max() 67 | print('t = %.2f: error = %.3g' % (t, error)) 68 | 69 | # Update previous solution 70 | u_n.assign(u) 71 | 72 | # Hold plot 73 | interactive() 74 | -------------------------------------------------------------------------------- /src/vol1/python/heat_gaussian.py: -------------------------------------------------------------------------------- 1 | """ 2 | FEniCS tutorial demo program: Diffusion of a Gaussian hill. 3 | 4 | u'= Laplace(u) + f in a square domain 5 | u = u_D on the boundary 6 | u = u_0 at t = 0 7 | 8 | u_D = f = 0 9 | 10 | The initial condition u_0 is chosen as a Gaussian hill. 11 | """ 12 | 13 | from __future__ import print_function 14 | from fenics import * 15 | import time 16 | 17 | T = 2.0 # final time 18 | num_steps = 50 # number of time steps 19 | dt = T / num_steps # time step size 20 | 21 | # Create mesh and define function space 22 | nx = ny = 30 23 | mesh = RectangleMesh(Point(-2, -2), Point(2, 2), nx, ny) 24 | V = FunctionSpace(mesh, 'P', 1) 25 | 26 | # Define boundary condition 27 | def boundary(x, on_boundary): 28 | return on_boundary 29 | 30 | bc = DirichletBC(V, Constant(0), boundary) 31 | 32 | # Define initial value 33 | u_0 = Expression('exp(-a*pow(x[0], 2) - a*pow(x[1], 2))', 34 | degree=2, a=5) 35 | u_n = interpolate(u_0, V) 36 | 37 | # Define variational problem 38 | u = TrialFunction(V) 39 | v = TestFunction(V) 40 | f = Constant(0) 41 | 42 | F = u*v*dx + dt*dot(grad(u), grad(v))*dx - (u_n + dt*f)*v*dx 43 | a, L = lhs(F), rhs(F) 44 | 45 | # Create VTK file for saving solution 46 | vtkfile = File('heat_gaussian/solution.pvd') 47 | 48 | # Time-stepping 49 | u = Function(V) 50 | t = 0 51 | for n in range(num_steps): 52 | 53 | # Update current time 54 | t += dt 55 | 56 | # Compute solution 57 | solve(a == L, u, bc) 58 | 59 | # Save to file and plot solution 60 | vtkfile << (u, t) 61 | plot(u) 62 | 63 | # Update previous solution 64 | u_n.assign(u) 65 | 66 | # Hold plot 67 | interactive() 68 | -------------------------------------------------------------------------------- /src/vol1/python/poisson.py: -------------------------------------------------------------------------------- 1 | """ 2 | FEniCS tutorial demo program: Poisson equation with Dirichlet conditions. 3 | Test problem is chosen to give an exact solution at all nodes of the mesh. 4 | 5 | -Laplace(u) = f in the unit square 6 | u = u_D on the boundary 7 | 8 | u_D = 1 + x^2 + 2y^2 9 | f = -6 10 | """ 11 | 12 | from __future__ import print_function 13 | from fenics import * 14 | import matplotlib.pyplot as plt 15 | 16 | # Create mesh and define function space 17 | mesh = UnitSquareMesh(8, 8) 18 | V = FunctionSpace(mesh, 'P', 1) 19 | 20 | # Define boundary condition 21 | u_D = Expression('1 + x[0]*x[0] + 2*x[1]*x[1]', degree=2) 22 | 23 | def boundary(x, on_boundary): 24 | return on_boundary 25 | 26 | bc = DirichletBC(V, u_D, boundary) 27 | 28 | # Define variational problem 29 | u = TrialFunction(V) 30 | v = TestFunction(V) 31 | f = Constant(-6.0) 32 | a = dot(grad(u), grad(v))*dx 33 | L = f*v*dx 34 | 35 | # Compute solution 36 | u = Function(V) 37 | solve(a == L, u, bc) 38 | 39 | # Plot solution and mesh 40 | plot(u) 41 | plot(mesh) 42 | 43 | # Save solution to file in VTK format 44 | vtkfile = File('poisson/solution.pvd') 45 | vtkfile << u 46 | 47 | # Compute error in L2 norm 48 | error_L2 = errornorm(u_D, u, 'L2') 49 | 50 | # Compute maximum error at vertices 51 | vertex_values_u_D = u_D.compute_vertex_values(mesh) 52 | vertex_values_u = u.compute_vertex_values(mesh) 53 | import numpy as np 54 | error_max = np.max(np.abs(vertex_values_u_D - vertex_values_u)) 55 | 56 | # Print errors 57 | print('error_L2 =', error_L2) 58 | print('error_max =', error_max) 59 | 60 | # Hold plot 61 | plt.show() 62 | -------------------------------------------------------------------------------- /src/vol1/python/poisson_membrane.py: -------------------------------------------------------------------------------- 1 | """ 2 | FEniCS tutorial demo program: Deflection of a membrane. 3 | 4 | -Laplace(w) = p in the unit circle 5 | w = 0 on the boundary 6 | 7 | The load p is a Gaussian function centered at (0, 0.6). 8 | """ 9 | 10 | from __future__ import print_function 11 | from fenics import * 12 | from mshr import * 13 | import numpy as np 14 | 15 | # Create mesh and define function space 16 | domain = Circle(Point(0, 0), 1) 17 | mesh = generate_mesh(domain, 64) 18 | V = FunctionSpace(mesh, 'P', 2) 19 | 20 | # Define boundary condition 21 | w_D = Constant(0) 22 | 23 | def boundary(x, on_boundary): 24 | return on_boundary 25 | 26 | bc = DirichletBC(V, w_D, boundary) 27 | 28 | # Define load 29 | beta = 8 30 | R0 = 0.6 31 | p = Expression('4*exp(-pow(beta, 2)*(pow(x[0], 2) + pow(x[1] - R0, 2)))', 32 | degree=1, beta=beta, R0=R0) 33 | 34 | # Define variational problem 35 | w = TrialFunction(V) 36 | v = TestFunction(V) 37 | a = dot(grad(w), grad(v))*dx 38 | L = p*v*dx 39 | 40 | # Compute solution 41 | w = Function(V) 42 | solve(a == L, w, bc) 43 | 44 | # Plot solution 45 | p = interpolate(p, V) 46 | plot(w, title='Deflection') 47 | plot(p, title='Load') 48 | 49 | # Save solution to file in VTK format 50 | vtkfile_w = File('poisson_membrane/deflection.pvd') 51 | vtkfile_w << w 52 | vtkfile_p = File('poisson_membrane/load.pvd') 53 | vtkfile_p << p 54 | 55 | # Curve plot along x = 0 comparing p and w 56 | import numpy as np 57 | import matplotlib.pyplot as plt 58 | tol = 0.001 # avoid hitting points outside the domain 59 | y = np.linspace(-1 + tol, 1 - tol, 101) 60 | points = [(0, y_) for y_ in y] # 2D points 61 | w_line = np.array([w(point) for point in points]) 62 | p_line = np.array([p(point) for point in points]) 63 | plt.plot(y, 50*w_line, 'k', linewidth=2) # magnify w 64 | plt.plot(y, p_line, 'b--', linewidth=2) 65 | plt.grid(True) 66 | plt.xlabel('$y$') 67 | plt.legend(['Deflection ($\\times 50$)', 'Load'], loc='upper left') 68 | plt.savefig('poisson_membrane/curves.pdf') 69 | plt.savefig('poisson_membrane/curves.png') 70 | 71 | # Hold plots 72 | interactive() 73 | plt.show() 74 | -------------------------------------------------------------------------------- /src/vol1/python/poisson_nonlinear.py: -------------------------------------------------------------------------------- 1 | """ 2 | FEniCS tutorial demo program: Nonlinear Poisson equation. 3 | 4 | -div(q(u)*grad(u)) = f in the unit square. 5 | u = u_D on the boundary. 6 | """ 7 | 8 | from __future__ import print_function 9 | 10 | # Warning: from fenics import * will import both `sym` and 11 | # `q` from FEniCS. We therefore import FEniCS first and then 12 | # overwrite these objects. 13 | from fenics import * 14 | 15 | def q(u): 16 | "Return nonlinear coefficient" 17 | return 1 + u**2 18 | 19 | # Use SymPy to compute f from the manufactured solution u 20 | import sympy as sym 21 | x, y = sym.symbols('x[0], x[1]') 22 | u = 1 + x + 2*y 23 | f = - sym.diff(q(u)*sym.diff(u, x), x) - sym.diff(q(u)*sym.diff(u, y), y) 24 | f = sym.simplify(f) 25 | u_code = sym.printing.ccode(u) 26 | f_code = sym.printing.ccode(f) 27 | print('u =', u_code) 28 | print('f =', f_code) 29 | 30 | # Create mesh and define function space 31 | mesh = UnitSquareMesh(8, 8) 32 | V = FunctionSpace(mesh, 'P', 1) 33 | 34 | # Define boundary condition 35 | u_D = Expression(u_code, degree=2) 36 | 37 | def boundary(x, on_boundary): 38 | return on_boundary 39 | 40 | bc = DirichletBC(V, u_D, boundary) 41 | 42 | # Define variational problem 43 | u = Function(V) # Note: not TrialFunction! 44 | v = TestFunction(V) 45 | f = Expression(f_code, degree=2) 46 | F = q(u)*dot(grad(u), grad(v))*dx - f*v*dx 47 | 48 | # Compute solution 49 | solve(F == 0, u, bc) 50 | 51 | # Plot solution 52 | plot(u) 53 | 54 | # Compute maximum error at vertices. This computation illustrates 55 | # an alternative to using compute_vertex_values as in poisson.py. 56 | u_e = interpolate(u_D, V) 57 | import numpy as np 58 | error_max = np.abs(u_e.vector().array() - u.vector().array()).max() 59 | print('error_max = ', error_max) 60 | 61 | # Hold plot 62 | interactive() 63 | -------------------------------------------------------------------------------- /src/vol2/notes.txt: -------------------------------------------------------------------------------- 1 | Chapters 2 | 3 | Nonlinear problems, advanced setting of parameters etc as referred 4 | to in volume 1 at end of nonlinear Poisson section. 5 | --------------------------------------------------------------------------------