notebook_adv_diff.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "from nutils import *\n",
    "import numpy, unittest\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import collections"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "nelems = 10\n",
    "degree = 1\n",
    "tol  = 1e-5\n",
    "ndims = 1\n",
    "extent = 1\n",
    "h = extent / nelems\n",
    "weak_bc = True\n",
    "v = 100    # convective velocity\n",
    "k = 1      # diffusivity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "domain, geom = mesh.rectilinear([numpy.linspace(0,extent,nelems+1)]*ndims)\n",
    "\n",
    "# prepare residual\n",
    "ns = function.Namespace()\n",
    "ns.pi = numpy.pi\n",
    "ns.x = geom\n",
    "ns.basis = domain.basis('discont', degree=degree)\n",
    "ns.u = 'basis_n ?lhs_n'\n",
    "ns.h = h\n",
    "ns.v = v\n",
    "ns.k = k\n",
    "# stabilization parameter\n",
    "if ns.k == 0:\n",
    "    ns.tau = ' h / (2 v)'\n",
    "else:\n",
    "    ns.peclet = ' 0.5 v h / k'\n",
    "    ns.tau = ' ((cosh(peclet) / sinh(peclet)) - (1 / peclet)) h / (2 v) '\n",
    "ns.D = 1       # continuity penalty coefficient\n",
    "ns.C = ' v '   # upwinding coefficient\n",
    "ns.ext = extent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# BCs and RHS\n",
    "\n",
    "# u(x) = [(gr-gl)/(exp(v/k) - 1)] [exp((v/k) x) - 1] + gl\n",
    "# u'(x)= (v/k)[(gr-gl)/(exp(v/k) - 1] [exp((v/k) x)]\n",
    "#   with u(0) = gl, u(extent) = gr \n",
    "ns.f = 0\n",
    "ns.gl = 1\n",
    "ns.gr = 0\n",
    "# Catch potential overflow exceptions\n",
    "if(numpy.exp(v/k) == float('inf')):\n",
    "    # exp(v/k) -> infinity (triggers overflow exception)\n",
    "    ns.dgl = ' 0 '\n",
    "    ns.dgr = '(v / k) (gr - gl) exp(ext)'\n",
    "else:\n",
    "    ns.dgl = '(v / k) ( (gr - gl) / (exp(v / k) - 1) )'\n",
    "    ns.dgr = '(v / k) ( (gr - gl) / (exp(v / k) - 1) ) (exp( (v / k) ext) )'\n",
    "\n",
    "# u(x) = exp(0.5x)\n",
    "#ns.f = ' (- 0.25 k + 0.5 v) exp( 0.5 x_0 )'\n",
    "#ns.dgl = ' 0.5 '\n",
    "#ns.dgr = ' 0.5 exp(0.5 ext) '\n",
    "#ns.gl = ' 1 '\n",
    "#ns.gr = ' exp(0.5 ext) '\n",
    "\n",
    "# u(x) = sin(2 pi x_0)\n",
    "#ns.f = ' (2 pi)^2 sin( 2 pi x_0 )'\n",
    "#ns.dg = ' 2 pi '\n",
    "#ns.g = '0'\n",
    "\n",
    "# u(x) = -cos(2 pi x_0)\n",
    "# ns.f = ' (2 pi)^2 cos( 2 pi x_0 )'\n",
    "# ns.dg = ' 0 '\n",
    "# ns.g = '1'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Imposing boundary conditions weakly.\n"
     ]
    }
   ],
   "source": [
    "# construct residual and inertia vector\n",
    "\n",
    "# Diffusive parts\n",
    "res = domain.integral('k basis_n,0 u_,0 - basis_n f' @ ns, geometry=ns.x, degree=5)\n",
    "res -= domain.interfaces.integral('- k [basis_n] n_0 {u_,0} - k {basis_n,0} n_0 [u]' @ ns, geometry=ns.x, degree=5)\n",
    "\n",
    "# Advective parts\n",
    "res += domain.integral('-v basis_n,0 u' @ ns, geometry=ns.x, degree=5)\n",
    "res += domain.interfaces.integral('- v [basis_n] n_0 ({u} - .5 C [u] n_0)' @ ns, geometry=ns.x, degree=5)\n",
    "# SUPG stabilized part\n",
    "res += domain.integral(' tau v basis_n,0 (v u_,0 - k (u_,0)_,0 - f )' @ ns, geometry=ns.x, degree=5)\n",
    "\n",
    "# C0 continuity residual\n",
    "res -= domain.interfaces.integral('D k [basis_n] n_0 [u]' @ ns, geometry=ns.x, degree=5)\n",
    "\n",
    "#Same BCs on both sides\n",
    "#    Diff\n",
    "#res += domain.boundary.integral('- k basis_n (0.5 (dg + u_,0)) n_0' @ ns, geometry=ns.x, degree=degree*2)\n",
    "#res += domain.boundary.integral(' D k basis_n,0 (g - u) n_0' @ ns, geometry=ns.x, degree=degree*2)\n",
    "#    Adv\n",
    "#res += domain.boundary.integral('v basis_n n_0 (0.5 (g + u) - .5 C (g - u) n_0)' @ ns, geometry=ns.x, degree=degree*2)\n",
    "\n",
    "if weak_bc:\n",
    "    print('Imposing boundary conditions weakly.')\n",
    "    # Differing BCs on both sides\n",
    "    #    Diff\n",
    "    res += domain.boundary['left'].integral('- k basis_n (0.5 (dgl + u_,0)) n_0' @ ns, geometry=ns.x, degree=degree*2)\n",
    "    res += domain.boundary['right'].integral('- k basis_n (0.5 (dgr + u_,0)) n_0' @ ns, geometry=ns.x, degree=degree*2)\n",
    "    res += domain.boundary['left'].integral(' D k basis_n,0 (gl - u) n_0' @ ns, geometry=ns.x, degree=degree*2)\n",
    "    res += domain.boundary['right'].integral(' D k basis_n,0 (gr - u) n_0' @ ns, geometry=ns.x, degree=degree*2)\n",
    "    #    Adv\n",
    "    res += domain.boundary['left'].integral('v basis_n n_0 (0.5 (gl + u) - .5 C (gl - u) n_0)' @ ns, geometry=ns.x, degree=degree*2)\n",
    "    res += domain.boundary['right'].integral('v basis_n n_0 (0.5 (gr + u) - .5 C (gr - u) n_0)' @ ns, geometry=ns.x, degree=degree*2)\n",
    "else:\n",
    "    print('Imposing boundary conditions strongly.')\n",
    "    #Strong BCs\n",
    "    # Enforce Dirichlet constraints\n",
    "    # Constraints are enforced by solving a least squares problem (can be solved exactly here)\n",
    "    sqr = domain.boundary['left'].integral('(u - gl)^2' @ ns, geometry=ns.x, degree=degree*2)\n",
    "    sqr += domain.boundary['right'].integral('(u - gr)^2' @ ns, geometry=ns.x, degree=degree*2)\n",
    "    cons = solver.optimize('lhs', sqr, droptol=1e-15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Here comes the Jacobian\n",
      "(20, 20)\n",
      "[[  5.03500454e+03   9.99545980e+00  -5.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
      " [ -8.50045402e+01   5.03900454e+03  -4.93900000e+03  -5.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
      " [ -5.00000000e+00  -5.03900000e+03   5.03900454e+03   9.99545980e+00\n",
      "   -5.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
      " [  0.00000000e+00  -5.00000000e+00  -9.00045402e+01   5.03900454e+03\n",
      "   -4.93900000e+03  -5.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
      " [  0.00000000e+00   0.00000000e+00  -5.00000000e+00  -5.03900000e+03\n",
      "    5.03900454e+03   9.99545980e+00  -5.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
      " [  0.00000000e+00   0.00000000e+00   0.00000000e+00  -5.00000000e+00\n",
      "   -9.00045402e+01   5.03900454e+03  -4.93900000e+03  -5.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
      " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "   -5.00000000e+00  -5.03900000e+03   5.03900454e+03   9.99545980e+00\n",
      "   -5.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
      " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00  -5.00000000e+00  -9.00045402e+01   5.03900454e+03\n",
      "   -4.93900000e+03  -5.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
      " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00  -5.00000000e+00  -5.03900000e+03\n",
      "    5.03900454e+03   9.99545980e+00  -5.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
      " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00  -5.00000000e+00\n",
      "   -9.00045402e+01   5.03900454e+03  -4.93900000e+03  -5.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
      " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "   -5.00000000e+00  -5.03900000e+03   5.03900454e+03   9.99545980e+00\n",
      "   -5.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
      " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00  -5.00000000e+00  -9.00045402e+01   5.03900454e+03\n",
      "   -4.93900000e+03  -5.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
      " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00  -5.00000000e+00  -5.03900000e+03\n",
      "    5.03900454e+03   9.99545980e+00  -5.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
      " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00  -5.00000000e+00\n",
      "   -9.00045402e+01   5.03900454e+03  -4.93900000e+03  -5.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
      " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "   -5.00000000e+00  -5.03900000e+03   5.03900454e+03   9.99545980e+00\n",
      "   -5.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
      " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00  -5.00000000e+00  -9.00045402e+01   5.03900454e+03\n",
      "   -4.93900000e+03  -5.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
      " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00  -5.00000000e+00  -5.03900000e+03\n",
      "    5.03900454e+03   9.99545980e+00  -5.00000000e+00   0.00000000e+00]\n",
      " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00  -5.00000000e+00\n",
      "   -9.00045402e+01   5.03900454e+03  -4.93900000e+03  -5.00000000e+00]\n",
      " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "   -5.00000000e+00  -5.03900000e+03   5.03900454e+03   1.49954598e+01]\n",
      " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "    0.00000000e+00  -5.00000000e+00  -9.00045402e+01   5.03500454e+03]]\n",
      "[-5040.   -10.     0.     0.     0.     0.     0.     0.     0.     0.\n",
      "     0.     0.     0.     0.     0.     0.     0.     0.     0.    50.]\n",
      "solve > solver returned with residual 3e-12\n"
     ]
    }
   ],
   "source": [
    "# find lhs such that res == 0 and substitute this lhs in the namespace\n",
    "if weak_bc:\n",
    "    lhs = solver.solve_linear('lhs', res)\n",
    "else:\n",
    "    lhs = solver.solve_linear('lhs', res, constrain=cons)\n",
    "ns = ns(lhs=lhs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f9b05175358>]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111855eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot solution\n",
    "bezier = domain.sample('bezier', 9)\n",
    "x, u = bezier.eval([ns.x, ns.u])\n",
    "fig=plt.figure(figsize=(18, 16), dpi= 80, facecolor='w', edgecolor='k')\n",
    "plt.plot(x, u)\n",
    "# plt.ylim(-2,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}