JuliaFEM.jl/docs/getfem_examples/A_step-by-step_basic_example_python.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#A step-by-step basic example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## import basic modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import getfem as gf\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## creation of a simple cartesian mesh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m = gf.Mesh('cartesian', np.arange(0,1.1,0.1), np.arange(0,1.1,0.1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## create a MeshFem of for a field of dimension 1 (i.e. a scalar field)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mf = gf.MeshFem(m, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## assign the Q2 fem to all convexes of the MeshFem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mf.set_fem(gf.Fem('FEM_QK(2,2)'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## view the expression of its basis functions on the reference convex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('1 - 3*x - 3*y + 2*x^2 + 9*x*y + 2*y^2 - 6*x^2*y - 6*x*y^2 + 4*x^2*y^2', '4*x - 4*x^2 - 12*x*y + 12*x^2*y + 8*x*y^2 - 8*x^2*y^2', '-x + 2*x^2 + 3*x*y - 6*x^2*y - 2*x*y^2 + 4*x^2*y^2', '4*y - 12*x*y - 4*y^2 + 8*x^2*y + 12*x*y^2 - 8*x^2*y^2', '16*x*y - 16*x^2*y - 16*x*y^2 + 16*x^2*y^2', '-4*x*y + 8*x^2*y + 4*x*y^2 - 8*x^2*y^2', '-y + 3*x*y + 2*y^2 - 2*x^2*y - 6*x*y^2 + 4*x^2*y^2', '-4*x*y + 4*x^2*y + 8*x*y^2 - 8*x^2*y^2', 'x*y - 2*x^2*y - 2*x*y^2 + 4*x^2*y^2')\n"
     ]
    }
   ],
   "source": [
    "print gf.Fem('FEM_QK(2,2)').poly_str()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## an exact integration will be used"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mim = gf.MeshIm(m, gf.Integ('IM_EXACT_PARALLELEPIPED(2)'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## detect the border of the mesh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "border = m.outer_faces()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## mark it as boundary #42"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m.set_region(42, border)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## empty real model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "md = gf.Model('real')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## declare that \"u\" is an unknown of the system on the finite element method `mf`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "md.add_fem_variable('u', mf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## add generic elliptic brick on \"u\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "md.add_Laplacian_brick(mim, 'u');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## add Dirichlet condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = mf.eval('x*(x-1) - y*(y-1)')\n",
    "md.add_initialized_fem_data('DirichletData', mf, g)\n",
    "md.add_Dirichlet_condition_with_multipliers(mim, 'u', mf, 42, 'DirichletData')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## solve the linear system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 1)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "md.solve()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## extracted solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "u = md.variable('u')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## export computed solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mf.export_to_pos('u.pos',u,'Computed solution')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting gscript\n"
     ]
    }
   ],
   "source": [
    "%%writefile gscript\n",
    "Print \"solution.png\";\n",
    "Exit;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Print \"solution.png\";\r\n",
      "Exit;"
     ]
    }
   ],
   "source": [
    "!cat gscript"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "!gmsh u.pos gscript"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from IPython.core.display import Image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAJYCAIAAAAxBA+LAAAADHRFWHRDcmVhdG9yAEdtc2j/U5Jh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\nIbau0ZsoKAHhOT2iH3u
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image('solution.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# add source term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = mf.eval('10')\n",
    "md.add_initialized_fem_data('VolumicData', mf, f)\n",
    "md.add_source_term_brick(mim, 'u', 'VolumicData')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "md.solve()\n",
    "u = md.variable('u')\n",
    "mf.export_to_pos('u.pos',u,'Computed solution')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting gscript\n"
     ]
    }
   ],
   "source": [
    "%%writefile gscript\n",
    "Print \"solution_with_source_term.png\";\n",
    "Exit;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "!gmsh u.pos gscript"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image('solution_with_source_term.png')"
   ]
  },
  {
   "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": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}