├── FEM-代码0--勒让德-高斯积分.ipynb
├── FEM-代码1--初次尝试FEM编程，分析和编程流程，线性形函数.ipynb
├── FEM-代码2--2次形函数（拉格朗日插值）.ipynb
├── FEM-代码3--形函数.ipynb
├── FEM-代码4--二维四边形单元的高斯-勒让德积分.ipynb
├── FEM-代码5.1--解二维泊松方程（Dirichlet边界条件）.ipynb
├── FEM-代码5.2--解二维传热方程，Dirichlet+Neumman边界.ipynb
├── FEM-代码5.3--解二维传热方程，Dirichlet+Neumman+Robin边界.ipynb
├── FEM-代码6-有限差分法.ipynb
├── FEM-代码7-有限差分法-隐函数.ipynb
├── Python matplotlib 应用.ipynb
└── python 处理矩阵数据.ipynb


/FEM-代码4--二维四边形单元的高斯-勒让德积分.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "id": "bb7cd5e9",
  6 |    "metadata": {},
  7 |    "source": [
  8 |     "# 2022年7月12日09:59:00"
  9 |    ]
 10 |   },
 11 |   {
 12 |    "cell_type": "markdown",
 13 |    "id": "09cc3900",
 14 |    "metadata": {},
 15 |    "source": [
 16 |     "## 1. 高斯-勒让德积分"
 17 |    ]
 18 |   },
 19 |   {
 20 |    "cell_type": "code",
 21 |    "execution_count": 7,
 22 |    "id": "7d28e366",
 23 |    "metadata": {},
 24 |    "outputs": [],
 25 |    "source": [
 26 |     "import numpy as np\n",
 27 |     "from numpy.polynomial.legendre import leggauss"
 28 |    ]
 29 |   },
 30 |   {
 31 |    "cell_type": "code",
 32 |    "execution_count": 8,
 33 |    "id": "c4fc787c",
 34 |    "metadata": {},
 35 |    "outputs": [],
 36 |    "source": [
 37 |     "# 需要继续积分域分别为x:[0-2];y:[0-2]\n",
 38 |     "# 因为这关系到dx转换到de之后的系数\n",
 39 |     "def f(x,y):\n",
 40 |     "    return 3*y**2+2*x"
 41 |    ]
 42 |   },
 43 |   {
 44 |    "cell_type": "markdown",
 45 |    "id": "52aa1ed0",
 46 |    "metadata": {},
 47 |    "source": [
 48 |     "假如要求的积分如下：  \n",
 49 |     "  \n",
 50 |     "$$I=\\int_{x_a}^{x_b}\\int_{y_a}^{y_b}f(x,y)dxdy$$"
 51 |    ]
 52 |   },
 53 |   {
 54 |    "cell_type": "markdown",
 55 |    "id": "cde1c2b9",
 56 |    "metadata": {},
 57 |    "source": [
 58 |     "利用变换可得到：  \n",
 59 |     "  \n",
 60 |     "$x=\\frac{(x_b-x_a)\\xi+(x_b+x_a)}{2}$，其中$\\xi \\in [-1,1]$  \n",
 61 |     "  \n",
 62 |     "    \n",
 63 |     "$y=\\frac{(y_b-y_a)\\eta+(y_b+y_a)}{2}$，其中$\\eta \\in [-1,1]$ \n",
 64 |     "  \n",
 65 |     "    \n",
 66 |     "$dx=\\frac{x_b-x_a}{2}d \\xi$  \n",
 67 |     "  \n",
 68 |     "    \n",
 69 |     "$dy=\\frac{y_b-y_a}{2}d \\eta$ "
 70 |    ]
 71 |   },
 72 |   {
 73 |    "cell_type": "markdown",
 74 |    "id": "5c1c496b",
 75 |    "metadata": {},
 76 |    "source": [
 77 |     "将上述变换公式带入原式可得：\n",
 78 |     "$$I=\\int_{-1}^1 \\int_{-1}^1 f(\\frac{(x_b-x_a)\\xi+(x_b+x_a)}{2},\\frac{(y_b-y_a)\\eta+(y_b+y_a)}{2})\\frac{x_b-x_a}{2}d \\xi \\frac{y_b-y_a}{2}d \\eta$$"
 79 |    ]
 80 |   },
 81 |   {
 82 |    "cell_type": "markdown",
 83 |    "id": "863f1820",
 84 |    "metadata": {},
 85 |    "source": [
 86 |     "将常数移出来，可得：\n",
 87 |     "$$I=\\frac{x_b-x_a}{2}\\frac{y_b-y_a}{2}\\int_{-1}^1 \\int_{-1}^1 f(\\frac{(x_b-x_a)\\xi+(x_b+x_a)}{2},\\frac{(y_b-y_a)\\eta+(y_b+y_a)}{2})d \\xi d \\eta$$"
 88 |    ]
 89 |   },
 90 |   {
 91 |    "cell_type": "markdown",
 92 |    "id": "b1393ada",
 93 |    "metadata": {},
 94 |    "source": [
 95 |     "对于从-1到1之间的积分，可以使用高斯-勒让德积分公式求得，首先令：\n",
 96 |     "$F(\\xi,\\eta)=f(\\frac{(x_b-x_a)\\xi+(x_b+x_a)}{2},\\frac{(y_b-y_a)\\eta+(y_b+y_a)}{2})$,则：\n",
 97 |     "\n",
 98 |     "$$\\int_{-1}^1\\int_{-1}^1 F(\\xi,\\eta)d\\xi d\\eta=\\sum_{i=1}^n\\sum_{j=1}^n w_i w_j F(\\xi_i,\\eta_j)$$\n",
 99 |     "  \n",
100 |     "其中，$w_i$，$w_j$，$\\xi_i$，$\\eta_j$表示高斯-勒让德积分中的权重和采样坐标，可以通过查表获得"
101 |    ]
102 |   },
103 |   {
104 |    "cell_type": "markdown",
105 |    "id": "93bb8537",
106 |    "metadata": {},
107 |    "source": [
108 |     "所以：\n",
109 |     "  \n",
110 |     "$$I=\\frac{x_b-x_a}{2}\\frac{y_b-y_a}{2}\\sum_{i=1}^n\\sum_{j=1}^n w_i w_j F(\\xi_i,\\eta_j)$$"
111 |    ]
112 |   },
113 |   {
114 |    "cell_type": "code",
115 |    "execution_count": 12,
116 |    "id": "631cd2c5",
117 |    "metadata": {},
118 |    "outputs": [],
119 |    "source": [
120 |     "def leg_gau_2d(f,n,xa,xb,ya,yb):\n",
121 |     "    x,w=leggauss(n)\n",
122 |     "    # x=(xb-xa)xi/2+(xb+xa)/2\n",
123 |     "    # y=(yb-ya)eta/2+(yb+ya)/2\n",
124 |     "    # dx=(xb-xa)/2 dxi\n",
125 |     "    # dy=(yb-ya)/2 deta\n",
126 |     "    summ=0\n",
127 |     "    for i in range(len(x)):\n",
128 |     "        # i 代表x,用a表示\n",
129 |     "        a=(xb-xa)*x[i]/2+(xb+xa)/2\n",
130 |     "        for j in range(len(x)):\n",
131 |     "            # j 代表y，用b表示\n",
132 |     "            b=(yb-ya)*x[j]/2+(yb+ya)/2\n",
133 |     "            summ+=w[i]*w[j]*f(a,b)\n",
134 |     "    \n",
135 |     "    return (xb-xa)/2*(yb-ya)/2*summ"
136 |    ]
137 |   },
138 |   {
139 |    "cell_type": "code",
140 |    "execution_count": 26,
141 |    "id": "f1e80392",
142 |    "metadata": {},
143 |    "outputs": [
144 |     {
145 |      "data": {
146 |       "text/plain": [
147 |        "24.0"
148 |       ]
149 |      },
150 |      "execution_count": 26,
151 |      "metadata": {},
152 |      "output_type": "execute_result"
153 |     }
154 |    ],
155 |    "source": [
156 |     "leg_gau_2d(f,2,0,2,0,2)"
157 |    ]
158 |   },
159 |   {
160 |    "cell_type": "markdown",
161 |    "id": "b82fa6f6",
162 |    "metadata": {},
163 |    "source": [
164 |     "## 2. 使用sympy试一下"
165 |    ]
166 |   },
167 |   {
168 |    "cell_type": "code",
169 |    "execution_count": 14,
170 |    "id": "f192f43d",
171 |    "metadata": {},
172 |    "outputs": [],
173 |    "source": [
174 |     "import sympy as sp"
175 |    ]
176 |   },
177 |   {
178 |    "cell_type": "code",
179 |    "execution_count": 17,
180 |    "id": "24fb299e",
181 |    "metadata": {},
182 |    "outputs": [
183 |     {
184 |      "data": {
185 |       "text/plain": [
186 |        "(xs, ys)"
187 |       ]
188 |      },
189 |      "execution_count": 17,
190 |      "metadata": {},
191 |      "output_type": "execute_result"
192 |     }
193 |    ],
194 |    "source": [
195 |     "xs,ys=sp.symbols('xs ys')\n",
196 |     "xs,ys"
197 |    ]
198 |   },
199 |   {
200 |    "cell_type": "code",
201 |    "execution_count": 18,
202 |    "id": "1598682b",
203 |    "metadata": {},
204 |    "outputs": [
205 |     {
206 |      "data": {
207 |       "text/latex": [
208 |        "$\\displaystyle 2 xs + 3 ys^{2}$"
209 |       ],
210 |       "text/plain": [
211 |        "2*xs + 3*ys**2"
212 |       ]
213 |      },
214 |      "execution_count": 18,
215 |      "metadata": {},
216 |      "output_type": "execute_result"
217 |     }
218 |    ],
219 |    "source": [
220 |     "fs=3*ys**2+2*xs\n",
221 |     "fs"
222 |    ]
223 |   },
224 |   {
225 |    "cell_type": "code",
226 |    "execution_count": 22,
227 |    "id": "c0aa48fc",
228 |    "metadata": {},
229 |    "outputs": [],
230 |    "source": [
231 |     "def int_sp(fs,xa,xb,ya,yb):\n",
232 |     "    return sp.integrate(fs,(xs,xa,xb),(ys,ya,yb))\n",
233 |     "    "
234 |    ]
235 |   },
236 |   {
237 |    "cell_type": "code",
238 |    "execution_count": 40,
239 |    "id": "663f2b09",
240 |    "metadata": {},
241 |    "outputs": [
242 |     {
243 |      "data": {
244 |       "text/latex": [
245 |        "$\\displaystyle 24$"
246 |       ],
247 |       "text/plain": [
248 |        "24"
249 |       ]
250 |      },
251 |      "execution_count": 40,
252 |      "metadata": {},
253 |      "output_type": "execute_result"
254 |     }
255 |    ],
256 |    "source": [
257 |     "int_sp(fs,0,2,0,2)"
258 |    ]
259 |   },
260 |   {
261 |    "cell_type": "markdown",
262 |    "id": "fc7535ff",
263 |    "metadata": {},
264 |    "source": [
265 |     "# 3. 两种方式做个比较"
266 |    ]
267 |   },
268 |   {
269 |    "cell_type": "code",
270 |    "execution_count": 39,
271 |    "id": "0acd1606",
272 |    "metadata": {},
273 |    "outputs": [
274 |     {
275 |      "data": {
276 |       "text/plain": [
277 |        "(2719.7592, 2719.75920000000)"
278 |       ]
279 |      },
280 |      "execution_count": 39,
281 |      "metadata": {},
282 |      "output_type": "execute_result"
283 |     }
284 |    ],
285 |    "source": [
286 |     "xa,xb=-2.8,5.9\n",
287 |     "ya,yb=-2.8,6.4\n",
288 |     "leg_gau_2d(f,2,xa,xb,ya,yb),int_sp(fs,xa,xb,ya,yb)"
289 |    ]
290 |   },
291 |   {
292 |    "cell_type": "code",
293 |    "execution_count": 41,
294 |    "id": "dfa1d4b4",
295 |    "metadata": {},
296 |    "outputs": [],
297 |    "source": [
298 |     "import matplotlib.pyplot as plt\n",
299 |     "plt.style.use(['science','grid','notebook'])"
300 |    ]
301 |   },
302 |   {
303 |    "cell_type": "code",
304 |    "execution_count": 52,
305 |    "id": "d5109e82",
306 |    "metadata": {},
307 |    "outputs": [
308 |     {
309 |      "data": {
310 |       "image/png": "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\n",
311 |       "text/plain": [
312 |        "<Figure size 576x432 with 1 Axes>"
313 |       ]
314 |      },
315 |      "metadata": {
316 |       "needs_background": "light"
317 |      },
318 |      "output_type": "display_data"
319 |     }
320 |    ],
321 |    "source": [
322 |     "# 其中的数值是任意取得\n",
323 |     "# 但是要保证xa<xb;ya<yb\n",
324 |     "xa=np.linspace(-3,3)\n",
325 |     "xb=np.linspace(2,5)\n",
326 |     "ya=np.linspace(-5,2)\n",
327 |     "yb=np.linspace(1,10)\n",
328 |     "res=[(leg_gau_2d(f,2,xa[i],xb[i],ya[i],yb[i]),int_sp(fs,xa[i],xb[i],ya[i],yb[i]))for i in range(len(xa))]\n",
329 |     "res=np.array(res)    \n",
330 |     "plt.plot(res[:,0],res[:,1],'-o')\n",
331 |     "plt.xlabel('leg_gau_2d')\n",
332 |     "plt.ylabel('int_sp')\n",
333 |     "plt.show()"
334 |    ]
335 |   },
336 |   {
337 |    "cell_type": "markdown",
338 |    "id": "e3e1151b",
339 |    "metadata": {},
340 |    "source": [
341 |     "可以看到，通过两种方式计算的结果基本上是一样的"
342 |    ]
343 |   }
344 |  ],
345 |  "metadata": {
346 |   "kernelspec": {
347 |    "display_name": "Python 3 (ipykernel)",
348 |    "language": "python",
349 |    "name": "python3"
350 |   },
351 |   "language_info": {
352 |    "codemirror_mode": {
353 |     "name": "ipython",
354 |     "version": 3
355 |    },
356 |    "file_extension": ".py",
357 |    "mimetype": "text/x-python",
358 |    "name": "python",
359 |    "nbconvert_exporter": "python",
360 |    "pygments_lexer": "ipython3",
361 |    "version": "3.9.7"
362 |   }
363 |  },
364 |  "nbformat": 4,
365 |  "nbformat_minor": 5
366 | }
367 | 


--------------------------------------------------------------------------------
/FEM-代码6-有限差分法.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "id": "2a719847",
  6 |    "metadata": {},
  7 |    "source": [
  8 |     "# 2022年7月30日21:57:46"
  9 |    ]
 10 |   },
 11 |   {
 12 |    "cell_type": "markdown",
 13 |    "id": "49ee6151",
 14 |    "metadata": {},
 15 |    "source": [
 16 |     "想象有这样一个二维空间场景：把一个高温的，比如为600℃，圆形铁饼放在一个正方形的空间内，该空间内的环境温度是固定的，比如为室温25℃，或者0℃。研究经过一个固定的时间，比如1小时，后铁饼的温度。"
 17 |    ]
 18 |   },
 19 |   {
 20 |    "cell_type": "markdown",
 21 |    "id": "5e44bdde",
 22 |    "metadata": {},
 23 |    "source": [
 24 |     "# 1. 物理模型"
 25 |    ]
 26 |   },
 27 |   {
 28 |    "cell_type": "markdown",
 29 |    "id": "12fa0db1",
 30 |    "metadata": {},
 31 |    "source": [
 32 |     "传热方程如下：\n",
 33 |     "$$\\frac{\\partial T}{\\partial t}=\\alpha (\\frac{\\partial^2 T}{\\partial x^2}+\\frac{\\partial^2 T}{\\partial y^2})$$"
 34 |    ]
 35 |   },
 36 |   {
 37 |    "cell_type": "markdown",
 38 |    "id": "19416e58",
 39 |    "metadata": {},
 40 |    "source": [
 41 |     "其中$\\alpha=\\frac{k}{\\rho c}$为热扩散系数，$k,\\rho,c$分别为材料的热导率($\\frac{W}{m\\cdot K}$)，密度($\\frac{kg}{m^3}$)，比热容($\\frac{J}{kg \\cdot K}$)"
 42 |    ]
 43 |   },
 44 |   {
 45 |    "cell_type": "markdown",
 46 |    "id": "89cb0768",
 47 |    "metadata": {},
 48 |    "source": [
 49 |     "不考虑对流和热辐射，且假定材料为铁，半径为0.2，温度为600℃；环境空间边长为1，温度为25℃"
 50 |    ]
 51 |   },
 52 |   {
 53 |    "attachments": {
 54 |     "image.png": {
 55 |      "image/png": "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"
 56 |     }
 57 |    },
 58 |    "cell_type": "markdown",
 59 |    "id": "446b897e",
 60 |    "metadata": {},
 61 |    "source": [
 62 |     "![image.png](attachment:image.png)"
 63 |    ]
 64 |   },
 65 |   {
 66 |    "cell_type": "markdown",
 67 |    "id": "bc569ef2",
 68 |    "metadata": {},
 69 |    "source": [
 70 |     "# 2. 离散化"
 71 |    ]
 72 |   },
 73 |   {
 74 |    "cell_type": "markdown",
 75 |    "id": "40fdd09f",
 76 |    "metadata": {},
 77 |    "source": [
 78 |     "对于时间的离散"
 79 |    ]
 80 |   },
 81 |   {
 82 |    "cell_type": "markdown",
 83 |    "id": "c1e9f419",
 84 |    "metadata": {},
 85 |    "source": [
 86 |     "$$\\frac{\\partial T}{\\partial t}=\\frac{T^{m+1}-T^{m}}{\\Delta t}$$"
 87 |    ]
 88 |   },
 89 |   {
 90 |    "cell_type": "markdown",
 91 |    "id": "f341e6a6",
 92 |    "metadata": {},
 93 |    "source": [
 94 |     "其中$T^m$表示当前时刻的温度，$T^{m+1}$表示下一个时刻的温度"
 95 |    ]
 96 |   },
 97 |   {
 98 |    "cell_type": "markdown",
 99 |    "id": "ff3b3d7c",
100 |    "metadata": {},
101 |    "source": [
102 |     "对于空间的离散"
103 |    ]
104 |   },
105 |   {
106 |    "attachments": {
107 |     "image.png": {
108 |      "image/png": "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"
109 |     }
110 |    },
111 |    "cell_type": "markdown",
112 |    "id": "5c889db8",
113 |    "metadata": {},
114 |    "source": [
115 |     "![image.png](attachment:image.png)"
116 |    ]
117 |   },
118 |   {
119 |    "cell_type": "markdown",
120 |    "id": "feb8ffcd",
121 |    "metadata": {},
122 |    "source": [
123 |     "根据公式$\\frac{\\partial T}{\\partial x}=\\frac{T_{i+1}-T_i}{\\Delta x}=\\frac{T_{i}-T_{i-1}}{\\Delta x}$可以推导出$\\frac{\\partial^2 T}{\\partial x^2}=\\frac{\\partial}{\\partial x}(\\frac{\\partial T}{\\partial x})=\\frac{T_{i+1}-2T_i+T_{i-1}}{\\Delta x^2}$"
124 |    ]
125 |   },
126 |   {
127 |    "cell_type": "markdown",
128 |    "id": "158aa491",
129 |    "metadata": {},
130 |    "source": [
131 |     "最后可得：\n",
132 |     "$$ \\frac{T_{i,j}^{(m+1)} - u_{i,j}^{(m)}}{\\Delta t}=\\alpha \\left( \\frac{T_{i+1,j}^{(m)} -2T_{i,j}^{(m)} + T_{i-1,j}^{(m)}}{\\Delta x^2} + \\frac{T_{i,j+1}^{(m)} -2T_{i,j}^{(m)} + T_{i,j-1}^{(m)}}{\\Delta y^2}\\right) $$"
133 |    ]
134 |   },
135 |   {
136 |    "cell_type": "markdown",
137 |    "id": "38aad3b2",
138 |    "metadata": {},
139 |    "source": [
140 |     "令$\\Delta x=\\Delta y$，移项可得：\n",
141 |     "$$T_{i,j}^{(m+1)} = u_{i,j}^{(m)} + \\alpha \\frac{\\Delta t}{\\Delta x^2} \\left( T_{i+1,j}^{(m)} + T_{i-1,j}^{(m)} +  T_{i,j+1}^{(m)} + T_{i,j-1}^{(m)}  -4T_{i,j}^{(m)} \\right)$$"
142 |    ]
143 |   },
144 |   {
145 |    "cell_type": "markdown",
146 |    "id": "28403193",
147 |    "metadata": {},
148 |    "source": [
149 |     "# 3. 编程"
150 |    ]
151 |   },
152 |   {
153 |    "cell_type": "code",
154 |    "execution_count": 1,
155 |    "id": "86a6666e",
156 |    "metadata": {},
157 |    "outputs": [],
158 |    "source": [
159 |     "import numpy as np\n",
160 |     "import matplotlib.pyplot as plt"
161 |    ]
162 |   },
163 |   {
164 |    "cell_type": "markdown",
165 |    "id": "230ed2ea",
166 |    "metadata": {},
167 |    "source": [
168 |     "## 1. 设定材料参数"
169 |    ]
170 |   },
171 |   {
172 |    "cell_type": "code",
173 |    "execution_count": 2,
174 |    "id": "dab4b126",
175 |    "metadata": {},
176 |    "outputs": [
177 |     {
178 |      "data": {
179 |       "text/plain": [
180 |        "2.200531361903662e-05"
181 |       ]
182 |      },
183 |      "execution_count": 2,
184 |      "metadata": {},
185 |      "output_type": "execute_result"
186 |     }
187 |    ],
188 |    "source": [
189 |     "k=76.2    # 热导率 W/(m*K)\n",
190 |     "rho=7870  # 密度 kg/(m**3)\n",
191 |     "c=440     # 比热容 J/(kg*K)\n",
192 |     "alpha=k/rho/c   # 热扩散系数 m**2/s\n",
193 |     "alpha"
194 |    ]
195 |   },
196 |   {
197 |    "cell_type": "markdown",
198 |    "id": "40536029",
199 |    "metadata": {},
200 |    "source": [
201 |     "## 2. 设定迭代参数"
202 |    ]
203 |   },
204 |   {
205 |    "cell_type": "code",
206 |    "execution_count": 3,
207 |    "id": "3aaa7bdb",
208 |    "metadata": {},
209 |    "outputs": [
210 |     {
211 |      "data": {
212 |       "text/plain": [
213 |        "(0.21567407878017789, 3600, 10.0)"
214 |       ]
215 |      },
216 |      "execution_count": 3,
217 |      "metadata": {},
218 |      "output_type": "execute_result"
219 |     }
220 |    ],
221 |    "source": [
222 |     "n=100\n",
223 |     "x,y=np.linspace(0,1,n),np.linspace(0,1,n)\n",
224 |     "\n",
225 |     "X,Y=np.meshgrid(x,y)\n",
226 |     "Z=((X-0.5)**2+(Y-0.5)**2<=0.04)\n",
227 |     "\n",
228 |     "T_am=25\n",
229 |     "T_Fe=600\n",
230 |     "T=np.ones((n,n))*T_am  # 环境温度\n",
231 |     "T[Z]=T_Fe             # 铁饼温度\n",
232 |     "\n",
233 |     "t=3600         # 也就是 1h\n",
234 |     "dt=1\n",
235 |     "times=int(t/dt)        # 循环次数\n",
236 |     "storage=360       # 要存储的时刻次数\n",
237 |     "f=times/storage   # 存储判断条件\n",
238 |     "\n",
239 |     "dx=x[1]-x[0]\n",
240 |     "s=(alpha*dt)/(dx**2)\n",
241 |     "s,times,f"
242 |    ]
243 |   },
244 |   {
245 |    "cell_type": "markdown",
246 |    "id": "42e4b2fe",
247 |    "metadata": {},
248 |    "source": [
249 |     "为了保证可解，对于二维情况，要保证$s<\\frac{1}{4}$"
250 |    ]
251 |   },
252 |   {
253 |    "cell_type": "markdown",
254 |    "id": "7919aa9b",
255 |    "metadata": {},
256 |    "source": [
257 |     "## 2.2设定存储变量"
258 |    ]
259 |   },
260 |   {
261 |    "cell_type": "code",
262 |    "execution_count": 4,
263 |    "id": "3f4a5679",
264 |    "metadata": {},
265 |    "outputs": [],
266 |    "source": [
267 |     "\n",
268 |     "TT=np.zeros((storage+1,n,n))\n",
269 |     "\n",
270 |     "TT[0]=T"
271 |    ]
272 |   },
273 |   {
274 |    "cell_type": "markdown",
275 |    "id": "2b7ff20f",
276 |    "metadata": {},
277 |    "source": [
278 |     "## 3. 检查参数"
279 |    ]
280 |   },
281 |   {
282 |    "cell_type": "markdown",
283 |    "id": "b4430f39",
284 |    "metadata": {},
285 |    "source": [
286 |     "## 3.1 空间"
287 |    ]
288 |   },
289 |   {
290 |    "cell_type": "code",
291 |    "execution_count": 5,
292 |    "id": "bf707c16",
293 |    "metadata": {},
294 |    "outputs": [
295 |     {
296 |      "data": {
297 |       "image/png": "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\n",
298 |       "text/plain": [
299 |        "<Figure size 360x288 with 2 Axes>"
300 |       ]
301 |      },
302 |      "metadata": {
303 |       "needs_background": "light"
304 |      },
305 |      "output_type": "display_data"
306 |     }
307 |    ],
308 |    "source": [
309 |     "plt.figure(figsize=(5,4))\n",
310 |     "plt.contourf(X,Y,Z)\n",
311 |     "plt.colorbar()\n",
312 |     "plt.axis('equal')\n",
313 |     "plt.show()"
314 |    ]
315 |   },
316 |   {
317 |    "cell_type": "markdown",
318 |    "id": "393ae4b3",
319 |    "metadata": {},
320 |    "source": [
321 |     "## 3.2 初始温度分布"
322 |    ]
323 |   },
324 |   {
325 |    "cell_type": "code",
326 |    "execution_count": 6,
327 |    "id": "245b5145",
328 |    "metadata": {},
329 |    "outputs": [
330 |     {
331 |      "data": {
332 |       "image/png": "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\n",
333 |       "text/plain": [
334 |        "<Figure size 1080x288 with 6 Axes>"
335 |       ]
336 |      },
337 |      "metadata": {
338 |       "needs_background": "light"
339 |      },
340 |      "output_type": "display_data"
341 |     }
342 |    ],
343 |    "source": [
344 |     "fig,axes=plt.subplots(1,3,figsize=(15,4))\n",
345 |     "ax0=axes[0]\n",
346 |     "a0=ax0.contourf(X,Y,T)\n",
347 |     "ax0.axis('equal')\n",
348 |     "\n",
349 |     "ax1=axes[1]\n",
350 |     "a1=ax1.contourf(X,Y,TT[0])\n",
351 |     "ax1.axis('equal')\n",
352 |     "\n",
353 |     "ax2=axes[2]\n",
354 |     "a2=ax2.contourf(X,Y,TT[18]) # 随便挑的\n",
355 |     "ax2.axis('equal')\n",
356 |     "fig.colorbar(a0,ax=ax0)\n",
357 |     "fig.colorbar(a1,ax=ax1)\n",
358 |     "fig.colorbar(a2,ax=ax2)\n",
359 |     "plt.show()"
360 |    ]
361 |   },
362 |   {
363 |    "cell_type": "markdown",
364 |    "id": "1345956c",
365 |    "metadata": {},
366 |    "source": [
367 |     "## 4. 开始迭代 "
368 |    ]
369 |   },
370 |   {
371 |    "cell_type": "code",
372 |    "execution_count": 7,
373 |    "id": "e5ab60a8",
374 |    "metadata": {},
375 |    "outputs": [],
376 |    "source": [
377 |     "# 因为for循环较多，且使用numpy数组，所以可以使用numba加速\n",
378 |     "# 使用time函数展示一下numba加速的情况\n",
379 |     "import time"
380 |    ]
381 |   },
382 |   {
383 |    "cell_type": "code",
384 |    "execution_count": 8,
385 |    "id": "92da0a66",
386 |    "metadata": {},
387 |    "outputs": [],
388 |    "source": [
389 |     "# 不使用加速情况\n",
390 |     "def solve(HT,Z):\n",
391 |     "    cT=HT[0].copy()  # 当前时刻温度 current T\n",
392 |     "    cf=0\n",
393 |     "    for tt in range(1,times+1):\n",
394 |     "        # 下一个时刻温度 next T\n",
395 |     "        nT=cT.copy()    # 这里copy的主要是环境温度，材料温度会进行迭代\n",
396 |     "        for i in range(1,n-1):     # 因为当前节点要通过前后，左右的节点来获得\n",
397 |     "            for j in range(1,n-1): # 现在这种写法是因为x，y方向的设置是一样的\n",
398 |     "                if Z[i,j]:         # 因为环境温度不变，只考虑材料即可\n",
399 |     "                    nT[i,j]=cT[i,j]+s*(cT[i+1,j]+cT[i-1,j]+cT[i,j+1]+cT[i,j-1]-4*cT[i,j])\n",
400 |     "        \n",
401 |     "        cT=nT.copy()   # 更新 \n",
402 |     "        if tt%f==0:\n",
403 |     "            cf+=1\n",
404 |     "            HT[cf]=cT.copy()\n",
405 |     "    \n",
406 |     "    return HT"
407 |    ]
408 |   },
409 |   {
410 |    "cell_type": "code",
411 |    "execution_count": null,
412 |    "id": "aabef852",
413 |    "metadata": {},
414 |    "outputs": [],
415 |    "source": [
416 |     "# 计算所用时间\n",
417 |     "start=time.time()\n",
418 |     "res=solve(TT,Z)\n",
419 |     "t1=time.time()-start"
420 |    ]
421 |   },
422 |   {
423 |    "cell_type": "code",
424 |    "execution_count": null,
425 |    "id": "9be480a8",
426 |    "metadata": {},
427 |    "outputs": [],
428 |    "source": []
429 |   },
430 |   {
431 |    "cell_type": "code",
432 |    "execution_count": null,
433 |    "id": "b176d55a",
434 |    "metadata": {},
435 |    "outputs": [],
436 |    "source": [
437 |     "# 展示结果\n",
438 |     "my_cmap = plt.get_cmap('inferno_r')\n",
439 |     "t_check=40 # 计算时，每隔10秒保存一次，所以检查的实际世界是 t_check*10\n",
440 |     "pc=plt.contourf(X,Y,TT[t_check],100,cmap=my_cmap)\n",
441 |     "cb=plt.colorbar(pc)\n",
442 |     "cb.set_label('Temp [℃]',fontsize=15)\n",
443 |     "plt.title('{:.2f} min'.format(t_check*10/60),fontsize=20)\n",
444 |     "plt.xlabel('x [m]', fontsize=16)\n",
445 |     "plt.ylabel('y [m]', fontsize=16)\n",
446 |     "plt.show()\n",
447 |     "(np.max(TT[t_check]),np.min(TT[t_check]))"
448 |    ]
449 |   },
450 |   {
451 |    "cell_type": "code",
452 |    "execution_count": null,
453 |    "id": "b7b32745",
454 |    "metadata": {},
455 |    "outputs": [],
456 |    "source": [
457 |     "import numba\n",
458 |     "from numba import jit"
459 |    ]
460 |   },
461 |   {
462 |    "cell_type": "code",
463 |    "execution_count": null,
464 |    "id": "7689cde6",
465 |    "metadata": {},
466 |    "outputs": [],
467 |    "source": [
468 |     "# 第一个f8[:,:,:]---- 函数返回值的数据类型，float，3维数组\n",
469 |     "# 第二个f8[:,:,:]---  函数第一个形参的数据类型，在括号内\n",
470 |     "# 第三个bl[:,:]---    函数第二个形参的数据类型，Boolean，2维数组\n",
471 |     "@numba.jit(\"f8[:,:,:](f8[:,:,:], b1[:,:])\", nopython=True, nogil=True)\n",
472 |     "def solve2(HT,Z):\n",
473 |     "    cT=HT[0].copy()  # 当前时刻温度 current T\n",
474 |     "    cf=0\n",
475 |     "    for tt in range(1,times+1):\n",
476 |     "        # 下一个时刻温度 next T\n",
477 |     "        nT=cT.copy()    # 这里copy的主要是环境温度，材料温度会进行迭代\n",
478 |     "        for i in range(1,n-1):     # 因为当前节点要通过前后，左右的节点来获得\n",
479 |     "            for j in range(1,n-1): # 现在这种写法是因为x，y方向的设置是一样的\n",
480 |     "                if Z[i,j]:         # 因为环境温度不变，只考虑材料即可\n",
481 |     "                    nT[i,j]=cT[i,j]+s*(cT[i+1,j]+cT[i-1,j]+cT[i,j+1]+cT[i,j-1]-4*cT[i,j])\n",
482 |     "        \n",
483 |     "        cT=nT.copy()   # 更新 \n",
484 |     "        if tt%f==0:\n",
485 |     "            cf+=1\n",
486 |     "            HT[cf]=cT\n",
487 |     "    \n",
488 |     "    return HT    "
489 |    ]
490 |   },
491 |   {
492 |    "cell_type": "code",
493 |    "execution_count": null,
494 |    "id": "c7360afa",
495 |    "metadata": {},
496 |    "outputs": [],
497 |    "source": [
498 |     "# 加速后 计算所用时间\n",
499 |     "start=time.time()\n",
500 |     "TT=solve2(TT,Z)\n",
501 |     "t2=time.time()-start"
502 |    ]
503 |   },
504 |   {
505 |    "cell_type": "code",
506 |    "execution_count": null,
507 |    "id": "7789bfa3",
508 |    "metadata": {},
509 |    "outputs": [],
510 |    "source": [
511 |     "# 加速倍数\n",
512 |     "t1/t2"
513 |    ]
514 |   },
515 |   {
516 |    "cell_type": "code",
517 |    "execution_count": null,
518 |    "id": "147a16e3",
519 |    "metadata": {},
520 |    "outputs": [],
521 |    "source": [
522 |     "my_cmap = plt.get_cmap('inferno_r')\n",
523 |     "t_check=240\n",
524 |     "pc=plt.contourf(X,Y,TT[t_check],100,cmap=my_cmap) # colorbar固定时，要把t_check置为0\n",
525 |     "cb=plt.colorbar(pc,format='%.1f')\n",
526 |     "cb.set_label('Temp [℃]', fontsize=15)\n",
527 |     "# plt.contourf(X,Y,TT[t_check],100,cmap=my_cmap,vmin=T_am,vmax=T_Fe) # colorbar固定时使用\n",
528 |     "plt.title('After {:.2f} min'.format(t_check*10/60),fontsize=20)\n",
529 |     "plt.xlabel('x [m]', fontsize=16)\n",
530 |     "plt.ylabel('y [m]', fontsize=16)\n",
531 |     "plt.show()\n",
532 |     "(np.max(TT[t_check]),np.min(TT[t_check]))"
533 |    ]
534 |   },
535 |   {
536 |    "cell_type": "markdown",
537 |    "id": "bd4fec29",
538 |    "metadata": {},
539 |    "source": [
540 |     "# 4. 数据展示——动画"
541 |    ]
542 |   },
543 |   {
544 |    "cell_type": "code",
545 |    "execution_count": null,
546 |    "id": "8a792741",
547 |    "metadata": {},
548 |    "outputs": [],
549 |    "source": [
550 |     "from matplotlib import animation"
551 |    ]
552 |   },
553 |   {
554 |    "cell_type": "code",
555 |    "execution_count": null,
556 |    "id": "383b98ec",
557 |    "metadata": {
558 |     "scrolled": true
559 |    },
560 |    "outputs": [],
561 |    "source": [
562 |     "fig, ax = plt.subplots(figsize=(8,6))\n",
563 |     "a = ax.contourf(X,Y,TT[40], 100, cmap=my_cmap,\n",
564 |     "                    vmin=T_am, vmax = T_Fe)\n",
565 |     "cbar = fig.colorbar(a)\n",
566 |     "cbar.set_label('Temp [$^\\circ C$]', fontsize=15)\n",
567 |     "ax.set_title('Time = {:.2f} min'.format(40*f/60), fontsize=20)\n",
568 |     "ax.set_xlabel('$x$ [$m$]',fontsize=20)\n",
569 |     "ax.set_ylabel('$y$ [$m$]',fontsize=20)"
570 |    ]
571 |   },
572 |   {
573 |    "cell_type": "code",
574 |    "execution_count": null,
575 |    "id": "00776fb9",
576 |    "metadata": {},
577 |    "outputs": [],
578 |    "source": [
579 |     "# 这个运行时间较长，现有参数下约十几秒\n",
580 |     "# 可以先把frames设定的小一些，如果效果满意再按实际设置\n",
581 |     "my_cmap = plt.get_cmap('inferno_r')\n",
582 |     "def init():\n",
583 |     "    a = ax.contourf(X,Y,TT[0], 100, cmap=my_cmap,\n",
584 |     "                    vmin=T_am, vmax = T_Fe)\n",
585 |     "    cbar = fig.colorbar(a)\n",
586 |     "    cbar.set_label('Temp [$^\\circ C$]',fontsize=16)\n",
587 |     "\n",
588 |     "def animate(i):\n",
589 |     "    ax.clear()\n",
590 |     "    ax.contourf(X,Y,TT[i], 100, cmap=my_cmap,\n",
591 |     "                vmin=T_am, vmax = T_Fe)\n",
592 |     "    ax.set_title('Time = {:.2f} min'.format(f*i/60), fontsize=20)\n",
593 |     "    ax.tick_params(axis='both',labelsize=16)\n",
594 |     "    ax.set_xlabel('$x$ [$m$]',fontsize=20)\n",
595 |     "    ax.set_ylabel('$y$ [$m$]',fontsize=20)\n",
596 |     "    return fig,\n",
597 |     "\n",
598 |     "fig, ax = plt.subplots(figsize=(8,6),dpi=100)\n",
599 |     "ani = animation.FuncAnimation(fig, animate, init_func=init,\n",
600 |     "                               frames=range(1,storage+1), interval=100)\n",
601 |     "ani.save('cool.gif',writer='pillow',fps=30)"
602 |    ]
603 |   },
604 |   {
605 |    "cell_type": "code",
606 |    "execution_count": null,
607 |    "id": "cee11bca",
608 |    "metadata": {},
609 |    "outputs": [],
610 |    "source": []
611 |   },
612 |   {
613 |    "cell_type": "code",
614 |    "execution_count": null,
615 |    "id": "6a500074",
616 |    "metadata": {},
617 |    "outputs": [],
618 |    "source": []
619 |   }
620 |  ],
621 |  "metadata": {
622 |   "kernelspec": {
623 |    "display_name": "Python 3 (ipykernel)",
624 |    "language": "python",
625 |    "name": "python3"
626 |   },
627 |   "language_info": {
628 |    "codemirror_mode": {
629 |     "name": "ipython",
630 |     "version": 3
631 |    },
632 |    "file_extension": ".py",
633 |    "mimetype": "text/x-python",
634 |    "name": "python",
635 |    "nbconvert_exporter": "python",
636 |    "pygments_lexer": "ipython3",
637 |    "version": "3.9.7"
638 |   }
639 |  },
640 |  "nbformat": 4,
641 |  "nbformat_minor": 5
642 | }
643 | 


--------------------------------------------------------------------------------