fefacevals.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "include(\"src/JuAFEM.jl\")\n",
    "using JuAFEM\n",
    "using Base.Test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Set up FEValues and FEFaceValues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "JuAFEM.Lagrange{2,JuAFEM.RefCube,1}()"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fs = Lagrange{2,RefCube,1}()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "JuAFEM.QuadratureRule{2,Float64}([0.308642,0.493827,0.308642,0.493827,0.790123,0.493827,0.308642,0.493827,0.308642],ContMechTensors.Tensor{1,2,Float64,2}[[-0.774597,-0.774597],[0.0,-0.774597],[0.774597,-0.774597],[-0.774597,0.0],[0.0,0.0],[0.774597,0.0],[-0.774597,0.774597],[0.0,0.774597],[0.774597,0.774597]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QR = QuadratureRule(Dim{1},RefCube(),3)\n",
    "QR2 = QuadratureRule(Dim{2},RefCube(),3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "feface = JuAFEM.FEFaceValues(QR,fs)\n",
    "feval = FEValues(QR2,fs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{ContMechTensors.Tensor{1,2,Float64,2},1}:\n",
       " [0.0,0.0] \n",
       " [5.0,3.0] \n",
       " [6.0,10.0]\n",
       " [1.0,9.0] "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [0.0 0.0;\n",
    "     5.0 3.0;\n",
    "     6.0 10.0;\n",
    "     1.0 9.0]';\n",
    "X = reinterpret(Vec{2,Float64},x,(4,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Reinit for all sides for luls\n",
    "reinit!(feface,X,1)\n",
    "reinit!(feface,X,2)\n",
    "reinit!(feface,X,3)\n",
    "reinit!(feface,X,4)\n",
    "reinit!(feval,X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Array{Float64,1},1}:\n",
       " [1.61971,2.59153,1.61971]\n",
       " [1.96419,3.1427,1.96419] \n",
       " [1.41639,2.26623,1.41639]\n",
       " [2.51538,4.02462,2.51538]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feface.detJdS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test sum of the detJdS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test Summary:  | Pass  Total\n",
      "  sum of weights |    4      4\n"
     ]
    }
   ],
   "source": [
    "@testset \"sum of weights\" begin\n",
    "    @test norm(X[1]-X[2]) == sum(feface.detJdS[1])\n",
    "    @test norm(X[2]-X[3]) == sum(feface.detJdS[2])\n",
    "    @test norm(X[3]-X[4]) == sum(feface.detJdS[3])\n",
    "    @test norm(X[4]-X[1]) == sum(feface.detJdS[4])\n",
    "end;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Utilities just as for FEValues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "JuAFEM.QuadratureRule{2,Float64}([0.308642,0.493827,0.308642,0.493827,0.790123,0.493827,0.308642,0.493827,0.308642],ContMechTensors.Tensor{1,2,Float64,2}[[-0.774597,-0.774597],[0.0,-0.774597],[0.774597,-0.774597],[-0.774597,0.0],[0.0,0.0],[0.774597,0.0],[-0.774597,0.774597],[0.0,0.774597],[0.774597,0.774597]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_quadrule(feval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "JuAFEM.QuadratureRule{2,Float64}([0.555556,0.888889,0.555556],ContMechTensors.Tensor{1,2,Float64,2}[[-1.0,-0.774597],[-1.0,0.0],[-1.0,0.774597]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_quadrule(feface)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "JuAFEM.Lagrange{2,JuAFEM.RefCube,1}()"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_functionspace(feval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "JuAFEM.Lagrange{2,JuAFEM.RefCube,1}()"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_functionspace(feface)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "JuAFEM.Lagrange{2,JuAFEM.RefCube,1}()"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "JuAFEM.get_geometricspace(feval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "JuAFEM.Lagrange{2,JuAFEM.RefCube,1}()"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "JuAFEM.get_geometricspace(feface)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.1711718114942853"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "detJdV(feval,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.515384760593727"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "JuAFEM.detJdS(feface,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7872983346207417"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shape_value(feval,1)\n",
    "shape_value(feval,1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8872983346207417"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shape_value(feface,1)\n",
    "shape_value(feface,1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element ContMechTensors.Tensor{1,2,Float64,2}:\n",
       " -0.129538 \n",
       " -0.0863585"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shape_gradient(feval,1)\n",
    "shape_gradient(feval,1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element ContMechTensors.Tensor{1,2,Float64,2}:\n",
       " -0.123411 \n",
       " -0.0973988"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shape_gradient(feface,1)\n",
    "shape_gradient(feface,1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.21589614735851378"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shape_divergence(feval,1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.22080996917163048"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shape_divergence(feface,1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Float64,1}:\n",
       " 0.594664\n",
       " 0.948973\n",
       " 0.861089\n",
       " 0.937698"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = rand(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6677821588390144"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function_scalar_value(feval,1,u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6333242997314001"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function_scalar_value(feface,1,u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element ContMechTensors.Tensor{1,2,Float64,2}:\n",
       " 0.0453971\n",
       " 0.0283856"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function_scalar_gradient(feval,1,u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element ContMechTensors.Tensor{1,2,Float64,2}:\n",
       " 0.0426263\n",
       " 0.0333787"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function_scalar_gradient(feface,1,u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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   "source": []
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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 ],
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