Poisson_3D_X3DOM.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from IPython.core.display import HTML\n",
    "from dolfin import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Create mesh and define function space\n",
    "mesh = UnitCubeMesh(32, 32, 32)\n",
    "V = FunctionSpace(mesh, \"Lagrange\", 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Define Dirichlet boundary at the bottom face\n",
    "def boundary(x):\n",
    "    return x[0] < DOLFIN_EPS \n",
    "\n",
    "# Define boundary condition\n",
    "bc = DirichletBC(V, Constant(0.0), boundary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calling FFC just-in-time (JIT) compiler, this may take some time.\n"
     ]
    }
   ],
   "source": [
    "# Define variational problem\n",
    "u = TrialFunction(V)\n",
    "v = TestFunction(V)\n",
    "f = Expression(\"10*exp(-(pow(x[0] - 0.5, 2) + pow(x[1] - 0.5, 2) + pow(x[2] - 0.5, 2)) / 0.02)\", degree=1)\n",
    "a = inner(grad(u), grad(v))*dx\n",
    "L = f*v*dx \n",
    "\n",
    "# Compute solution\n",
    "u = Function(V)\n",
    "solve(a == L, u, bc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<!DOCTYPE html>\n",
       "<html>\n",
       "  <head>\n",
       "    <meta http-equiv=\"content-type\" content=\"text/html;charset=UTF-8\" />\n",
       "    <meta name=\"generator\" content=\"FEniCS/DOLFIN (http://fenicsproject.org)\" />\n",
       "    <title>FEniCS/DOLFIN X3DOM plot</title>\n",
       "    <script type=\"text/javascript\" src=\"http://www.x3dom.org/download/x3dom.js\"></script>\n",
       "    <link rel=\"stylesheet\" type=\"text/css\" href=\"http://www.x3dom.org/download/x3dom.css\" />\n",
       "  </head>\n",
       "  <body>\n",
       "    <x3d showStat=\"false\" xmlns=\"http://www.web3d.org/specifications/x3d-namespace\" width=\"500.000000px\" height=\"400.000000px\">\n",
       "      <scene>\n",
       "        <shape>\n",
       "          <appearance>\n",
       "            <material diffuseColor=\"1.000000 1.000000 1.000000\" emissiveColor=\"0.000000 0.000000 0.000000\" specularColor=\"0.000000 0.000000 0.000000\" ambientIntensity=\"0\" shininess=\"0.5\" transparency=\"0\"></material>\n",
       "          </appearance>\n",
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