IPython notebook demonstrating setting an internal boundary condition in FiPy

internal_conductor.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import fipy as fp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mesh = fp.Grid1D(nx=200, dx=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "V = fp.CellVariable(mesh=mesh, name=\"V\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "fipy/viewers/matplotlibViewer/__init__.py:113: UserWarning: Matplotlib1DViewer efficiency is improved by setting the 'datamax' and 'datamin' keys\n",
      "  return Matplotlib1DViewer(vars=vars, title=title, axes=axes, **kwlimits)\n"
     ]
    },
    {
     "data": {
      "image/png": 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ZW8v9D6XHd/rpEyqrq+p4t30cWD2k5lzg6LT2sa4PYAPwa0m+kGQqySt6zEXSErFytsEk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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1065d3190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "viewer = fp.MatplotlibViewer(vars=V)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "charge = -1. * (mesh.x < 0.5) + 1. * (mesh.x > 1.5)\n",
    "charge.name = \"rho\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "conductor = (mesh.x > 0.7) & (mesh.x < 1.2)\n",
    "conductor.name = \"conductor\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dielectric = 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "largeValue = 1e6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "conductorPotential = 12."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "eq = fp.DiffusionTerm(coeff=dielectric) + charge == fp.ImplicitSourceTerm(coeff=conductor * largeValue) - conductor * largeValue * conductorPotential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "eq.solve(var=V)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10692a950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "viewer.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}