adr-complete-parallel.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Interactive Proteus parallel example\n",
    "\n",
    "##Load IPython support for working with MPI tasks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from IPython import parallel\n",
    "rc = parallel.Client(profile=\"mpi\")\n",
    "view = rc[:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Load interactive Proteus module, physics, and numerics on the MPI tasks and solve problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%px --block\n",
    "from proteus.iproteus import * \n",
    "from proteus import default_n as n\n",
    "from proteus import default_p as p\n",
    "from proteus import default_s,default_so\n",
    "from proteus.TransportCoefficients import *\n",
    "\n",
    "class LAD(TC_base):\n",
    "    \"\"\"\n",
    "    The coefficients of the linear advection-diffusion equation\n",
    "    \"\"\"\n",
    "    def __init__(self,M,A,B):\n",
    "        TC_base.__init__(self, \n",
    "                         nc=1, #number of components\n",
    "                         variableNames=['u'],\n",
    "                         mass      = {0:{0:'linear'}},\n",
    "                         advection = {0:{0:'linear'}},\n",
    "                         diffusion = {0:{0:{0:'constant'}}},\n",
    "                         potential = {0:{0:'u'}},\n",
    "                         reaction  = {0:{0:'linear'}})\n",
    "        self.M=M;\n",
    "        self.A=A;\n",
    "        self.B=B;\n",
    "    \n",
    "    def evaluate(self,t,c):\n",
    "        c[('m',0)][:]         = self.M*c[('u',0)]  \n",
    "        c[('dm',0,0)][:]      = self.M\n",
    "        c[('f',0)][...,0]     = self.B[0]*c[('u',0)]\n",
    "        c[('f',0)][...,1]     = self.B[1]*c[('u',0)]\n",
    "        c[('df',0,0)][...,0]  = self.B[0]\n",
    "        c[('df',0,0)][...,1]  = self.B[1]\n",
    "        c[('a',0,0)][...,0,0] = self.A[0][0]\n",
    "        c[('a',0,0)][...,1,1] = self.A[1][1]\n",
    "\n",
    "#physics\n",
    "p.name = \"ladr_2d\"\n",
    "p.nd = 2; #Two dimensions\n",
    "p.L=(1.0,1.0,1.0); \n",
    "p.T=1.0\n",
    "\n",
    "p.coefficients=LAD(M=1.0,\n",
    "                 A=[[0.001,0.0],\n",
    "                    [0.0,0.001]],\n",
    "                 B=[2.0,1.0])\n",
    "\n",
    "def getDBC(x,flag):\n",
    "    if x[0] == 0.0 or x[1] == 0.0:\n",
    "        return lambda x,t: 1.0\n",
    "    elif x[0] == 1.0 or x[1] == 1.0:\n",
    "        return lambda x,t: 0.0\n",
    "\n",
    "p.dirichletConditions = {0:getDBC}\n",
    "p.advectiveFluxBoundaryConditions = {}\n",
    "p.diffusiveFluxBoundaryConditions = {0:{}}\n",
    "p.periodicDirichletConditions = None\n",
    "class IC:\n",
    "    def __init__(self):\n",
    "        pass\n",
    "    def uOfXT(self,x,t):\n",
    "        if x[0] <= 0.0 or x[1] <= 0.0:\n",
    "            return 1.0\n",
    "        else:\n",
    "            return 0.0\n",
    "\n",
    "p.initialConditions  = {0:IC()}\n",
    "#numerics\n",
    "n.timeIntegration = n.BackwardEuler_cfl\n",
    "n.stepController = n.Min_dt_cfl_controller\n",
    "n.runCFL=1.0\n",
    "n.femSpaces = {0:n.C0_AffineLinearOnSimplexWithNodalBasis}\n",
    "n.elementQuadrature = n.SimplexGaussQuadrature(p.nd,3)\n",
    "n.elementBoundaryQuadrature = n.SimplexGaussQuadrature(p.nd-1,3)\n",
    "n.subgridError = n.AdvectionDiffusionReaction_ASGS(p.coefficients,p.nd,lag=False)\n",
    "n.shockCapturing = n.ResGradQuad_SC(p.coefficients,p.nd,\n",
    "                               shockCapturingFactor=0.99,\n",
    "                               lag=True)\n",
    "n.numericalFluxType = n.Advection_DiagonalUpwind_Diffusion_SIPG_exterior\n",
    "n.nnx=41; n.nny=41\n",
    "n.tnList=[float(i)/40.0 for i in range(11)]\n",
    "n.matrix = n.SparseMatrix\n",
    "n.multilevelLinearSolver = n.KSP_petsc4py\n",
    "n.linearSmoother = n.Jacobi\n",
    "n.l_atol_res = 1.0e-8\n",
    "n.parallelPartitioningType = n.MeshParallelPartitioningTypes.element\n",
    "n.nLayersOfOverlapForParallel = 1\n",
    "n.periodicDirichletConditions = None\n",
    "\n",
    "from proteus import Comm\n",
    "comm = Comm.get()\n",
    "pList = [p]\n",
    "nList = [n]\n",
    "so = default_so\n",
    "so.name = pList[0].name = \"ladr_2d\"\n",
    "so.sList=[default_s]\n",
    "so.tnList = n.tnList\n",
    "nList[0].multilevelLinearSolver=default_n.KSP_petsc4py\n",
    "#opts.viewer='vtk'\n",
    "#viewers = Viewers.viewerOn(so.name+`comm.rank()`,opts.viewer)\n",
    "ns = NumericalSolution.NS_base(so,pList,nList,so.sList,opts)\n",
    "ns.calculateSolution('run1')\n",
    "x = ns.modelList[0].levelModelList[-1].mesh.nodeArray[:,0]\n",
    "y = ns.modelList[0].levelModelList[-1].mesh.nodeArray[:,1]\n",
    "triangles = ns.modelList[0].levelModelList[-1].mesh.elementNodesArray\n",
    "u = ns.modelList[0].levelModelList[-1].u[0].dof\n",
    "n = len(x)\n",
    "#if comm.isMaster():\n",
    "#    imageList = [window.png for window in viewers.windowDict.values()]\n",
    "#else:\n",
    "#    imageList = []"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Combine subdomain solutions and plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ElCdA6hAiMJEBg0SAAMMSIBkipA4RAhMaJEYECDAsAZIjQuoQIUCPUfKp9gMAlPL4pfYT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\njn0+ipBlOW4N+R8pVOHQJtDWMgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from parplot import parallel_plot\n",
    "import numpy as np\n",
    "r = parallel.Reference\n",
    "png = parallel_plot(view, 'tricontourf',\n",
    "                    r('x'),\n",
    "                    r('y'),\n",
    "                    r('triangles'),\n",
    "                    r('u'),\n",
    "                    levels=np.linspace(0,1.01,6),\n",
    "                    xlim=(0,1),\n",
    "                    ylim=(0,1),\n",
    "                   )"
   ]
  }
 ],
 "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
}