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February 18, 2022 01:55
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Trouble-shooting Curvature Phase Field Model
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "id": "2b859146-29e9-4221-ad4d-d1727057a268", | |
| "metadata": {}, | |
| "source": [ | |
| "## Imports" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "id": "e8190553-03f7-47f5-abe7-076f31542a7a", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import os\n", | |
| "os.environ['FIPY_SOLVERS'] = 'scipy'" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "id": "7f185c1a-6fac-472b-a07d-29f18840059d", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import matplotlib.pyplot as plt\n", | |
| "import fipy as fp" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "c8db6911-d1af-496e-bd06-387ee98a36ed", | |
| "metadata": {}, | |
| "source": [ | |
| "## Domain" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "66474df5-14a4-44d5-8fbf-43feff332b4c", | |
| "metadata": {}, | |
| "source": [ | |
| "create a 2D solution mesh" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 154, | |
| "id": "579f7110-268b-482c-b3ee-df30e2a27de7", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "nx = ny = 50\n", | |
| "dx = dy = 0.001\n", | |
| "mesh = fp.Grid2D(nx=nx, ny=ny, dx=dx, dy=dy)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "e8e16a2b-59e9-4f8f-bd54-541d7c6b5a9c", | |
| "metadata": {}, | |
| "source": [ | |
| "## Variables" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 310, | |
| "id": "0c254a1e-7258-43f7-96cb-d48bf6eb8d2b", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "phi = fp.CellVariable(name=r\"$\\phi$\", mesh=mesh, hasOld=True)\n", | |
| "psi = fp.CellVariable(name=r\"$\\psi$\", mesh=mesh)\n", | |
| "sigma = fp.CellVariable(name=r\"$\\sigma$\", mesh=mesh, hasOld=True)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "d351fcf5-117c-421d-a13f-d214963ade02", | |
| "metadata": {}, | |
| "source": [ | |
| "## Initial condition\n", | |
| "\n", | |
| "initiate phi as a circle of 1. in a field of -1." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 311, | |
| "id": "6995b77f-51ca-4de8-90f8-4096c4b7db7c", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "Lx = nx * dx\n", | |
| "Ly = ny * dy\n", | |
| "r0 = fp.numerix.sqrt(Lx**2 + Ly**2)/4 #radius\n", | |
| "x0 = Lx/2 #position of center of circle\n", | |
| "y0 = Ly/2\n", | |
| "phi.setValue(-1)\n", | |
| "phi.setValue(1., where=(mesh.x - x0)**2 + (mesh.y - y0)**2 < r0**2)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "raw", | |
| "id": "411c3415-4759-423f-a614-6b30feecd15e", | |
| "metadata": {}, | |
| "source": [ | |
| "psi.value = 0.\n", | |
| "xi.value = 0.\n", | |
| "sigma.value = sigma0" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "4cd848fd-31e8-4cbb-9e4b-de02e6133f14", | |
| "metadata": {}, | |
| "source": [ | |
| "## Parameters" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 312, | |
| "id": "5c80ced4-d511-459d-9ece-53fa8c5bd49a", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "kappa = 0.01\n", | |
| "epsilon = dx # 0.2\n", | |
| "a0 = 10" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "232220ab-5370-437a-8c19-7ff72279317d", | |
| "metadata": {}, | |
| "source": [ | |
| "## Equations" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "48295e94-1ac9-4b72-8f3e-0491a2d93b61", | |
| "metadata": {}, | |
| "source": [ | |
| "$$\\begin{align*}\n", | |
| "\\frac{\\partial \\phi}{\\partial t}\n", | |
| "&= 2\\kappa\\nabla^2\\left[\n", | |
| " \\left(\n", | |
| " 3\\phi^2 - 1\n", | |
| " \\right)\\psi\n", | |
| " - \\epsilon^2\\nabla^2\\psi\n", | |
| " + \\epsilon^2\\nabla\\cdot\\left(\\sigma\\nabla\\phi\\right)\n", | |
| "\\right]\n", | |
| "\\\\\n", | |
| "&= 2\\kappa\\nabla^2\\xi\n", | |
| "\\end{align*}$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 313, | |
| "id": "002f3968-9151-4da0-8617-ffc07302c21a", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "xi = fp.CellVariable(name=r\"$\\xi$\", mesh=mesh)\n", | |
| "eq1 = (fp.TransientTerm(var=phi) == fp.DiffusionTerm(coeff=2 * kappa, var=xi))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "8f3dedcd-0ebb-4d18-bed7-cbc0f28cde3b", | |
| "metadata": {}, | |
| "source": [ | |
| "$$\\begin{align*}\n", | |
| "\\psi = \\phi^3 - \\phi - \\epsilon^2\\nabla^2\\phi\n", | |
| "\\end{align*}$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 314, | |
| "id": "17246fc5-d3f3-4ac4-9eb4-431753b888be", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "eq2 = (fp.ImplicitSourceTerm(coeff=1., var=psi)\n", | |
| " == fp.ImplicitSourceTerm(coeff=(phi**2 - 1), var=phi)\n", | |
| " - fp.DiffusionTerm(coeff=epsilon**2, var=phi))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "c497ae31-1ba1-43a1-8c25-c35902bbcf75", | |
| "metadata": {}, | |
| "source": [ | |
| "$$\\begin{align*}\n", | |
| "\\frac{\\partial\\sigma}{\\partial t}\n", | |
| "&= \\frac{1}{2}\\lvert\\nabla\\phi\\rvert^2 - a_0\n", | |
| "\\\\\n", | |
| "&= \\frac{1}{2}\\nabla\\phi\\cdot\\nabla\\phi - a_0\n", | |
| "\\\\\n", | |
| "&= \\frac{1}{2}\\nabla\\cdot\\left(\\phi\\nabla\\phi\\right)\n", | |
| "- \\frac{\\phi}{2}\\nabla^2\\phi\n", | |
| "- a_0\n", | |
| "\\end{align*}$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 315, | |
| "id": "db4d7039-2cf7-4dab-8245-1a47c460026f", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "eq3 = (fp.TransientTerm(var=sigma)\n", | |
| " == fp.DiffusionTerm(coeff=phi / 2, var=phi) \n", | |
| " - fp.ImplicitSourceTerm(coeff=phi.faceGrad.divergence / 2, var=phi)\n", | |
| " - a0)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "e26a048e-8f86-4b62-9477-5fd4d512b834", | |
| "metadata": {}, | |
| "source": [ | |
| "$$\\begin{align*}\n", | |
| "\\xi\n", | |
| "&= \\left(\n", | |
| " 3\\phi^2 - 1\n", | |
| "\\right)\\psi\n", | |
| "- \\epsilon^2\\nabla^2\\psi\n", | |
| "+ \\epsilon^2\\nabla\\cdot\\left(\\sigma\\nabla\\phi\\right)\n", | |
| "\\end{align*}$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 316, | |
| "id": "6908c6cb-44b0-4b25-a4f1-a2b7ba7bb107", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "eq4 = (fp.ImplicitSourceTerm(coeff=1., var=xi)\n", | |
| " == fp.ImplicitSourceTerm(coeff=3 * phi * psi, var=phi)\n", | |
| " - fp.ImplicitSourceTerm(coeff=1, var=psi)\n", | |
| " - fp.DiffusionTerm(coeff=epsilon**2, var=psi)\n", | |
| " + fp.PowerLawConvectionTerm(coeff=epsilon**2 / 1e3 * phi.faceGrad, var=sigma))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "89b8f05e-6af4-4c1a-a395-17a2a0cd5ab4", | |
| "metadata": {}, | |
| "source": [ | |
| "### To de-couple $\\sigma$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "c9e317bb-987a-4f06-babf-ee8360a77b0f", | |
| "metadata": {}, | |
| "source": [ | |
| "$$\\begin{align*}\n", | |
| "\\xi\n", | |
| "&= \\left(\n", | |
| " 3\\phi^2 - 1\n", | |
| "\\right)\\psi\n", | |
| "- \\epsilon^2\\nabla^2\\psi\n", | |
| "\\end{align*}$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "raw", | |
| "id": "9c9fb157-e002-4b8c-88af-dbfa32370905", | |
| "metadata": {}, | |
| "source": [ | |
| "eq4 = (fp.ImplicitSourceTerm(coeff=1., var=xi)\n", | |
| " == fp.ImplicitSourceTerm(coeff=3 * phi * psi, var=phi)\n", | |
| " - fp.ImplicitSourceTerm(coeff=1, var=psi)\n", | |
| " - fp.DiffusionTerm(coeff=epsilon**2, var=psi))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 317, | |
| "id": "af5883cf-7c95-4488-9bdc-58a934dba615", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "eq = eq1 & eq2 & eq3 & eq4" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "e30daf7c-5fff-4896-b276-804426c0847e", | |
| "metadata": {}, | |
| "source": [ | |
| "## Viewers" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 318, | |
| "id": "93abcf21-fb34-49d0-a35f-15a6432359c8", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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zMJ/5p7cxcQAzajZbkmuAiQPgM//8NoLNaZtjkjEeY9dph9FviraAicir+WdtXVOUX9bUY9fp0j5rz8I8NIWN8RhO2Iwc/yjaAqZMGnnp5d0v2n6mKF8ftWdhHppiRFo8xrCpugZBRI4TkTtFZL2InJ1yX0TkE+H920TkiMbFz0Cyauvx+8nzZOvBZZwlL/+4jqJ00haS+qg9jyoequOforhdYi0ew4kqtTURGQc+DRxL8Irem0Rkpar+KBbseGB+eBwJnBt+1iJ8Y+O4qm6pm5aPuIyPZJ27jo245O+6/sV1zMU1blfa8yjroTr+cYxbRsulwBrgNmC1qv6qSjoR1uIxnNBwDUL8cOB5wHpVvVtVHwMuAxYnwiwGLtaAG4E5IjKvjlYRORPYCKwXkXXhWxwNo1MqeKiOf1zilmE5wRtO/wK4WkSuiF6tXQUreAwnJsM1CPEDmCsiq2PHkkS0g4BfxM43hNfKhnFCRM4RkdOAM4FnqupBwAuABSLyvippGvWoOhDfB5rWXsFDdfzTmK9CngR8F1iqqocDXwH+sWpi/j4VRqtkdBM8oKoLc6KlLazSCmFc+S7wHGAu8J8i8jBB18DtwFIR+Yiq/rZi2t6Rto9Y0eJJ1/TS0knLz2XbmbT7PmvPooKH6vinSV8BPB14FUEl7ncEvvpTEfkGcFvZrjcreAwnojUIJdkAHBI7Pxi4t0IYJ1T1CuAKETkKeAtBd9uzgT8G9gGuE5E9VHU4W3j3jLxxjiozs4rGUvLSdJ3FlhfeF+1ZVPBQHf/s4hC3DJ+IChcReQKwkGB86W+ADwHPLZOYFTyGE4pUWXdwEzBfRA4DfgmcDPx1IsxKYJmIXEYwOPqQqm6sKfeNwJcIBkNvB54J3K6qLwwnHRhG61TwUGX/iMivHOKW4aqwwFkH3Ak8A7hUVc+skpgVPIYTVVo8qrotHNj/NjAOXKCqa0VkaXh/ObAKWASsJxi8PKOuVlW9S0SOJJjRczhBt8A7wnuP1U3fd+rsgZa1n1qdfdaGFbYobtvay3qojn+y4jpnvqOW54Qz5Z4B/AHBevVvVU1vRAqeDbzuPZ/k3DPfxPfnBH+RmcgxwMJH4DWzPwPvvr/RtCcrbnCoqqsIzBG/tjz2XQlaKI0SFjDfCA8jRtUf7rS4yfPoh7jqQs8mwxbFbVt7FQ/V8U9a3Dqo6nZgbXjUwmlWW9VFTCJyiIh8J5zSujac5joE1vM5eYBd5kzy/NorQPzl+UfDrD0e4yK5n6AC1Bz29sTq9N8/9am7qr9L2tJuHpqisMVTcxHgNuBtqnpLOOf7ZhG5uuoiJqM7Kk4umPF07Z8mu6baxmftaZiHpnBp8VRexKSqG1X1FgBV/R3BwFSdueRGR2SsQTCK6cw/advHlF2b4rqZZxWytqSJp+uj9izMQ1O4/OXSFiIlO7SyFisNZieJyKEEayxm8IsL/MU2OKxMZ/5JGzhvevyiyTGX5D1ftWdhHprCpcVTexGgiOwBXA6cpaoPp2YisiRavRtMzqjCNtg7WLAx09hn8J/Hh5J+MBV0l2mH4UTr/vn9r6b8k5ytldeCcH11gGt6aWmWecWAz9rTMA9N4VLw1FoEKCI7E5jmC6r61axMVHWFqi4MVvFWrRX8G7JI+Yb+Oy+smIKPHAN8Tb+O/KkCmX/iWtjbEyvTun9m7zf1bxP/cUzO2MpatZ+3OaZLesk4yc94S6ZoRwBftadhHprCpeAZLGIKF9+dTLBoKc5K4LRwds5RTC1iEuBzwDpV/WijylNZD2dNcNVzF/Pk4WfWG+YD//GcE+HtEzQ9my1iUsfY/NisaYfhRKf+abrLqYkB+7K7RDeRVtmww0jDPDRFYVux5iLAo4FTgdtFZE147V3h/HLDIya3j7HlkZlbQ6tKX/yTN8urjzPA4visPY55aAqnTsqqi5hU9QbS+68Nz1Ad47FHZ+66gzr0wT9l9iKLr+gvipsWr+iay708fXn3+qY9jnloihHZucAYOtsFHjHTzASqjmHkjZO4hq9Lr7WbhwaM5vt47oHDlsPEM2DnrrUMkZ0J/h8POA+4Z8iZTQKPJA7DCLH37jhgHhowmgXPAx9Flq5FLtGRnmTwNEAuVOT1a+G3Q567MQk8mjiM3tP0j6rrVOIqU46zpkg3RZvaUzEPDRjNgoeHgS/B2fDqa2FiUdd6mmfipfBX1wFnQ/AGgNTlHc1htTUvSa6FiX8mcVkn45pPlS6vvE08fdOeinlogL/tYxeu+Rfkmss4UJ/LWfJUtnStpyFmAftesYEHd7oB+Jd2Mo1MY3iLy1qXtO9pcfs2dtNn7QPMQwNGtMUTsQVYx31veAqv192YeE3Xeuoz8Tp4ve7Gg0sPIti6q6XidDtWW5uh5K3qbyLNqjsBlM0n71rVNEtpNw8NGPGCJ2T5BPvKBH/1fy/sWkltXnne59lXJuD8iXYzbrh/WkT2EZGrReSu8PMJGeHuEZHbRWRNsJ2S0TZpXV5pU4+rpjnM1xL0Snt3Hkp9LYeITIjIL0NvrRGR1gYlZkbBA8AWtjPetYjaBO/w6KDTsPn+6bOBa1V1PnBteJ7Fi1T18GA7JaMOVWr7ya1m0u6VWS9TFZ+1A514KPZajuOBBcApIrIgFuRjobcOb3Nh/wwqeIxaNG+axcBF4feLgJNqp2gMyBpsd6ntRxtopv0wl92Msyj/UdOeSzcecnktR+uM9uSCBJe/9NVs1WAB165s5StnnMrEhd1qKmLidUH3WvS2wiuPfxUNvHm2PNuB3+1wdW6i+2uFqq5wTPEAVd0IEO5Ltn9GOAWuEhEFPlsi/RmN6+sEqi6czOpiKptenGhGma/aHQJ14aGi13IsE5HTgNUELx38jWPetZhRBQ9XTnDlYAOSWTy8bWdmXfh4b2e7zQIePG83LpdfMtW91kGhA8HP/9Ydrj6Q1/0lItcAB6bceneJnI9W1XtDU10tIj9W1etLxJ+RxKcFx7eRKdoNOm0X56y04hT9QCfzTmpKy8NH7bl046G8V26cC7wvPH8f8BHgbx3TrcXMKnimsYW9lz7G3o/ex29fMY+Jnm1bOvFSmPPljZx9xoHARNdypmbklEBVj8m6JyL3R2/ZFJF5wKaMNO4NPzeJyBUEXQdW8BRQZQDcpSXQ1JY0ea0Pn7Xn0o2HNpDxyg1VvT+W1nnAleXUVWdmj/GcP8FDu30X3gbPpB/b6+wMPAvgbQTaLpzoVlDEJEE3Qfyox0rg9PD76cDXkgFEZLaI7Bl9B/4MuKN2zjOE5MvOiq7XSTMtnMt51niOz9oz6cBD5LyWIyysIl5Oi96a2QUPAPcg71NOvlF59/yutcC7nwGvvEGRf1CGvwFbCSYJugniRz0+BBwrIncBx4bniMgTRSRqfx4A3CAiPwR+AHxDVb9VO+cZQnK8pOh6nTTTwkWkdUW5tHR81Z5JBx5S1W3AMoLXcqwDvqSqUX/9v4ZLFW4DXgS8pbYiR2ZwV1vEFrhuAo46HT4Fb1g2/e5dwDVDyvkYgpe4TeMs4Pk/ItgGp0c0vOpaVX8NvCTl+r0E76ZBVe8Gnt1crjOPsuMZ8Thlxj6yvkfpFI2TjJr2VDrwUHi+w2s5wuunNqemHFbwDPh60Mo4fPrVE2/9Mi+Sv2x8J7S9gPfq14M3h8Y5G6CFl7WWJX1GjtFz0n4Yi34wXX9M4z++RbX/vFZDlh6ftadiHhpgBc+AB+G3E7Bm+tUrPzvB1xcBD02/fsP33FtCxwDPPzpxcW9420dOhDUTFbR2wCTw+65FGK4ka/5Fs8fKpJsXP6s1kDUTLCsNX7XnYh4aYAVPEUsvQXiI6X+qnZn89S5cs69bEgsfAdnjMeDx2NVtsOqS5nQOm2i7D8MLkj+weeMSWT+gZVoXefnEz9M+07q3fNWei3logBU8hawnretr6T7n8Nl/OcsphVNnrwA+0Kiq1olm5BhekfejmNbVlIybVSiUyaeqRp+1p2IeGmAFT0VWyL6s2HG8Lp2/v784TN/ZjnUTjBhlZ3j1CS+1m4cGWMFTmfXhMUNQOtmb1CiPhovVy45BxMdW0sYzonvx8EVTj/PSjYh3myXD+aY9F/PQACt4DGPEkHBHlLI1/rxpxGljKlljIXGyurvSCgiXbjEftBvFWMFjODKJVddmFmk/plULhLwWzDB+tPup3TwUYQWP4ch2aHw1kzFTaKIg6IrmtJuHImzLHMORqIM6fhh9p+q+Zq7pZqVfJd+iPdKaog3t6ZiHIqzgMRyJamvxw+greZtsupxnfUakLejM01L0PUrTd+35mIcirKvNcMT2+/AJ1zGJrIH4rM+stPIG612+j4r2fMxDEdbiMRyx2ppvZNX481oaWWnkpZd2P/m9qBUyStqzMQ9FWIvHcMQWIfhGmanDRWnkpZd3PyvvIg0+a8/GPBTh1OIRkeNE5E4RWS8iZ6fcFxH5RHj/NhE5wjWu4QvN1tZE5FUislZEJkUk79W/3j8/Xfgnq7Yev588T7YeXMZZ8vKP6yhKJ9k68VV7UcoNe2gfEblaRO4KP5+QEe4CEdkkIndUiT8MCgseERkHPg0cDywAThGRBYlgxxO8WmY+sITgXd6ucQ0viPqnG3t94h3AK8h5jfUoPD9d+Sda1OjacnBtHbjW9uNpuKSTzN9X7fk07qGzgWtVdT5wbXiexoXAcTXiN45Li+d5wHpVvVtVHwMuAxYnwiwGLtaAG4E54WtVXeIaXtBsbU1V16nqnQXBRuH5Mf8YIY2P8SwGLgq/XwSclBZIVa8HHqwafxi4tBEPAn4RO98AHOkQ5iDHuACIyBKC2h7AVvjH1t7/7chc4IGuRaTQlK4n59++99vwD3MTF3cTkdWx8xWquqIBLRHOz0+P6cQ/75cP9s0/0E8PNampbQ8doKobAVR1o4js76y0mfiVcSl4JOWaOoZxiRtcDP7YKwBEZLWqZvb7d0EfNUF7ulQ1ramei4hcAxyYcuvdqvo1lyTSpJTV0THmn5A+6mpTU9Meqq+oO1wKng3AIbHzg4F7HcPs4hDXGFFU9ZiaSbg8e33H/GNUJs9DInK/iMwLWyvzgE0lk68bvzIuYzw3AfNF5DAR2QU4GViZCLMSOC2cnXMU8FDYhHOJaxhZjMLzY/4xhsVK4PTw++mASy9Ck/Gro6qFB7AI+AnwU4JuEoClwNLwuxDMvvkpcDuwMC+uQ35LXMK1efRRU591Oeh+OUFNfytwP/Dt8PoTgVWxcKWfn74d5p/+6uqjphLa9yWYjXZX+LlPeD3poUuBjcDjoedemxe/jUNCAYZhGIbRCrZljmEYhtEqVvAYhmEYrdJqwdPXrXeq6hKRQ0TkOyKyLtz+5cyuNcXuj4vIrSJyZVOajO7po4f66J86umL3zUPDosWBsHGCAdKnEEwT/SGwIBFmEfBNgsHWo4Dvu8btSNc84Ijw+54Eg8C1ddXRFLv/VuCLwJVt/RvbMdyjjx7qo3/q6ordNw8N6WizxdPXrUMq61LVjap6C4Cq/g5YR7DavDNNACJyMHACcH4DWoz+0EcP9dE/tXSBeWjYtFnwZG0L4hLGJW4XugaIyKHAc4Dv90DTOcA7gMkGtBj9oY8e6qN/mtB1DuahodFmwdPK1iEVqKMruCmyB3A5cJaqNvF2p8qaROREYJOq3tyADqNf9NFDffRPLV3moeHTZsFTZ+uQYW6dUkcXIrIzgWm+oKpf7YGmo4GXicg9BN0LLxaRSxrSZXRLHz3UR//U1WUeGjZtDSYR7At3N3AYU4N9f5gIcwLTB/t+4Bq3I10CXAyc05e/VSLMC7GB0ZE5+uihPvqnrq5EGPPQEI7WXn2tqttEZBnwbYIZJxeo6loRWRreXw6sIphpsh7YDJyRF7drXQQ1o1OB20VkTXjtXaq6qkNNxojSRw/10T8N6DKGjG2ZYxiGYbSK7VxgGIZhtIoVPIZhGEarWMFjGIZhtIoVPIZhGEarWMFjGIZhtIoVPIZhGEarWMFjGIZhtIoVPIZhGEarWMFjGIZhtIoVPIZhGEarWMFjGIZhtIoVPIZhGEarWMFjGIZhtIoVPIZhGEarWMFjGEbniMi4iNwvIpMiouFxcde6jOHQ2ovgDMMwchgHvgdsBM4D1qnq1m4lGcPCWjwNICI7i8gHROQeEXk8VmP7YdfaDMMT/gZAVd+oqmus0BltrOBphvcDLwH+JzAHuBa4Anh5h5oMwydmAYeKyOEisnPXYozhYgVPTURkT+DNwKmq+gtV/T1wObCPqt7drTrD8IZLgC3ArcBjIrKoYz3GELGCpz4vAO5W1bti154A3NeRHsPwChHZF7iBoKfgD4BdVHVVt6qMYWKTC+qzH/Cb6EREhKCL7eOdKTIMv/g7YI2qvqdrIUY7WIunPncAR4R907OADwIK/Fu3sgzDG+YATxORJ3UtxGgHK3hqoqqrgQ8Aq4C7gQOBRar6eKfCDMMfPgz8ArhFRDaLyDdEZLxrUcbwEFXtWoNhGAYAIrIrsAE4VlXXdCzHGBLW4jEMo088G9gZuKdjHcYQsYLHGCoicpyI3Cki60Xk7JT7zxCR/xKRrSLy9jJxjZFkBfBGVf1t10L6wKj6x7rajKER9tP/BDiWoPvkJuAUVf1RLMz+wJOBk4DfqOqHXeMaxigzyv6xFo8xTJ4HrFfVu1X1MeAyYHE8gKpuUtWbgORkjMK4hjHijKx/ermOZ/e5u+ucQ/fuWgYAiiD42Soso/239zzE5gc2S9b9p4vo7xPX7oW1wKOxSytUdUXs/CCC2UoRG4AjnQTVizujMf80Q1ntG2++7wFV3S/rfgUPjax/elnwzDl0b167+gy2h/LG2Ta4t52dGGfb4LMM8fTS0knLL5lvXtpJnT5pv3Dhebn5PwokO4nfDI+q6sKcaGkFmauT68Sd0Zh/utH+fvngz/M0VPDQyPqnlwVPRNo/dnSt7IOXjJOWTl6aRfkl7/usPY0xgl0cS7IBOCR2fjBwbwtxDfx+Bn3WnkUFD42sf2yMx3BiHNgzcThwEzBfRA4TkV2Ak4GVjlnWiWsYvaOCh0bWP71u8WRRpamdFTer+V4mj2GFLYrbpvYxYK+SelV1m4gsA75N4LsLVHWtiCwN7y8XkQOB1WHykyJyFrBAVR9Oi1tSgpGCr89g2bBFcdvWXtZDo+wfLwueqg9eWtzkefQglcljWGGL4rapfZzyBQ9AuMvwqsS15bHv9xF0AzjFNerj6zNYNmxR3Pa1V6q8jaR/vCx4hkGd/uOuaUN7xTEeY4Zg/inGPDRF7wueJpvWbeOz9iRR/7ThFz4/gz5rT8M8NEWvJxdEUxy3x8rH7SXLyqLwZdNLxs2K77P2NKL+6fhh9Bufn0GftWdhHpqi1y2etIG/pvtfm+wzTt7zVXsaYwKzdk1cfDQ1qNETfH4GfdaehXloil63eGDHBWR5NaC0WlLafdf00tLM+hw17UnGx2Cv2dMPo//4/Az6rD0N89AUvS944v+4yRkn0ffkquOs2khUiypKLxkn+RmvieXVfHzWnpIYzE4cRu/x+Rn0WXuGCPNQSK+72qD5JnMTA47uU5D91b4DY8xoo/iKz8+gz9pTMQ8N6H2LJyKvWVtnkLANfNY+QIBdE4fhDT4/gz5rn4Z5aIA3BU/RQGSceB9smQczr5/XNbyLvrx7fdM+IKqtWTeBl/j8DPqsfRrmoQEeVRfcqdoHm9fP6xq+Lr3VPg7sUS6K4Se9fQZLaOildvPQAKcWj8PrV0VEPhHev01EjkjcHxeRW0XkyqaEN41XTfYErWi32lplzD/9pjXt5qEBhQVP+ArVTwPHAwuAU0RkQSLY8cD88FgCnJu4fyawrorAph8K16mQVaZMZk3xbIphatfU13fEGMP6pytg/pkZ/nEKax4a4NLicXmF6mLgYg24EZgjIvMARORg4ATg/CoCk3P5459JXOb5u+ZTpcmeDOuT9sI3LVptrSrmnwpa09LM09E37amYhwa4FDxpr1A9qESYc4B3AJN5mYjIEhFZLSKrf/+rzalhXObqp31Pi9u3vuc+awfMNNUx/zSAz9oHmIcGuBQ8Lq9QTQ0jIicCm1T15qJMVHWFqi5U1YWz99vdQZY7ZWeslE2z6krmsvnkXauaZvTdqattt8ThQJ3xDRG5R0RuF5E1IrLaLcfeYf4pSHMU/OPc1VbSQ6PqH5d/gQ0Uv0I1K8wrgZeJyCKCP/NeInKJqr66uuTypDWl06ZhVm1aV17JXDKfYWp37morQWx841iCZ+QmEVmpqj+KBYuPbxxJML5xZOz+i1T1gXI59wrzT0Gao+CfUl1tjoyyf1xaPC6vUF0JnBaWvkcBD6nqRlV9p6oerKqHhvH+o65pqtRWkltlpN1zffDq1JZ81l6xm6DW+MaIYP6pmX+duH3RDlTx0Mj6p7DgUdVtwDKCV6iuA74UvX41egUrwVvu7gbWA+cB/6uusKzBwqyHJ3ktvoCs6iClS/6jpj2TdNPMjcYVwmNJIlbd8Q0FrhKRm1PS9gLzj/lnQHkPjax/nIpwh9evKvDGgjSuA65zFZY3WJgVrkz4rCZy2fTipDXlfdHuPJ16Og+o6sKcWJXHN8LPo1X1XhHZH7haRH6sqtfnC+0f5p/R90+p6dTTyfPQyPqnt1vmVBnAi4eL13qy0kqGc9WTpineT+yjdqcxnj0SRzF1xjdQ1ehzE3AFQdeD4YCPz6DP/nEe4ynnoZH1T28LnioDePFw8ZpTVlrJcK560jRl1dJ8055JtTGeyuMbIjJbRPYEEJHZwJ8Bdzjlanj9DPqsPZfyHhpZ/zQ/f7FBsgb/yg4KVombrMVknSdraslamy/aC7vaoneJlEBVt4lINL4xDlwQjW+E95cTdEEtIhjf2AycEUY/ALhCRCB4Tr+oqt8qp2Bm49sz6LN/nLraSnpolP3T64In6wGp8tCVjZv34MXvF9XUquZfJ24V7YVdbdGW7iWpOr6hqncDzy6foxHh2zPos3+c0q7goVH1T2+72iLK9sfG47iEK/oODGo3aXHz8vFZ+w7Yqmsv8fkZ9Fl7KuahAb1u8UB6TaJoMK9MzSZKq6j2klfrydLjs/YdsLcneonPz6DP2lMxDw3obYsnWXMpmv1SJt3496w+ZJeZLHlp+Ko9k4pb5hjd4PMz6LP2XMxDA3pb8EQ1keSAYFrtJOshLHo4k325WfmkXU/WekZFexY6BttmTz+M/uLzM+iz9jzMQ1N42dUWkdZUTsZN1kraHLT0WXuSyXFh8+ydE1cfq5yv0Q4+P4M+a0/DPDRF7wuePFz+0es8VMPEN+2TjLF5fFbi6sw0zajg2zMYx0ft5qEpetnVFq0pKduPG+8bTvvM6rvNOi9KN60vuuqMl661F63jUYTH2HXaYfQT80832oswD03RyxZPtKakbI0l2ayON7XjfcJFfblxsprr8fTTmv2+aS9axzPJGJtJ1taMPmL+6VZ7FuahKXpZ8DRF2sNQ9YHOm8EyjCZ937RPMsYWmn3BmNFv+vYMVsm3Tj5NazcPTTHSBU+TNPEgd0UT2oPampnGqMZM9w+Yh+L0cownTpX5+mXSrTod0yWOT9rdxnh2mXYY/cenZ9Bn/7iP8ZiHoMcFT9qAYHTd5TzrMyLZD5z34GQNIqal6at2tzGe3acdRn/x8Rn02T/uYzzmIehxV5trn2rWQGLWZ1ZaeYONLt9HRXsW1k3gFz4/gz5rz8M8NEVvWzyQXWPJqyllpZGXXtr9rKmTRWmMgvY0rJvAP3x+Bn3WnoV5aIretnggu8ZSpraRNR3SNb+svIs0+Kw9Daut+YfPz6DP2rMwD03R2xZPVm0jfj95nqz9uPQT5+Uf11GUTrJ25av2LKI1CPHDBRE5TkTuFJH1InJ2yn0RkU+E928TkSNc4xrZ+PwM+qw9jyoeGlX/9LbgGSf7FbZF5659u0X5x3UUpZPM31ftWURrEOJHESIyDnwaOB5YAJwiIgsSwY4H5ofHEuDcEnGdEZH3Vo3rIz4/gz5rz6Osh/rkn6bpdVeb0R8mGWNr+S0+ngesD9+GiIhcBiwGfhQLsxi4OHyT4o0iMkdE5gGHOsQtw3tFZHdgH+AW4DJV/U3FtAyjNBU81Bv/iMhbVPVjVeKm0dsWT1+oOpDYB5rUrghbmDXtAOaKyOrYsSQR7SDgF7HzDeE1lzAuccv9L8CjBO+vPwT4TxHp7auBRwXzzxQVPNQn/yyLvojIyfEbInKAiBwvIsmttzPp9VMR/cPHm7JRf268X7dKemnppOUXv5eXX/K+b9qLyBgYfUBVF+ZES1uVmlwwlBXGJW4ZfqyqUXfbV0TkQmA58OIaafYa355Bn/3j2l1d0kN98s+TRGRPVf0dQXfeZbF7FwMbgTOAv3RJrNcFT17/apWZJUV9wXlpus7CyQvvi/Y0Ks7I2UDQuog4GLjXMcwuDnHL8ICI/Imq3gygqj8Rkf1qpNd7fH4GfdaeRQUP9ck/DwL/LCLXADuJyAtU9frw3jxV/XMROcE1sV4XPEZ/mGSsyrqDm4D5InIY8EvgZOCvE2FWAsvCPugjgYdUdaOI/MohbhneDFwmIjcDtwN/DPysRnqGUYoKHuqTf14FHAC8Hngl8EkR+QhwILAJQFW/4ZqYlwVPlaZ2Vtys5nuZPIYVtihum9qrtHhUdZuILCMYVxkHLlDVtSKyNLy/HFgFLALWA5sJmuuZcUsJmK7lhyJyOHAM8EfAd4BLq6bnM74+g2XDFsVtW3tZD/XMP1Hr5ssAInIP8HfAbgSFUSm8LHiqPnhpcZPn0YNUJo9hhS2K26b2qu8SUdVVBOaIX1se+67AG13j1kFVtwLfCI8Zi6/PYNmwRXHb1l7FQ33yTyLtO4G3Vo3vNKut6iImETlERL4jIutEZK2InFlV6LCp03/cNW1or7KOxwgw//SbtrSbh6YoLHjqLGICtgFvU9VnAkcBbyy7iKnOlMaup3L6rD2JImxl12mHUYz5pzo+a0/DPDSFS4tnsIhJVR8jmEa3OBFmsIhJVW8E5ojIPFXdqKq3AITT8NZRYi552vYXZR+oovB1H+6s+D5rTyOore2wBsEoxvyTE3em+AfMQ3Fc/nJpC5GOdAhzEMHcbgBE5FDgOcD30zIJF04tAdjrSXsB0+fcRzTd/9pkn3Hynq/a07ANDitj/qkQ12ftWZiHpnBp8dRZxBTcFNkDuBw4S1UfTstEVVeo6kJVXTh7v6l/nORsk7waUN4GgVnhi2pUyTSzPtPwWXuSoJtgl2mH4YT5x+EzDZ+1p2EemsLlL1dnERPhNgqXA19Q1a+WFRiv9WTNSknORsmqjSRrUVUWrRWlMSrak0QDo0ZpzD+Yf8A8FMelxTNYxCQiuxAsRFqZCLMSOC2cnXMUU4uYBPgcsE5VP1pFYNNN5iZmrrim4bP2JJOTY2zevPu0w3DC/FMxDZ+1p2EemqKwxVNnERNwNHAqcLuIrAmvvSucX16KvIVadRaVtYHP2iMmt4+x+XczdzC0Kuaf+visPY55aAqnTsqqi5hU9QbS+69LUzQQGSe+Irkoblq8omsu9/L05d3rm/YBKkxunbnTP+tg/jH/AOahGP2b7N4AVftg8/p5XcPXpbfaJwUeGcnHxUjQ22ewhIZeajcPDbC/QohPTfYkrWjfDvxuuFkY/mL+ccrIPBTS+xfB1VnklZee6+KyMvlnTfFsimFq16IenUng94nD6D0+PYM++8cprHloQO8LnnhNpMxc/bIPcTKfKk32vCmafdcuRe+ImiR4f2f8MHqPT8+gz/5xCmseGuBVV5vLXP2072lx+9b33GftQGAa6ybwGp+fQZ+1DzAPDeh9i6cJ8lYlN5Fm1ZXMZfPJu1Y1zeh7YVfbdhrtJhCRfUTkahG5K/x8Qka41J2dRWRCRH4pImvCY1E9RUYW5p/s+KW0m4cGzIiCJ63JnjZ1smqaVWfSlM1nmNoLu9qUprsJzgauVdX5wLXh+TQcdnb+mKoeHh5Dee+IYf7JS7OUdvPQAO8Kniq1lXicrIeuzHz/qvisfTAjJ37UYzFwUfj9IuCklDAuOzsbJfD5GfRZe5iAeSiktwVP1mChS21lOzsNjmScMoOULvmPmvZM0mfkzBWR1bFjSYkUD1DVjQDh5/4pYbJ2bY5YFr447YKsboaZis/PoM/aczEPDejt5IK8wcKscGXCZzWRy6YXJ5oR46N2pzGeR3a4+oCqLsyKIiLXAAem3Hq3k6j8XZvPBd4Xnr8P+Ajwt47pjjw+PoM++8d5jMc8BPS44IlPa4y+x6/lxUnWUrLSilP0gCXzTmpKy8Mn7c5jPCVQ1WOy7onI/dHLzkRkHrApJdgGMnZtVtX7Y2mdB1xZTt1o4+Mz6LN/So3xlGBUPdTbrrYqA3jxcPGaU1ZayXCuetI0ZdXSfNOeSVRbix/1WAmcHn4/HfhaSpjMnZ1Do0W8HLijtqIRwudn0GftuZiHBvS24IGp/lrX63XSTAvncp7VH+2bdqedC5o1zYeAY0XkLuDY8BwReaKIrIJgZ2dgGcHOzuuAL6nq2jD+v4rI7SJyG/Ai4C21FY0Yvj2DPvvHSZN5aEBvu9oguybhXMOoETetaZ12v6imVjX/OnGraC/samt4nylV/TXwkpTr9xK8IiA632Fn5/D6qc2pGU18ewZ99o9zr4F5COh5iwemz1JxrelUqdnk1V7S+oWLZsj4rn0HFNiaOIze4/Mz6LP2VMxDA3rd4oH0mkTRYF6Zmk2UVlHtJa/Wk6XHZ+0pwpvoGjBaxudn0GftqZiHBvS2xZOsucRrGdE/dJW+3mSayYcmqzaTvJ6mZxS0ZxLtM9Xc4jdjiPj8DPqsPRfz0IDeFjxRTST6R87rV816CIsezmRfblY+adeTtZ5R0Z7JJNZN4BE+P4M+a8/FPDTAy662iLSmcjJuslbS5qClz9p3IJqRY3iFz8+gz9pTMQ8N6H3Bk4fLP3qdh2qYeKfd3p44cnj3DMbwUrt5aEAvu9qiNSVl+3HjfcNpn1l9t1nnRemm9UVXnfHStfbCdTwA2xKH0UvMP91od8I8BPS0xROtKSlbY0k2q+NN7XifcFFfbpys5no8/bRmv2/aC9fxGN5g/ulWu1FMLwuepkh7GKo+0HkzWIbx0PVP+3bg4VL5G37Tv2ewfL518mleu3koYqQLniZp4kHuima0m2mM6ph/wDw0RS/HeOJUma9fJt2q0zFd4vikvXiMxxYh+IhPz6DP/nGLYx6K6G3BkzYgGF13Oc/6jEj2A+c9OFmDiGlp+qq9eIxnEtiSOIy+4uMz6LN/3FpA5qGI3na1ufapZg0kZn1mpZU32OjyfVS0Z2PdBD7h8zPos/Z8zEMRvW3xQHaNJa+mlJVGXnpp97OmThalMQra07FuAt/w+Rn0WXs25qGI3rZ4ILvGUqa2kTUd0jW/rLyLNPisPZ1JYHOFeEZX+PwM+qw9G/NQhFOLR0SOE5E7RWS9iJydcl9E5BPh/dtE5AjXuFlk1Tbi95PnydqPSz9xXv5xHUXpJGtXvmrPS7XJ2pqI7CMiV4vIXeHnEzLCXSAim0Tkjirx+4D5x/wThTQPBRQWPCIyDnwaOB5YAJwiIgsSwY4H5ofHEuDcEnFTGSf7FbZF5659u0X5x3UUpZPM31ft2UT90/GjFmcD16rqfODa8DyNC4HjasTvFPOP+WcK81CES4vnecB6Vb1bVR8DLgMWJ8IsBi7WgBuBOeH7vF3iGl7QbG2N4Dm4KPx+EXBSWiBVvR54sGr8HmD+MULMQxEubcSDgF/EzjcARzqEOcgxLgAisoSgtgew9f3ywTvSwnXIXOCBrkWk0JSuJ+ff3vhtmJibuLibiKyOna9Q1RWO+R2gqhsBVHWjiOzvrLSZ+G1h/pmijx5qUpN5yBGXgidtZWFy0UdWGJe4wcXgj70CQERWq+pCB22t0UdN0J4uVU1rquciItcAB6bcend9Rd5g/gnpo642NZmHpnApeDYAh8TODwbudQyzi0NcY0RR1WOy7onI/SIyL6xpzQM2lUy+bvy2MP8YlRlVD7mM8dwEzBeRw0RkF+BkYGUizErgtHB2zlHAQ2ETziWuMTNZCZwefj8d+FrL8dvC/GMMC389pKqFB7AI+AnwU+Dd4bWlwNLwuxDMvvkpcDuwMC+uQ35LXMK1efRRU591Oejel2AmzV3h5z7h9ScCq2LhLgU2Ao8TtAxemxe/j4f5p7+6+qiphHZvPSShAMMwDMNohV5vmWMYhmGMHlbwGIZhGK3SasHTxdYhw9QlIoeIyHdEZJ2IrBWRM7vWFLs/LiK3isiVTWkyuqePHuqjf+roit03Dw2LFgfCxgkGSJ9CME30h8CCRJhFwDcJBluPAr7vGrcjXfOAI8LvexIMAtfWVUdT7P5bgS8CV7b1b2zHcI8+eqiP/qmrK3bfPDSko80WT1+3DqmsS1U3quotAKr6O2AdwWrzzjQBiMjBwAnA+Q1oMfpDHz3UR//U0gXmoWHTZsGTtS2ISxiXuF3oGiAihwLPAb7fA03nAO8g2IfdGB366KE++qcJXedgHhoabRY8rWwdUoE6uoKbInsAlwNnqWoTrxisrElETgQ2qerNDegw+kUfPdRH/9TSZR4aPm0WPHW2DnGJ24UuRGRnAtN8QVW/2gNNRwMvE5F7CLoXXiwilzSky+iWPnqoj/6pq8s8NGzaGkwi2BfubuAwpgb7/jAR5gSmD/b9wDVuR7oEuBg4py9/q0SYF2IDoyNz9NFDffRPXV2JMOahIRytvfpaVbeJyDLg2wQzTi5Q1bUisjS8vxxYRTDTZD3BO2LPyIvbtS6CmtGpwO0isia89i5VXdWhJmNE6aOH+uifBnQZQ8a2zDEMwzBaxXYuMAzDMFrFCh7DMAyjVazgMQzDMFrFCh7DMAyjVazgMQzDMFrFCh7DMAyjVazgMQzDMFrl/wN6V/BSgpJEagAAAABJRU5ErkJggg==\n", | |
| "text/plain": [ | |
| "<fipy.viewers.matplotlibViewer.matplotlib2DGridViewer.Matplotlib2DGridViewer at 0x1925e8970>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 8 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "viewers = [fp.Viewer(vars=var, axes=plt.subplot(2,2,i+1))\n", | |
| " for i, var in enumerate((phi, psi, sigma, xi))]\n", | |
| "plt.tight_layout()\n", | |
| "viewer = fp.MultiViewer(viewers=viewers)\n", | |
| "viewer.plot()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "7ec145e7-157f-4a8c-bf13-73c5aad51d30", | |
| "metadata": {}, | |
| "source": [ | |
| "## Solve" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "id": "0fdebd7b-8486-471e-8a7c-41b46dcb2af3", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<fipy.viewers.matplotlibViewer.matplotlib2DGridViewer.Matplotlib2DGridViewer at 0x1925e8970>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "dt = 1e-5\n", | |
| "elapsed = 0.\n", | |
| "duration = 500\n", | |
| "\n", | |
| "while elapsed < duration:\n", | |
| " phi.updateOld()\n", | |
| " sigma.updateOld()\n", | |
| " elapsed += dt\n", | |
| " for sweep in range(1):\n", | |
| " res = eq.sweep(dt=dt)\n", | |
| " # print(elapsed, sweep, res)\n", | |
| " viewer.plot()\n", | |
| " # input(\"...\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "id": "864675d8-ec47-4de4-b457-ffdab3c605c6", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "6bcc2b07-3034-434c-b5b4-dfb7d75cadea", | |
| "metadata": {}, | |
| "source": [ | |
| "## Matrix Diagnostics" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 135, | |
| "id": "b3c19195-1d2e-4fd1-8917-5377c54d4449", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "solver = eq._prepareLinearSystem(var=None, solver=None, boundaryConditions=(), dt=1)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 136, | |
| "id": "6cf9bd2a-c928-4ee4-91f6-f7c8f6cd4322", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "LinearLUSolver(tolerance=1e-10, iterations=1000)\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "print(solver)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 137, | |
| "id": "9b407ee5-2a13-4fb6-86ff-8059eff9297d", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| " 1.000000 --- --- 0.020000 -0.020000 --- --- --- --- --- --- --- \n", | |
| " --- 1.000000 --- -0.020000 0.040000 -0.020000 --- --- --- --- --- --- \n", | |
| " --- --- 1.000000 --- -0.020000 0.020000 --- --- --- --- --- --- \n", | |
| "-1.00e-06 1.00e-06 --- --- --- --- --- --- --- 1.000000 --- --- \n", | |
| " 1.00e-06 -2.00e-06 1.00e-06 --- --- --- --- --- --- --- 1.000000 --- \n", | |
| " --- 1.00e-06 -1.00e-06 --- --- --- --- --- --- --- --- 1.000000 \n", | |
| " --- --- --- --- --- --- 1.000000 --- --- --- --- --- \n", | |
| " --- --- --- --- --- --- --- 1.000000 --- --- --- --- \n", | |
| " --- --- --- --- --- --- --- --- 1.000000 --- --- --- \n", | |
| " --- --- --- 1.000000 --- --- -2.00e-26 -2.00e-06 --- -2.000001 1.00e-06 --- \n", | |
| " --- --- --- --- 1.000000 --- 2.00e-26 4.00e-06 --- 1.00e-06 -2.000002 1.00e-06 \n", | |
| " --- --- --- --- --- 1.000000 --- -2.00e-06 --- --- 1.00e-06 -2.000001 \n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "print(solver.matrix)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "id": "c5800e0a-5293-498d-a01d-704591df7827", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "Python 3 (ipykernel)", | |
| "language": "python", | |
| "name": "python3" | |
| }, | |
| "language_info": { | |
| "codemirror_mode": { | |
| "name": "ipython", | |
| "version": 3 | |
| }, | |
| "file_extension": ".py", | |
| "mimetype": "text/x-python", | |
| "name": "python", | |
| "nbconvert_exporter": "python", | |
| "pygments_lexer": "ipython3", | |
| "version": "3.10.2" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 5 | |
| } |
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