V&V.ipynb

{
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   "source": [
    "# Verification and Validation\n",
    "\n",
    "Now we have a working solver (the fast version of SOR) we need to know if\n",
    "* we are solving the the right equations?\n",
    "* we are solving the equations right?\n",
    "\n",
    "These two questions are related to the process of Validation and Verification (often called V&V).   \n",
    "\n",
    "The fist question asks if the PDE we are solving is a proper representation of the physical problem we are trying to understand.  More on this later.\n",
    "\n",
    "The second is all about the errors in our solution. We need to think about sources of error in our calculation and decide if our solver is behaving properly.\n",
    "\n",
    "## Sources of Error\n",
    "1. Round off - Are the numerical equations implemented in a way which maintains accuracy?  Are we using a sufficiently precise representation of the numbers?\n",
    "2. Implementation - Have we got bugs in the code? \n",
    "3. Accuracy - In solving the equations have we acheived a sufficient degree of convergence?\n",
    "4. Truncation - The order of accuracy of our numerical scheme.\n",
    "\n",
    "To look at this we need a solver (which needs some libraries and our Grid class)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "smooth-terrace",
   "metadata": {
    "jupyter": {
     "source_hidden": true
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    "tags": []
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "\n",
    "class Grid:\n",
    "    '''Class defining a 2D computational grid.  The grid object\n",
    "    contains is a regular cartesian grid with a single variable, u.\n",
    "    It stores information about the number of grid points in the i\n",
    "    and j directions, the ordinates of these points and the bottom\n",
    "    left corner of the gird (the origin) and the top right corner\n",
    "    (the extent).\n",
    "    \n",
    "    Written by Prof David Ingram, School of Engineering\n",
    "    (c) 2021 The University of Edinburgh\n",
    "    Licensed under CC-BY-NC.'''\n",
    "    \n",
    "    def __init__(self,ni,nj):\n",
    "        # set up information about the grid\n",
    "        self.origin = (0.0, 0.0)  # bottom left\n",
    "        self.extent = (1.0, 1.0)  # top right\n",
    "        self.Ni = ni # grid points in i direction\n",
    "        self.Nj = nj # grid points in j direction\n",
    "        \n",
    "        # initialse x,y and u arrays\n",
    "        self.u = np.zeros((nj, ni))\n",
    "        self.x = np.zeros((nj, ni))\n",
    "        self.y = np.zeros((nj, ni))\n",
    "\n",
    "    def set_origin(self,x0,y0):\n",
    "        self.origin = (x0, y0)\n",
    "    \n",
    "    def set_extent(self,x1,y1):\n",
    "        self.extent = (x1, y1)\n",
    "        \n",
    "    def generate(self,Quiet=True):\n",
    "        '''generate a uniformly spaced grid covering the domain from the\n",
    "        origin to the extent.  We are going to do this using linspace from\n",
    "        numpy to create lists of x and y ordinates and then the meshgrid\n",
    "        function to turn these into 2D arrays of grid point ordinates.'''\n",
    "        x_ord = np.linspace(self.origin[0], self.extent[0], self.Ni)\n",
    "        y_ord = np.linspace(self.origin[1], self.extent[1], self.Nj)\n",
    "        self.x, self.y = np.meshgrid(x_ord,y_ord)\n",
    "        if not Quiet:\n",
    "            print(self)\n",
    "\n",
    "    def Delta_x(self):\n",
    "        # calculate delta x\n",
    "        return self.x[0,1]-self.x[0,0]\n",
    "    \n",
    "    def Delta_y(self):\n",
    "        # calculate delta y\n",
    "        return self.y[1,0]-self.y[0,0]\n",
    "    \n",
    "    def find(self,point):\n",
    "        '''find the i and j ordinates of the grid cell which contains \n",
    "        the point (x,y).  To do this we calculate the distance from\n",
    "        the point to the origin in the x and y directions and then\n",
    "        divide this by delta x and delta y.  The resulting real ordinates\n",
    "        are converted to indices using the int() function.'''\n",
    "        grid_x = (point[0] - self.origin[0])/self.Delta_x()\n",
    "        grid_y = (point[1] - self.origin[1])/self.Delta_y()\n",
    "        return int(grid_x), int(grid_y)\n",
    "    \n",
    "    def __str__(self):\n",
    "        # describe the object when asked to print it\n",
    "        return 'Uniform {}x{} grid from {} to {}.'.format(self.Ni, self.Nj, self.origin, self.extent)\n",
    "    \n",
    "def SOR(mesh,tol=0.5e-7,maxit=10000):\n",
    "    '''Sucessive over Relaxation method for the solution of\n",
    "    the Laplace equation with checkerboarding.  The solver \n",
    "    assumes a uniform Cartesian mesh and uses the optimal\n",
    "    value of the acceleration parameter, omega.\n",
    "    \n",
    "    The method works on the grid stored in the mesh object.  \n",
    "    It will continue itterating until the relative difference \n",
    "    between u^{n+1} and u^n is less than tol. It will also stop \n",
    "    if we have done more than maxit itterations.\n",
    "    \n",
    "    The solution stored in the mesh.u variable is updated\n",
    "            \n",
    "    Written by Prof David Ingram, School of Engineering\n",
    "    (c) 2021 The University of Edinburgh\n",
    "    Licensed under CC-BY-NC.'''\n",
    "\n",
    "    # calculate the optimal value of omega\n",
    "    lamda = (np.cos(np.pi/mesh.Ni)+np.cos(np.pi/mesh.Nj))**2/4\n",
    "    omega = 2/(1+np.sqrt(1-lamda))\n",
    "\n",
    "    # calculate the coefficients\n",
    "    beta = mesh.Delta_x()/mesh.Delta_y()\n",
    "    beta_sq = beta**2\n",
    "    C_beta = 1/(2*(1+beta_sq))\n",
    "    \n",
    "    # initialise u_new \n",
    "    u_new = mesh.u.copy()\n",
    "    \n",
    "    # build the list of k values    \n",
    "    offset = mesh.u.shape[1] # how far away are j+1 and j-1\n",
    "\n",
    "    # create some empty lists\n",
    "    centre = []; north = []; east = []; south=[]; west = []  \n",
    "    # loop over all the interior points\n",
    "    for j in range(1,mesh.Nj-1):\n",
    "        for i in range(1,mesh.Ni-1):\n",
    "            k=i+offset*j  # calculate the k value\n",
    "            # save the south, west, centre, east and north points\n",
    "            centre.append(k)\n",
    "            north.append(k+offset)\n",
    "            east.append(k+1)\n",
    "            south.append(k-offset)\n",
    "            west.append(k-1)\n",
    "\n",
    "    # itteration\n",
    "    for it in range(maxit):\n",
    "        \n",
    "        # red squares [::2] means from 0 to n in steps of 2, remember\n",
    "        # we are taking alternate values from the lists centre, east,\n",
    "        # north, west and south and using them as indicies into the \n",
    "        # u_new array.\n",
    "        u_new.flat[centre[::2]] = (1-omega) * u_new.flat[centre[::2]] + \\\n",
    "                                    omega * C_beta*(u_new.flat[north[::2]]+ \\\n",
    "                                    u_new.flat[south[::2]]+ \\\n",
    "                                    beta_sq*(u_new.flat[east[::2]]+ \\\n",
    "                                             u_new.flat[west[::2]]))\n",
    "        \n",
    "        # black squares [1::2] means from 1 to n in steps of 2\n",
    "        u_new.flat[centre[1::2]] = (1-omega) * u_new.flat[centre[1::2]] + \\\n",
    "                                    omega * C_beta*(u_new.flat[north[1::2]]+ \\\n",
    "                                    u_new.flat[south[1::2]]+ \\\n",
    "                                    beta_sq*(u_new.flat[east[1::2]]+ \\\n",
    "                                             u_new.flat[west[1::2]]))\n",
    "\n",
    "        # compute the difference between the new and old solutions\n",
    "        err = np.max(np.abs(mesh.u-u_new))\n",
    "        \n",
    "        # update the solution\n",
    "        mesh.u = np.copy(u_new)\n",
    "        \n",
    "        # converged?\n",
    "        if err < tol:\n",
    "            break\n",
    "    \n",
    "    if it+1 == maxit:\n",
    "        print('Checkerboard Gauss-Seidel itteration failed to converge, error = {}'.format(err))\n",
    "    return it+1,err"
   ]
  },
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   "cell_type": "markdown",
   "id": "dietary-share",
   "metadata": {},
   "source": [
    "## The test problem\n",
    "Were going to use the same test problem as before:  \n",
    "\n",
    "$$0=u_{xx}+u_{yy}$$\n",
    "subject to the boundary conditions\n",
    "$$\\begin{align*}\n",
    "u(x,0)&=0&0\\le x\\le 2 \\\\\n",
    "u(x,1)&=0&0\\le x\\le 2 \\\\\n",
    "u(0,y)&=0&0\\le y \\le 1\\\\\n",
    "u(2,y)&=\\sin 2\\pi y&0\\le y \\le 1.\n",
    "\\end{align*}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "solid-maine",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Example929(ni,nj):\n",
    "    # set up a mesh\n",
    "    mesh = Grid(ni,nj)\n",
    "    mesh.set_extent(2.0,1.0)\n",
    "    mesh.generate()\n",
    "    # now the RHS boundary condition\n",
    "    mesh.u[:,-1]=np.sin(2*np.pi*mesh.y[:,-1])\n",
    "    return mesh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "sudden-valuable",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Test problem on a fine grid\n",
    "test = Example929(161,81)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "governmental-marathon",
   "metadata": {},
   "source": [
    "## Round off\n",
    "\n",
    "The `numpy.finfo()` function can be used to tell us some useful information about the representation of numbers in Python.  If we apply this to the u array, we get:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "genetic-atmosphere",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Machine parameters for float64\n",
      "---------------------------------------------------------------\n",
      "precision =  15   resolution = 1.0000000000000001e-15\n",
      "machep =    -52   eps =        2.2204460492503131e-16\n",
      "negep =     -53   epsneg =     1.1102230246251565e-16\n",
      "minexp =  -1022   tiny =       2.2250738585072014e-308\n",
      "maxexp =   1024   max =        1.7976931348623157e+308\n",
      "nexp =       11   min =        -max\n",
      "---------------------------------------------------------------\n",
      "\n"
     ]
    }
   ],
   "source": [
    "info  = np.finfo(test.u.dtype)\n",
    "print(info)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "matched-trigger",
   "metadata": {},
   "source": [
    "This tells us\n",
    "* u is stored as a 64 bit (8 byte) floating point number.\n",
    "* we have approximately 15 decimal places of accuracy\n",
    "* 11 bits are used to store the exponent which can be between (-1022 and 1024)\n",
    "* the smallest representible number (at which a number becomes indistinguishable from zero) is 2.2250738585072014e-308\n",
    "* the largest representible number (at which an overflow error occurs) is 1.7976931348623157e+308\n",
    "* the largest number, ε, for which 1 + ε = 1 is 2.2204460492503131e-16\n",
    "\n",
    "Double precision is considered standard for most numeric computations.  We can use more precision but this will slow down the computation.\n",
    "\n",
    "The ammount of memory used to store u is 8 times the size of u:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "empirical-liberal",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "102 kbytes\n"
     ]
    }
   ],
   "source": [
    "print('{:.0f} kbytes'.format(test.u.size*8/1024))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "individual-booking",
   "metadata": {},
   "source": [
    "## Implementation\n",
    "\n",
    "Now we need to check for bugs in the code. \n",
    "\n",
    "Oddly the best way to do this is to try to solve probkems where we know **nothing** should happen.  If we solve\n",
    "$$0=u_{xx}+u_{yy}$$\n",
    "subject to the boundary conditions\n",
    "$$\\begin{align*}\n",
    "u(x,0)&=0&0\\le x\\le 1 \\\\\n",
    "u(x,1)&=0&0\\le x\\le 1 \\\\\n",
    "u(0,y)&=0&0\\le y \\le 1\\\\\n",
    "u(1,y)&=0&0\\le y \\le 1.\n",
    "\\end{align*}$$\n",
    "starting with the initial conditions $$u(x,y)=0$$ nothing should change."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "annual-bobby",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged after 1 itterations, final residual is 0.0\n",
      "[[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "nulltest = Grid(11,11)\n",
    "nulltest.generate()\n",
    "itt, err = SOR(nulltest)\n",
    "print('Converged after {} itterations, final residual is {}'.format(itt,err))\n",
    "print(nulltest.u)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "widespread-shaft",
   "metadata": {},
   "source": [
    "Now we can try again with a problem where u is zero and all the boundary conditions are 1.  We are going to set `tol = 1.0e-15` to ensure that we have a completely converged solution! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "paperback-reference",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
      " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
      " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
      " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
      " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
      " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
      " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
      " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
      " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
      " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]]\n",
      "Converged after 63 itterations, final residual is 6.661338147750939e-16\n",
      "[[1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]]\n"
     ]
    }
   ],
   "source": [
    "nulltest.u[:,:] = 1\n",
    "nulltest.u[1:-1,1:-1] = 0\n",
    "print(nulltest.u)\n",
    "itt, err = SOR(nulltest,tol=1e-15)\n",
    "print('Converged after {} itterations, final residual is {}'.format(itt,err))\n",
    "print(nulltest.u)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "suburban-exclusive",
   "metadata": {},
   "source": [
    "## Accuracy\n",
    "\n",
    "For problem 9.29 we have an analytical solution,\n",
    "$$u=\\sin2\\pi y\\frac{\\sinh 2\\pi x}{\\sinh 4\\pi}.$$\n",
    "\n",
    "If we create a model solution we can compare the two, looking at the error between them.  This can be done eirther by plotting the local error against x and y or by calculating the L2 norm:\n",
    "$$||e(x,y)||_2=\\sqrt{\\sum_i\\sum_j e^2_{ij}}$$\n",
    "\n",
    "We don't have to do this by hand as numpy provides the function `numpy.linalg.norm()` to compute the L2 norm.\n",
    "\n",
    "We need a function to compute the analytical solution and then we want to compare.  In this case I'm going to use a high value of `tol=0.5e-4` which will give us around 4 decimal places of accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "above-break",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solver took 0.701 seconds.\n",
      "Converged after 146 itterations, final residual is 4.606725047696249e-05\n",
      "L2 norm = 0.006046492778863192\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "def analytical929(mesh):\n",
    "    # take a copy of the u array\n",
    "    u = np.copy(mesh.u)\n",
    "    # calculate the analytical solution\n",
    "    u[:,:] = np.sin(2*np.pi*mesh.y)*np.sinh(2*np.pi*mesh.x)/np.sinh(4*np.pi)\n",
    "    return u\n",
    "\n",
    "exact = analytical929(test)\n",
    "\n",
    "start = time.process_time()\n",
    "itt, err = SOR(test,tol=0.5e-4)\n",
    "stop = time.process_time()\n",
    "print(\"Solver took {:.3g} seconds.\".format(stop-start))\n",
    "print('Converged after {} itterations, final residual is {}'.format(itt,err))\n",
    "\n",
    "err = test.u - exact\n",
    "print('L2 norm =',np.linalg.norm(err))\n",
    "\n",
    "# plot the solution\n",
    "fig, ax1 = plt.subplots()\n",
    "cmap = plt.get_cmap('PiYG')\n",
    "cf = ax1.contourf(test.x,test.y,test.u,cmap=cmap)\n",
    "fig.colorbar(cf, ax=ax1)\n",
    "ax1.set_title(f'Example 9.29 ({test.Ni} x {test.Nj} grid)')\n",
    "plt.show()\n",
    "\n",
    "# plot the error\n",
    "fig, ax1 = plt.subplots()\n",
    "cf = ax1.contour(test.x,test.y,err)\n",
    "ax1.set_title(f'Absolute error on a {test.Ni} x {test.Nj} grid')\n",
    "fig.colorbar(cf, ax=ax1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "governing-wells",
   "metadata": {},
   "source": [
    "You can see that the We could try converging further, setting `tol=1.0e-15`.  If we call the solver again without re-initialising test we will just continue from where we were,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "sitting-folder",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solver took an additional 4.12 seconds.\n",
      "Converged after 987 itterations, final residual is 9.992007221626409e-16\n",
      "L2 norm = 0.005798100391264446\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "start = time.process_time()\n",
    "it2, err = SOR(test,tol=1e-15)\n",
    "stop = time.process_time()\n",
    "print(\"Solver took an additional {:.3g} seconds.\".format(stop-start))\n",
    "print('Converged after {} itterations, final residual is {}'.format(itt+it2,err))\n",
    "\n",
    "err = test.u - exact\n",
    "print('L2 norm =',np.linalg.norm(err))\n",
    "\n",
    "# plot the solution\n",
    "fig, ax1 = plt.subplots()\n",
    "cmap = plt.get_cmap('PiYG')\n",
    "cf = ax1.contourf(test.x,test.y,test.u,cmap=cmap)\n",
    "fig.colorbar(cf, ax=ax1)\n",
    "ax1.set_title(f'Example 9.29 ({test.Ni} x {test.Nj} grid)')\n",
    "plt.show()\n",
    "\n",
    "# plot the error\n",
    "fig, ax1 = plt.subplots()\n",
    "cf = ax1.contour(test.x,test.y,err)\n",
    "ax1.set_title(f'Absolute error on a {test.Ni} x {test.Nj} grid')\n",
    "fig.colorbar(cf, ax=ax1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "muslim-genealogy",
   "metadata": {},
   "source": [
    "## Truncation error\n",
    "Now we know we have an accurate and precise (i.e. properly implemented with accurate arithmetic) solution, we see if the truncation error is behaving the way we expect.  Remember that the central difference approximation to the 2nd derivative is:\n",
    "$$\\frac{\\partial^2 u}{\\partial x^2} = \\frac{u_W-2u_O+u_E}{\\Delta x^2}+O(\\Delta x^2).$$\n",
    "\n",
    "Since the truncation error is O(Δx<sup>2</sup>) we expect the errors to decrease proortionately to Δx<sup>2</sup>.\n",
    "\n",
    "The GCI analysis (see the lecture) allows us to:\n",
    "* estimate the apparent order of accuracy, p (i.e. the errors are decreasing proportionate to Δx<sup>p</sup>), and\n",
    "* test to see if the grid is sufficiently fine that this is the case.\n",
    "\n",
    "Recall that we need:\n",
    "* a sequence of grids (N=1, 2, 3 ... ) where Δx and Δy approximately double each time (N=1 is the finest grid).\n",
    "* an integrated quantity which we measure over the same region of the domain on each grid. I'm going to use\n",
    "$$U=\\int_{1.0}^{1.95}u(x,0.25)\\,dx$$\n",
    "* some routines to compute p, the Grid Convergence Index and to estimate U on a grid where Δx=0.\n",
    "\n",
    "Were going to use the `refinement_analysis` class which can be downloaded from LEARN. It should be placed in the same directory as this Jupyter notebook.  We also need a function to do the integration (we can use  Simpson's rule from `scipy.integrate`)  to do this and the `find` function from the `Grid` class.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "greatest-might",
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.integrate as integrate\n",
    "from refinement_analysis import refinement_analysis\n",
    "\n",
    "def integrate_u_dx(mesh,x0,x1,y):\n",
    "    '''Calculate U=\\int_{1.0}^{1.95)u(x,0.25) dx  using the\n",
    "    u value stored on the grid and simpsons rule'''\n",
    "    \n",
    "    # find the left and right grid points\n",
    "    i0,j = mesh.find((x0,y))\n",
    "    i1,j = mesh.find((x1,y))\n",
    "\n",
    "    # add 1 to i1 as we are going to use it as an upper \n",
    "    # bound forarray slicing\n",
    "    i1 = i1 +1\n",
    "    \n",
    "    # integrate\n",
    "    return integrate.simps(mesh.u[j,i0:i1],mesh.x[j,i0:i1])\n",
    "\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "encouraging-boards",
   "metadata": {},
   "source": [
    "We then need to set up a sequence of grids based on grid doubling. The number of grid points in each direction should be given by $$N =2^n m + 1$$ where n is the grid index and m is an integer.  For our problem we are going to use\n",
    "$$N_i=2^n 20 + 1\\text{ and }N_j=2^n 10 + 1$$\n",
    "\n",
    "The following script creates a sequence of grids and solves them all.  The upper limit on the `range(5,-1,-1)` is the grid index of the finest grid.  Grid 7 takes about 40 minutes to run on my macbook pro. Grid 6, takes a much more reasonable three and a half minutes. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "apart-import",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Uniform 1281x641 grid from (0.0, 0.0) to (2.0, 1.0).\n",
      "The solver converged after 4061 itterations, it took 0:47:17, final residual is 4.9960036108132044e-15\n",
      "Integrated value is  0.11595119458119807 \n",
      "\n",
      "Uniform 641x321 grid from (0.0, 0.0) to (2.0, 1.0).\n",
      "The solver converged after 2018 itterations, it took 0:05:59, final residual is 4.884981308350689e-15\n",
      "Integrated value is  0.11595482347649985 \n",
      "\n",
      "Uniform 321x161 grid from (0.0, 0.0) to (2.0, 1.0).\n",
      "The solver converged after 1020 itterations, it took 0:00:38, final residual is 4.827735433643454e-15\n",
      "Integrated value is  0.11596933925855846 \n",
      "\n",
      "Uniform 161x81 grid from (0.0, 0.0) to (2.0, 1.0).\n",
      "The solver converged after 517 itterations, it took 0:00:03, final residual is 4.911869522228329e-15\n",
      "Integrated value is  0.11602740558304181 \n",
      "\n",
      "Uniform 81x41 grid from (0.0, 0.0) to (2.0, 1.0).\n",
      "The solver converged after 264 itterations, it took 0:00:00, final residual is 3.845881946240581e-15\n",
      "Integrated value is  0.11625972091743786 \n",
      "\n",
      "Uniform 41x21 grid from (0.0, 0.0) to (2.0, 1.0).\n",
      "The solver converged after 136 itterations, it took 0:00:00, final residual is 3.885780586188048e-15\n",
      "Integrated value is  0.11731643012556958 \n",
      "\n",
      "Uniform 21x11 grid from (0.0, 0.0) to (2.0, 1.0).\n",
      "The solver converged after 71 itterations, it took 0:00:00, final residual is 3.913536161803677e-15\n",
      "Integrated value is  0.08531986116064406 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "import datetime # just seconds may not be enough\n",
    "\n",
    "# we need some lists u and dx values\n",
    "U_val = []\n",
    "dx_val = []\n",
    "run_time = []\n",
    "n_pts =[]\n",
    "for grid_index in range(6,-1,-1):\n",
    "    ni = 20*2**grid_index + 1\n",
    "    nj = 10*2**grid_index + 1\n",
    "    n_pts.append(ni*nj)\n",
    "    \n",
    "    # set up the problem\n",
    "    test = Example929(ni,nj)\n",
    "    print(test)\n",
    "    \n",
    "    # solve it with 14 d.p. precision and a lot of itterations\n",
    "    start = time.process_time()\n",
    "    itt, err = SOR(test,tol=0.5e-14,maxit=1000000)\n",
    "    stop = time.process_time()\n",
    "    print(\"The solver converged after {} itterations, it took {}, final residual is {}\" \\\n",
    "          .format(itt,datetime.timedelta(seconds=int(stop-start)),err))\n",
    "\n",
    "    # save dx and the integral\n",
    "    dx_val.append(test.Delta_x())\n",
    "    U_val.append(integrate_u_dx(test,1.0,1.95,0.25))\n",
    "    run_time.append(stop-start)\n",
    "          \n",
    "    print('Integrated value is ',U_val[-1],'\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "pleasant-cemetery",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Refinement Analysis on 7 grids.\n",
      "\n",
      "Grid Delta x ratio  \\int_{1.0}^{1.95}u(x,0.25) dx\n",
      "-------------------------------------------------\n",
      "   1 0.001563     2  0.115951\n",
      "   2 0.003125     2  0.115955\n",
      "   3 0.00625     2  0.115969\n",
      "   4  0.0125     2  0.116027\n",
      "   5   0.025     2   0.11626\n",
      "   6    0.05     2  0.117316\n",
      "   7     0.1   --- 0.0853199\n",
      "------------------------------------------------- \n",
      "\n",
      "order of convergence, p =   2.00\n",
      "\n",
      "Grids       GCI\n",
      "---------------\n",
      " 1  2 1.304e-05\n",
      " 2  3 5.216e-05\n",
      " 3  4 0.0002086\n",
      " 4  5 0.0008343\n",
      " 5  6  0.003787\n",
      " 6  7    0.1136\n",
      "---------------\n",
      "\n",
      " Grid Step  GCI Ratio Converged\n",
      "-------------------------------\n",
      " 1 2  2 3           1 True\n",
      " 2 3  3 4           1 True\n",
      " 3 4  4 5           1 True\n",
      " 4 5  5 6      0.8812 False\n",
      " 5 6  6 7      0.1333 False\n",
      "-------------------------------\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# lets to the refinement analysis\n",
    "analysis = refinement_analysis(dx_val,U_val)\n",
    "analysis.report(r'\\int_{1.0}^{1.95}u(x,0.25) dx')\n",
    "analysis.plot(True,r'$\\int_{1.0}^{1.95}u(x,0.25) dx$')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "friendly-plenty",
   "metadata": {},
   "source": [
    "### Analysis\n",
    "\n",
    "The refinement analysis shows\n",
    "* _p_ = 2.0, so our 2nd order method has an apparent order of accuracy of 2.  Which is reasuring.\n",
    "* The graph shows that the coarsest grid (Δx = 0.1) is behaving differently from the other grids which seem to be converging as Δx goes to zero.\n",
    "* The GCI Ratios show that the solution on the five finest grids is safely in the asymptotic region where the error is proprtional to Δx<sup>2</sup>.  This means (for the test problem) we need Δx < 0.025 m. This means we need to use at least the 81 x 41 gird. Which takes less than 1 second to run.\n",
    "\n",
    "Our final choice of grid depends on \n",
    "* How accurate a solution we want, and\n",
    "* How long we are prepared to wait.\n",
    "\n",
    "All this means that the 161 x 81 grid (grid 4, Δx=0.0125) we've been using is fine enough to give a **grid converged** solution and we can be confident that the solution can be used.   If we are prepared to wait a little longer than 2 seconds we can use the 321 x 161 grid and wait 20 seconds for a more accurate answer."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "modular-narrow",
   "metadata": {},
   "source": [
    "## Runtime\n",
    "It's interesting to look at the time taken to get a solution on different sizes of grid. The following log-log graph shows the totoal number of grid points (i.e. _N_ = _Ni_ x _Nj_) plotted against the runtime in seconds.  Plotted like this we can see there is a dramatic increase in the work needed with increasing _N_.  It can be shown that the number of mathematical opperations performed is O(_N_<sup>2</sup>_m_) where _m_ is the number of itterations performed.  \n",
    "\n",
    "Although SOR converges faster than Gauss-Siedel and Jacobi all three can only be proved to converge after an infinite number of itterations.  \n",
    "\n",
    "Faster (but more complicated) Krylov subspace methods can be used which converge in a finite number of itterations. Fortunately for us `scipy.linalg` provides some efficient implementations of these methods which will be looked at in annother workbook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "labeled-first",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the runtime\n",
    "plt.loglog(n_pts,run_time,'o')\n",
    "plt.title('Runtime')\n",
    "plt.xlabel('N')\n",
    "plt.ylabel('runtime (s)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "august-whole",
   "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": "3.9.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}