{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Theory" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are studying the 1D heat equation on an interval $[0, x_0] \\subset \\mathbb{R}$:\n", "\n", "$$\n", "\\frac{\\partial T}{\\partial t}(x, t) = \\chi \\frac{\\partial^2 T}{\\partial x^2} (x,t)\n", "$$\n", "\n", "with initial conditions:\n", "\n", "$$\n", "T(x, t=0) = \\left\\{ \n", " \\begin{array}{l l}\n", " 2 \\, T_0 \\frac{x}{x_0} & \\text{if $0 \\leq x \\leq \\frac{x_0}{2}$}\\\\\n", " 2 \\, T_0 \\frac{x_0 - x}{x_0} & \\text{if $\\frac{x_0}{2} \\leq x \\leq x_0 $}\n", " \\end{array} \\right.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are two terms in this equation:\n", "\n", "- a first order partial derivative (in time)\n", "- a second order partial derivative (in space)\n", "\n", "To discretize them, we are using a finite difference technique. To derive the discretization, we start with the well-known Taylor expansion of a function $f$ at point $a$ up to the second order in $h$, a variable that is taken as \"small\":\n", "\n", "$$\n", "f(a + h) = f(a) + h \\, f'(a) + \\frac{h^2}{2} f''(a) + o(h^2)\n", "$$\n", "\n", "Replacing $h$ by $-h$ yields the following:\n", "\n", "$$\n", "f(a - h) = f(a) - h \\, f'(a) + \\frac{h^2}{2} f''(a) + o(h^2)\n", "$$\n", "\n", "Summing the last two relations and reorganizing terms yields:\n", "\n", "$$\n", "f''(a) \\approx \\frac{1}{h^2} \\left( f(a - h) - 2 f(a) + f(a + h) \\right)\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using terms up to the the first order yields the following discretization for a first order derivative in the neighborhood of a point $a$:\n", "\n", "$$\n", "f'(a) \\approx \\frac{1}{h} \\left( f(a + h) - f(a) \\right)\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Time and space are both discretized. This means that the temperature distribution we are solving for are indexed by integer indices for the space and the time variable. \n", "\n", "- time is denoted by a superscript: $T(t=n) = T^n$. There is a theoretically unlimited number of timesteps for which we will solve the equation, therefore we don't specify a maximum numbering for the time steps.\n", "- space is denoted by a subscript: $T(x=i) = T_i$. The segment $[0, x_0]$ is meshed with $N$ meshpoints.\n", "\n", "We denote by $X^n$ the vector of unknowns at a given timestep (we exclude $T_1$ and $T_N$, as they are equal to zero):\n", "\n", "$$\n", "X^n = \\begin{pmatrix}\n", "T_2^n \\\\\n", "T_3^n \\\\\n", "\\vdots \\\\\n", "T_{N-2}^n \\\\\n", "T_{N-1}^n\n", "\\end{pmatrix}\n", "$$\n", "\n", "Discretizing the original equation with this notation we can obtain multiple systems of equations to solve. We'll derive the most general case, using a parameter $\\theta$ that acts as a weight for which values of time to consider in the spatial derivative. We obtain the following:\n", "\n", "$$\n", "\\frac{X^{n+1} - X^n}{\\delta t} = \\frac{1 - \\theta}{(\\delta x)^2} M X^n + \\frac{\\theta}{(\\delta x)^2} M X^{n+1} \n", "$$\n", "\n", "Where $\\delta t$ and $\\delta x$ are the mesh steps in time and space and $M$ a tridiagonal $N - 2 \\times N -2$ size matrix with values $(1, -2, 1)$ on the tridiagonal.\n", "\n", "Reordering the terms in the above equation yields the following:\n", "\n", "$$\n", "\\left( I_n - \\lambda \\theta M \\right) X^{n+1} = \\left(I_n + \\lambda (1 - \\theta) M \\right) X^n\n", "$$\n", "\n", "This last equation is a linear matrix system that can be solved with standard tools of linear algebra that ship with Numpy or Scipy. This is what we're going to do below." ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Practical implementation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We start by activating the pylab mode for this notebook." ] }, { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline\n", "rcParams[\"figure.figsize\"] = (10, 6)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We then specify our space mesh." ] }, { "cell_type": "code", "collapsed": false, "input": [ "meshsize = 101\n", "x = linspace(0, 2 * pi, num=meshsize)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We then construct the tridiagonal matrix $M$ using the following [snippet from StackOverflow](http://stackoverflow.com/questions/5842903/block-tridiagonal-matrix-python)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import scipy.sparse\n", "\n", "def get_matrix_M(meshsize):\n", " diag_rows = np.array([[1] * meshsize,\n", " [-2] * meshsize,\n", " [1] * meshsize])\n", " \n", " positions = [-1, 0, 1]\n", " return scipy.sparse.spdiags(diag_rows, positions, meshsize, meshsize)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We verify that this works correctly below:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "M = get_matrix_M(x.shape[0])\n", "print M.shape\n", "M.todense()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(101, 101)\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [ "matrix([[-2, 1, 0, ..., 0, 0, 0],\n", " [ 1, -2, 1, ..., 0, 0, 0],\n", " [ 0, 1, -2, ..., 0, 0, 0],\n", " ..., \n", " [ 0, 0, 0, ..., -2, 1, 0],\n", " [ 0, 0, 0, ..., 1, -2, 1],\n", " [ 0, 0, 0, ..., 0, 1, -2]])" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now define the initial conditions as specified above." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def get_initial_conditions(x, T_0, x_0):\n", " T = zeros(x.shape)\n", " T[x=x_0/2] = 2 * T_0 * (1 - x[x>=x_0/2]/x_0)\n", " return T" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We plot this function to verify that we did code it well." ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot(x, get_initial_conditions(x, 1, x.max()))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 6, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAlEAAAFwCAYAAACYZC7QAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now on to the next step: solving the linear system for which we have already constructed the matrix $M$. We proceed by building a class called *Solution*. The idea behind this is to initialize it with an initial state and calculate the matrix that solves the problem once, in the *init* procedure." ] }, { "cell_type": "code", "collapsed": false, "input": [ "T_0 = get_initial_conditions(x, 1, x.max())" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "class Solution():\n", " def __init__(self, x, T_0, lambda_value, theta):\n", " self.x = x[1:-1]\n", " self.T = matrix(T_0[1:-1]).T\n", " self.t = 0\n", " dx = x[1] - x[0]\n", " self.dt = lambda_value * dx ** 2 # needed for updating the total time\n", " right_hand_matrix = identity(self.T.shape[0]) + lambda_value * (1 - theta) * get_matrix_M(self.T.shape[0])\n", " left_hand_matrix = identity(self.T.shape[0]) - lambda_value * theta * get_matrix_M(self.T.shape[0])\n", " self.inv_matrix = dot(inv(left_hand_matrix), right_hand_matrix)\n", " \n", " def solve_step(self):\n", " self.T = self.inv_matrix * self.T\n", " self.t += self.dt\n", " \n", " def solve_n_steps(self, n):\n", " for i in range(n):\n", " self.solve_step()\n", " " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "sol = Solution(x, T_0, 0.5, 0.1)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "sol.solve_n_steps(100)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(sol.x, array(sol.T), label='t = %.2f' % sol.t)\n", "legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 11, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAlEAAAFwCAYAAACYZC7QAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n", "text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Plotting different simulation case results " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have defined the problem and checked that our implementation behaves as expected, we're going to plot some solutions with different parameters to highlight different types of behaviors. To achieve this, we build a function that provides the solution at different timesteps and plots it." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_iterations(theta, lambda_value, plot_legend=True):\n", " sol = Solution(x, T_0, lambda_value, theta)\n", " plot(sol.x, array(sol.T), label='t = %.2f' % sol.t)\n", " sol.solve_n_steps(2)\n", " plot(sol.x, array(sol.T), label='t = %.3f' % sol.t)\n", " sol.solve_n_steps(8)\n", " plot(sol.x, array(sol.T), label='t = %.2f' % sol.t)\n", " sol.solve_n_steps(15)\n", " plot(sol.x, array(sol.T), label='t = %.2f' % sol.t)\n", " sol.solve_n_steps(25)\n", " plot(sol.x, array(sol.T), label='t = %.2f' % sol.t)\n", " sol.solve_n_steps(50)\n", " plot(sol.x, array(sol.T), label='t = %.2f' % sol.t)\n", " if plot_legend:\n", " legend()\n", " title(u\"$\\lambda=%.2f$ and $\\\\theta=%.1f$\" %(lambda_value, theta))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now use that function to compare different parameter sets. Here, we compare the case $\\lambda = 0.5$ to $\\lambda = 1$ across the explicit Euler and the implicit Euler scheme ($\\theta = 0$ and $\\theta = 1$). As one can see, a value of $\\lambda = 1$ is unstable with the explicit Euler scheme, while it is stable in the implicit Euler." ] }, { "cell_type": "code", "collapsed": false, "input": [ "subplot(221)\n", "plot_iterations(0, 0.5)\n", "subplot(222)\n", "plot_iterations(0, 1.0)\n", "subplot(223)\n", "plot_iterations(1, 0.5)\n", "subplot(224)\n", "plot_iterations(1, 1.0)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAlEAAAF7CAYAAADyo94TAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can study the explicit Euler scheme more closely for parameters around $0.5$. We can really observe how the instability develops with this set of parameters." ] }, { "cell_type": "code", "collapsed": false, "input": [ "subplot(221)\n", "plot_iterations(0, 0.5, plot_legend=False)\n", "subplot(222)\n", "plot_iterations(0, 0.51, plot_legend=False)\n", "subplot(223)\n", "plot_iterations(0, 0.52, plot_legend=False)\n", "subplot(224)\n", "plot_iterations(0, 0.53, plot_legend=False)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAlkAAAF7CAYAAADhdJ7nAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another thing to study is that stability does not necessarily mean convergence or good sampling. With the plots below, one sees that even though the scheme is stable (it doesn't explode), the solution can be not necessarily well discretized and thus exhibit \"strange\" behaviour, which disappears in the case of the implicit Euler scheme." ] }, { "cell_type": "code", "collapsed": false, "input": [ "subplot(231)\n", "plot_iterations(0.5, 20, plot_legend=False)\n", "subplot(232)\n", "plot_iterations(0.5, 60, plot_legend=False)\n", "subplot(233)\n", "plot_iterations(0.5, 100, plot_legend=False)\n", "ylim(0, 1) #automatic scale somehow not good fit\n", "subplot(234) \n", "plot_iterations(1, 20, plot_legend=False)\n", "subplot(235)\n", "plot_iterations(1, 60, plot_legend=False)\n", "subplot(236)\n", "plot_iterations(1, 100, plot_legend=False)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAlEAAAF7CAYAAADyo94TAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSkBAQEBAQECgHfwfuR1pDErObZEAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 16 } ], "metadata": {} } ] }