elliptic3D.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3D Staggering example using a 3D Mimetic laplacian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.sparse.linalg import spsolve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from core import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/nutrik/Documents/Science/scodes/Python/pymole/core/div3D.py:27: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  Im[1:m+1, :] = sparse.eye(m, m, dtype=np.float, format='csr')\n",
      "/Users/nutrik/Documents/Science/scodes/Python/pymole/core/div3D.py:28: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  In[1:n+1, :] = sparse.eye(n, n, dtype=np.float, format='csr')\n",
      "/Users/nutrik/Documents/Science/scodes/Python/pymole/core/div3D.py:29: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  Io[1:o+1, :] = sparse.eye(o, o, dtype=np.float, format='csr')\n",
      "/Users/nutrik/Documents/Science/scodes/Python/pymole/core/div1D.py:53: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  D[i, j:j+k] = coeffs\n",
      "/Users/nutrik/Documents/Science/scodes/Python/pymole/core/grad1D.py:52: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  G[i, j:j+k] = coeffs\n",
      "/Users/nutrik/Documents/Science/scodes/Python/pymole/core/grad1D.py:72: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  A[i, 0:q] = coeffs\n",
      "/Users/nutrik/Documents/Science/scodes/Python/pymole/core/grad1D.py:78: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  G[0:p, 0:q] = A\n",
      "/Users/nutrik/Documents/Science/scodes/Python/pymole/core/grad1D.py:95: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  G[n_rows-p:n_rows, n_cols-q:n_cols] = A\n",
      "/Users/nutrik/Documents/Science/scodes/Python/pymole/core/grad3D.py:31: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  Im[1:m+1, :] = sparse.eye(m, m, dtype=np.float, format='csr')\n",
      "/Users/nutrik/Documents/Science/scodes/Python/pymole/core/grad3D.py:32: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  In[1:n+1, :] = sparse.eye(n, n, dtype=np.float, format='csr')\n",
      "/Users/nutrik/Documents/Science/scodes/Python/pymole/core/grad3D.py:33: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  Io[1:o+1, :] = sparse.eye(o, o, dtype=np.float, format='csr')\n",
      "/Users/nutrik/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:9: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  if __name__ == '__main__':\n"
     ]
    }
   ],
   "source": [
    "m = 5  # -> 7\n",
    "n = 6  # -> 8\n",
    "o = 7  # -> 9\n",
    "\n",
    "L = lap3D(2, m, 1, n, 1, o, 1)  # 3D Mimetic laplacian operator\n",
    "\n",
    "for i in range((m+2)*(n+2)*(o+2)):\n",
    "    if L[i,i] == 0:\n",
    "        L[i,i] = 1  # Impose Dirichlet BC\n",
    "\n",
    "RHS = np.zeros((m+2, n+2, o+2), dtype=np.float)\n",
    "\n",
    "RHS[..., 0] = 100  # Known value at the cube's front face\n",
    "\n",
    "RHS = np.reshape(RHS, ((m+2)*(n+2)*(o+2)), order='F')\n",
    "\n",
    "SOL = spsolve(L, RHS)  # L\\RHS\n",
    "\n",
    "SOL = np.reshape(SOL, ((m+2), (n+2), (o+2)), order='F')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = 1 #  Page to be displayed\n",
    "page = SOL[..., p]\n",
    "\n",
    "cs = plt.imshow(page.T)\n",
    "plt.colorbar(cs)\n",
    "plt.title('Poisson''s eq-n with Dirichlet BC: slice - {}'.format(p))\n",
    "plt.xlabel('m')\n",
    "plt.ylabel('n');"
   ]
  }
 ],
 "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}