{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Adaptive PDE discretizations on Cartesian grids\n", "## Volume : Non-divergence form PDEs\n", "## Part : One space dimension\n", "## Chapter : Static problems\n", "\n", "This notebook illustrates the use of monotone finite difference schemes to compute viscosity solutions of PDEs, in one space dimension. (See the other notebooks for two dimensional examples.) We address both first order and second order, linear and non-linear schemes. \n", "\n", "For the best convenience, the numerical scheme jacobian matrix is assembled using automatic differentiation.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[**Summary**](Summary.ipynb) of volume Non-Divergence form PDEs, this series of notebooks.\n", "\n", "[**Main summary**](../Summary.ipynb) of the Adaptive Grid Discretizations \n", "\tbook of notebooks, including the other volumes.\n", "\n", "# Table of contents\n", " * [1. A first order linear equation](#1.-A-first-order-linear-equation)\n", " * [2. A second order linear equation](#2.-A-second-order-linear-equation)\n", " * [3. A non-linear equation](#3.-A-non-linear-equation)\n", "\n", "\n", "\n", "**Acknowledgement.** Some of the experiments presented in these notebooks are part of \n", "ongoing research with Ludovic Métivier and Da Chen.\n", "\n", "Copyright Jean-Marie Mirebeau, Centre Borelli, ENS Paris-Saclay, CNRS, University Paris-Saclay" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 0. Importing the required libraries" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:47:59.989323Z", "iopub.status.busy": "2024-04-30T08:47:59.988559Z", "iopub.status.idle": "2024-04-30T08:48:00.005061Z", "shell.execute_reply": "2024-04-30T08:48:00.004234Z" } }, "outputs": [], "source": [ "import sys; sys.path.insert(0,\"..\") # Allow import of agd from parent directory (useless if conda package installed)\n", "#from Miscellaneous import TocTools; TocTools.displayTOC('MonotoneSchemes1D','NonDiv')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.008617Z", "iopub.status.busy": "2024-04-30T08:48:00.008378Z", "iopub.status.idle": "2024-04-30T08:48:00.068095Z", "shell.execute_reply": "2024-04-30T08:48:00.067677Z" } }, "outputs": [], "source": [ "from agd import FiniteDifferences as fd\n", "from agd import AutomaticDifferentiation as ad" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.069985Z", "iopub.status.busy": "2024-04-30T08:48:00.069819Z", "iopub.status.idle": "2024-04-30T08:48:00.254580Z", "shell.execute_reply": "2024-04-30T08:48:00.254216Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some utility functions" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.257104Z", "iopub.status.busy": "2024-04-30T08:48:00.256710Z", "iopub.status.idle": "2024-04-30T08:48:00.259094Z", "shell.execute_reply": "2024-04-30T08:48:00.258811Z" } }, "outputs": [], "source": [ "newton_root = ad.Optimization.newton_root\n", "stop = ad.Optimization.stop_default\n", "def LInfNorm(a): return np.max(np.abs(np.array(a)))" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "ExoSplit" ] }, "source": [ "## 1. A first order linear equation\n", "\n", "We numerically compute the *viscosity* solution of the equation\n", "$$\n", " f(x) - u'(x)=0\n", "$$\n", "over some interval, with dirichlet boundary conditions.\n", "Unless the mean value of $f$ is compatible with the boundary conditions, this equation admits no classical solution. However the *viscosity* solution exists and is unique. It has a jump at the left endpoint. \n", "\n", "The monotone numerical scheme for this equation is \n", "$$\n", " f(x) - \\frac{u(x+h)-u(x)} h = 0,\n", "$$\n", "in the interior, with the adequate boundary conditions.\n", "\n", "\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.260527Z", "iopub.status.busy": "2024-04-30T08:48:00.260423Z", "iopub.status.idle": "2024-04-30T08:48:00.262462Z", "shell.execute_reply": "2024-04-30T08:48:00.262230Z" }, "tags": [ "ExoRemove" ] }, "outputs": [], "source": [ "def Scheme(u,f,bc,gridScale):\n", " residue = f - fd.DiffUpwind(u,(1,),gridScale) # f-u' = 0 \n", " residue[0] = u[0]-bc[0]; residue[-1]= u[-1]-bc[1] # u[0]=0 and u[1]-1=0\n", " return residue" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.263908Z", "iopub.status.busy": "2024-04-30T08:48:00.263779Z", "iopub.status.idle": "2024-04-30T08:48:00.266033Z", "shell.execute_reply": "2024-04-30T08:48:00.265720Z" } }, "outputs": [], "source": [ "X = np.linspace(0,1,21,endpoint=True)\n", "gridScale=X[1]-X[0]\n", "f = np.sin(np.pi*X)\n", "bc = (0,1)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.267586Z", "iopub.status.busy": "2024-04-30T08:48:00.267474Z", "iopub.status.idle": "2024-04-30T08:48:00.333913Z", "shell.execute_reply": "2024-04-30T08:48:00.333621Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "u=X \n", "residue = Scheme(u,f,bc,gridScale)\n", "plt.title('Scheme residue for u=X')\n", "plt.plot(X,residue);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The next step is to assemble the linear system underlying the PDE. For that purpose we rely on sparse automatic differentiation." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.335516Z", "iopub.status.busy": "2024-04-30T08:48:00.335395Z", "iopub.status.idle": "2024-04-30T08:48:00.337675Z", "shell.execute_reply": "2024-04-30T08:48:00.337381Z" } }, "outputs": [], "source": [ "u = ad.Sparse.identity(X.shape)\n", "residue = Scheme(u,f,bc,gridScale)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we solve and plot the solution. Note the (expected) discontinuity at the boundary due to the selection of the viscosity solution." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.339107Z", "iopub.status.busy": "2024-04-30T08:48:00.339005Z", "iopub.status.idle": "2024-04-30T08:48:00.378042Z", "shell.execute_reply": "2024-04-30T08:48:00.377763Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.6637359812630166e-15\n" ] } ], "source": [ "solution = residue.solve()\n", "solution_residue = Scheme(solution,f,bc,gridScale)\n", "print(LInfNorm(solution_residue))" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.379702Z", "iopub.status.busy": "2024-04-30T08:48:00.379594Z", "iopub.status.idle": "2024-04-30T08:48:00.435270Z", "shell.execute_reply": "2024-04-30T08:48:00.435005Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title('Viscosity solution of a first order linear equation')\n", "plt.plot(X,solution);" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "ExoSplit" ] }, "source": [ "## 2. A second order linear equation\n", "\n", "We consider the second order linear equation \n", "$$\n", " -u''(x) + a(x) u'(x) + b(x) = 0,\n", "$$\n", "with again Dirichlet boundary conditions.\n", "\n", "There are two main differences w.r.t. the previous example:\n", "* We can use centered finite differences, for the first order term, provided the grid scale is small enough. Indeed, the monotony of the second order derivative dominates the first order.\n", "* There exists a classical solution, so the boundary conditions will be met at both endpoints.\n", "\n", "The monotone numerical scheme for this equation is \n", "$$\n", " {-} \\frac{u(x+h)-2 u(x) +u(x-h)}{h^2} + a(x) \\frac{u(x+h)-u(x-h)}{2h} + b(x) = 0\n", "$$\n", "in the interior, with the adequate boundary conditions.\n", "\n", "\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.436816Z", "iopub.status.busy": "2024-04-30T08:48:00.436709Z", "iopub.status.idle": "2024-04-30T08:48:00.438791Z", "shell.execute_reply": "2024-04-30T08:48:00.438546Z" }, "tags": [ "ExoRemove" ] }, "outputs": [], "source": [ "def Scheme(u,a,b,bc,gridScale):\n", " residue = -fd.Diff2(u,(1,),gridScale) + a*fd.DiffCentered(u,(1,),gridScale) + b\n", " residue[0] = u[0]-bc[0]; residue[-1]=u[-1]-bc[1]\n", " return residue" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.440137Z", "iopub.status.busy": "2024-04-30T08:48:00.440034Z", "iopub.status.idle": "2024-04-30T08:48:00.441906Z", "shell.execute_reply": "2024-04-30T08:48:00.441671Z" } }, "outputs": [], "source": [ "X = np.linspace(0,1,21,endpoint=True)\n", "gridScale=X[1]-X[0]\n", "a = 3*np.sin(np.pi*X)\n", "b=1.\n", "bc = (0,0.1)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.443284Z", "iopub.status.busy": "2024-04-30T08:48:00.443191Z", "iopub.status.idle": "2024-04-30T08:48:00.445493Z", "shell.execute_reply": "2024-04-30T08:48:00.445274Z" } }, "outputs": [], "source": [ "u = ad.Sparse.identity(X.shape)\n", "residue = Scheme(u,a,b,bc,gridScale)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.446868Z", "iopub.status.busy": "2024-04-30T08:48:00.446771Z", "iopub.status.idle": "2024-04-30T08:48:00.449116Z", "shell.execute_reply": "2024-04-30T08:48:00.448868Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.6431300764452317e-14\n" ] } ], "source": [ "solution = u.value+residue.solve()\n", "print(LInfNorm(Scheme(solution,a,b,bc,gridScale)))" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.450566Z", "iopub.status.busy": "2024-04-30T08:48:00.450464Z", "iopub.status.idle": "2024-04-30T08:48:00.501534Z", "shell.execute_reply": "2024-04-30T08:48:00.501281Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(X,solution);" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "ExoSplit" ] }, "source": [ "## 3. A non-linear equation\n", "\n", "We consider the non-linear equation\n", "$$\n", " -a(x)u''(x)+\n", " d(x)|u'(x)-\\omega(x)|^2 -1 = 0,\n", "$$\n", "where $a$ is a non-negative function. \n", "We use again Dirichlet boundary conditions.\n", "\n", "When $a\\equiv 0$, and $d >0$ this problem becomes a particular case of an eikonal equation, with drift $\\omega$.\n", "If $d|\\omega|^2\\geq 1$, somewhere in the domain, then the undelying optimal control problem looses local controllability, and a discontinuity or boundary layer appears at an endpoint of the domain.\n", "\n", "In contrast with the previous examples, this equation is non-linear. Two discretization schemes can be considered, depending on the treatment of the first order term:\n", "* *Centered finite differences.* This discretization is second order consistent, and monotone provided the second order term dominates the first order term. This is typically the case if $a \\gtrsim h$, $d = \\mathcal O(1)$ and the first order derivative of the solution is bounded. \n", "$$\n", " -a(x) \\frac{u(x+h)-2 u(x)+u(x-h)} {h^2} + d(x) \\left(\\frac{u(x+h)-u(x-h)}{2h} -\\omega(x)\\right)^2 - 1 = 0\n", "$$\n", "* *Upwind finite differences.* This discretization is only first order consistent, but remains monotone even if the second order coefficient $a$ vanishes (we still require $a \\geq 0$). \n", "$$\n", " -a(x) \\frac{u(x+h)-2 u(x)+u(x-h)} {h^2} + d(x) \\max\\left\\{0, \\omega(x) - \\frac{u(x+h)-u(x)}{h}, -\\omega(x) -\\frac{u(x-h)-u(x)}{h}\\right\\}^2 - 1 = 0\n", "$$\n", "\n", "\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.503062Z", "iopub.status.busy": "2024-04-30T08:48:00.502972Z", "iopub.status.idle": "2024-04-30T08:48:00.505884Z", "shell.execute_reply": "2024-04-30T08:48:00.505654Z" }, "tags": [ "ExoRemove" ] }, "outputs": [], "source": [ "def SchemeCentered(u,a,d,omega,bc,h):\n", " residue = (-a*fd.Diff2(u,(1,),h) \n", " + d*(fd.DiffCentered(u,(1,),h)-omega)**2\n", " -1.)\n", " residue[0] = u[0]-bc[0]; residue[-1]=u[-1]-bc[1]\n", " return residue\n", "\n", "def SchemeUpwind(u,a,d,omega,bc,h):\n", " maxi = np.maximum\n", " residue = (-a*fd.Diff2(u,(1,),h) \n", " + d*maxi(0.,maxi( omega - fd.DiffUpwind(u,(1,),h), \n", " -omega - fd.DiffUpwind(u,(-1,),h)) )**2\n", " -1.)\n", " residue[0] = u[0]-bc[0]; residue[-1]=u[-1]-bc[1]\n", " return residue" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.507248Z", "iopub.status.busy": "2024-04-30T08:48:00.507151Z", "iopub.status.idle": "2024-04-30T08:48:00.509066Z", "shell.execute_reply": "2024-04-30T08:48:00.508836Z" } }, "outputs": [], "source": [ "X = np.linspace(0,1,51,endpoint=True)\n", "gridScale=X[1]-X[0]\n", "a=0.1\n", "d=1.\n", "omega=-0.4\n", "bc = (0,0.1)\n", "\n", "guess = np.zeros(X.shape)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.510331Z", "iopub.status.busy": "2024-04-30T08:48:00.510239Z", "iopub.status.idle": "2024-04-30T08:48:00.520468Z", "shell.execute_reply": "2024-04-30T08:48:00.520192Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Centered discretization\n", "Iteration: 1 Residue norm: 29.898197384689052\n", "Iteration: 2 Residue norm: 7.217807693143865\n", "Iteration: 3 Residue norm: 1.3527690097989034\n", "Iteration: 4 Residue norm: 0.05365424942043995\n", "Iteration: 5 Residue norm: 3.8327705599972006e-05\n", "Iteration: 6 Residue norm: 1.1762812945903534e-11\n", "Target residue reached. Terminating.\n", "\n", "Upwind discretization\n", "Iteration: 1 Residue norm: 29.588778291338716\n", "Iteration: 2 Residue norm: 7.118351544328192\n", "Iteration: 3 Residue norm: 1.3622987631308292\n", "Iteration: 4 Residue norm: 0.08101479548291834\n", "Iteration: 5 Residue norm: 0.0002119788463035288\n", "Iteration: 6 Residue norm: 1.0399192618137931e-09\n", "Target residue reached. Terminating.\n" ] } ], "source": [ "params = (a,d,omega,bc,gridScale)\n", "print(\"Centered discretization\"); \n", "solution_centered = newton_root(SchemeCentered,guess,params)\n", "print()\n", "print(\"Upwind discretization\"); \n", "solution_upwind = newton_root(SchemeUpwind,guess,params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When the solution is smooth, there is not much difference between the centered and the upwind discretization." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.521872Z", "iopub.status.busy": "2024-04-30T08:48:00.521790Z", "iopub.status.idle": "2024-04-30T08:48:00.618277Z", "shell.execute_reply": "2024-04-30T08:48:00.618004Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title(\"Centered and upwind scheme, smooth test case\")\n", "plt.plot(X,solution_centered,label=\"centered\")\n", "plt.plot(X,solution_upwind, label=\"upwind\");\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Increasing the drift value yields a boundary layer.\n", "(The first order part of the PDE does not correspond anymore to a locally controllable problem.)\n", "Because the first order derivative of the solution is not bounded, the centered second order scheme looses monotony, and the resulting numerical solution may be incorrect. " ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.619867Z", "iopub.status.busy": "2024-04-30T08:48:00.619760Z", "iopub.status.idle": "2024-04-30T08:48:00.697797Z", "shell.execute_reply": "2024-04-30T08:48:00.697501Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Centered discretization\n", "Iteration: 1 Residue norm: 14.497311217649024\n", "Iteration: 2 Residue norm: 3.772179877026524\n", "Iteration: 3 Residue norm: 0.31762164370180557\n", "Iteration: 4 Residue norm: 0.023603400737059133\n", "Iteration: 5 Residue norm: 0.00010808252084615333\n", "Iteration: 6 Residue norm: 2.191988812683121e-09\n", "Target residue reached. Terminating.\n", "\n", "Upwind discretization\n", "Iteration: 1 Residue norm: 6.009152075099161\n", "Iteration: 2 Residue norm: 0.12080838760273593\n", "Iteration: 3 Residue norm: 4.851760041901798e-05\n", "Iteration: 4 Residue norm: 3.1526781185675645e-11\n", "Target residue reached. Terminating.\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "omega2 = 1.4\n", "params = (a,d,omega2,bc,gridScale)\n", "print(\"Centered discretization\"); \n", "solution_centered = newton_root(SchemeCentered,guess,params)\n", "print()\n", "print(\"Upwind discretization\"); \n", "solution_upwind = newton_root(SchemeUpwind,guess,params)\n", "\n", "plt.title(\"Centered and upwind scheme, with boundary layer\")\n", "plt.plot(X,solution_centered,label=\"centered\")\n", "plt.plot(X,solution_upwind, label=\"upwind\");\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We next remove the second order term, to get the standard eikonal equation.\n", "A problem arises : the jacobian matrix $J$ of the scheme may not be invertible. Fortunately, by degenerate ellipticity, \n", "$$\n", " J+\\epsilon \\mathrm{Id},\n", "$$\n", "is guaranteed to be invertible, for any $\\epsilon>0$. \n", "(The non-invertibility issue may or may not arise depending on the initial conditions.)\n", "\n", "We note in this setting that:\n", "* The centered scheme looses monotonicity, and indeed fails to converge.\n", "* The upwind scheme requires $\\epsilon>0$ for solving the linear problems." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.699377Z", "iopub.status.busy": "2024-04-30T08:48:00.699268Z", "iopub.status.idle": "2024-04-30T08:48:00.806534Z", "shell.execute_reply": "2024-04-30T08:48:00.806243Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Centered discretization\n", "Iteration: 1 Residue norm: 1.0170748113143362\n", "Iteration: 2 Residue norm: 35.89906406436457\n", "Iteration: 3 Residue norm: 8.35933364491549\n", "Iteration: 4 Residue norm: 1.4874380253485957\n", "Iteration: 5 Residue norm: 0.6737384280319145\n", "Iteration: 6 Residue norm: 0.653455981756095\n", "Iteration: 8 Residue norm: 0.646660402481339\n", "Iteration: 10 Residue norm: 0.6458469590647455\n", "Iteration: 12 Residue norm: 0.6457316194653311\n", "Iteration: 14 Residue norm: 0.6457015780480164\n", "Iteration: 16 Residue norm: 0.6456941027843102\n", "Iteration: 20 Residue norm: 0.6456917657746287\n", "Max iterations exceeded. Aborting.\n", "\n", "Upwind discretization\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 1 Residue norm: 705.2273268435152\n", "Iteration: 2 Residue norm: 176.1775175937498\n", "Iteration: 3 Residue norm: 96.75023856617977\n", "Iteration: 4 Residue norm: 91.71254599177115\n", "Iteration: 5 Residue norm: 79.86122878563275\n", "Iteration: 6 Residue norm: 64.05715532164896\n", "Iteration: 8 Residue norm: 32.52211848671483\n", "Iteration: 10 Residue norm: 11.924303093653023\n", "Iteration: 12 Residue norm: 1.067622291649359\n", "Iteration: 14 Residue norm: 0.0065282559543760055\n", "Iteration: 16 Residue norm: 1.6623668072091036e-06\n", "Iteration: 20 Residue norm: 1.0759137580862443e-07\n", "Iteration: 24 Residue norm: 6.724472756403088e-09\n", "Target residue reached. Terminating.\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# No second order term\n", "a2=0\n", "params = (a2,d,omega,bc,gridScale)\n", "\n", "# Relaxation of the linear problems\n", "epsilon=1\n", "relax = epsilon*ad.Sparse.identity(X.shape)\n", "\n", "print(\"Centered discretization\"); \n", "solution_centered = newton_root(SchemeCentered,guess,params,relax=relax,\n", " stop=stop(niter_max=20,raise_on_abort=False))\n", "print()\n", "print(\"Upwind discretization\"); \n", "solution_upwind = newton_root(SchemeUpwind,guess,params,relax=relax)\n", "\n", "plt.title(\"Centered and upwind scheme, eikonal equation\")\n", "plt.plot(X,solution_centered,label=\"centered\")\n", "plt.plot(X,solution_upwind, label=\"upwind\");\n", "plt.legend();" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:48:00.808073Z", "iopub.status.busy": "2024-04-30T08:48:00.807971Z", "iopub.status.idle": "2024-04-30T08:48:00.861296Z", "shell.execute_reply": "2024-04-30T08:48:00.861036Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title(\"Upwind scheme, eikonal equation\")\n", "plt.plot(X,solution_upwind);" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Format de la Cellule Texte Brut", "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": "3.10.8" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }