{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Numerical Solution of the Wave Equation using the Finite Element Method" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook illustrates the numerical time-domain solution of the wave equation using the [Finite Element Method](https://en.wikipedia.org/wiki/Finite_element_method) (FEM). The method aims at an approximate solution by subdividing the area of interest into smaller parts with simpler geometry, linking these parts together and applying methods from the calculus of variations to solve the problem numerically. The FEM is a well established method for the numerical approximation of the solution of partial differential equations (PDEs). The solutions of PDEs are often known analytically only for rather simple geometries. FEM based simulations allow to gain insights into other more complex cases." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem Statement\n", "\n", "The linear and lossless propagation of sound is governed by the inhomogeneous linear [wave equation](https://en.wikipedia.org/wiki/Wave_equation)\n", "\n", "\\begin{equation}\n", "\\Delta p(\\mathbf{x}, t) - \\frac{1}{c^2} \\frac{\\partial^2}{\\partial t^2} p(\\mathbf{x}, t) = - q(\\mathbf{x}, t) ,\n", "\\end{equation}\n", "\n", "where $p(\\mathbf{x}, t)$ denotes the sound pressure at position $\\mathbf{x}$, $c$ the speed of sound and $q(\\mathbf{x}, t)$ the inhomogeneity.\n", "We aim in the following for a numerical solution of the wave equation on the domain $V$ with respect to the homogeneous Dirichlet boundary condition\n", "\n", "\\begin{equation}\n", "p(\\mathbf{x}, t) = 0 \\qquad \\text{for } x \\in \\partial V , \n", "\\end{equation}\n", "\n", "or the homogeneous Neumann boundary condition\n", "\n", "\\begin{equation}\n", "\\frac{\\partial}{\\partial n} p(\\mathbf{x}, t) = 0 \\qquad \\text{for } x \\in \\partial V ,\n", "\\end{equation}\n", "\n", "where $\\partial V $ denotes the boundary of $V$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Variational Formulation\n", "\n", "The FEM is based on expressing the partial differential equation (PDE) to be solved in its [variational](https://en.wikipedia.org/wiki/Calculus_of_variations) or weak form.\n", "The first step towards this is to approximate the second-order temporal derivative in the wave equation by its backward [finite difference](https://en.wikipedia.org/wiki/Finite_difference)\n", "\n", "\\begin{equation}\n", "\\frac{\\partial^2}{\\partial t^2} p(\\mathbf{x}, t) \\approx \\frac{p(\\mathbf{x}, t) - 2 p(\\mathbf{x}, t - T) + \n", "p(\\mathbf{x}, t- 2 T)}{T^2} ,\n", "\\end{equation}\n", "\n", "where $T$ denotes the temporal stepsize (i.e. the sampling interval).\n", "Introducing this approximation into the wave equation and rearranging terms yields\n", "\n", "\\begin{equation}\n", "c^2 T^2 \\Delta p(\\mathbf{x}, t) - p(\\mathbf{x}, t) = - 2 p(\\mathbf{x}, t - T) + \n", "p(\\mathbf{x}, t- 2 T) - c^2 T^2 q(\\mathbf{x}, t) .\n", "\\end{equation}\n", "\n", "In order to derive the variational formulation we follow the [procedure outlined for the Helmholz equation](FEM_Helmholtz_equation_2D.ipynb#Variational-Formulation).\n", "Multiplication by the test function $v(\\mathbf{x}, t)$, integration over the domain $V$ and application of Green's first identity yields\n", "\n", "\\begin{equation}\n", "{-} \\int_V \\left( c^2 T^2 \\nabla p(\\mathbf{x}, t) \\cdot \\nabla v(\\mathbf{x}, t) + p(\\mathbf{x}, t) v(\\mathbf{x}, t) \\right) \\mathrm{d}x = \\int_V \\left( - 2 p(\\mathbf{x}, t - T) + p(\\mathbf{x}, t- 2 T) - c^2 T^2 q(\\mathbf{x}, t) \\right) v(\\mathbf{x}, t) \\mathrm{d}x ,\n", "\\end{equation}\n", "\n", "where $v(\\mathbf{x}, t) = 0$ on $\\partial V$ where $p(\\mathbf{x}, t)$ is known - for instance due to fixed boundary conditions - was exploited in case of a pure Dirichlet boundary condition or $\\frac{\\partial}{\\partial n} p(\\mathbf{x}, t) = 0$ on $\\partial V$ in case of a pure Neumann boundary condition.\n", "It is common to express the integral equation above in terms of the bilinear $a(P, V)$ and linear $L(V)$ forms \n", "\n", "\\begin{equation}\n", "a(P, V) = \\int_V \\left( c^2 T^2 \\nabla p(\\mathbf{x}, t) \\cdot \\nabla v(\\mathbf{x}, t) +\n", "p(\\mathbf{x}, t) v(\\mathbf{x}, t) \\right) \\mathrm{d}x ,\n", "\\end{equation}\n", "\n", "\\begin{equation}\n", "L(V) = \\int_V \\left( 2 p(\\mathbf{x}, t - T) - p(\\mathbf{x}, t- 2 T) + c^2 T^2 q(\\mathbf{x}, t) \\right) v(\\mathbf{x}, t) \\mathrm{d}x ,\n", "\\end{equation}\n", "\n", "where\n", "\n", "\\begin{equation}\n", "a(P, V) = L(V) .\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numerical Solution\n", "\n", "The numerical solution of the variational problem is based on [FEniCS](https://fenicsproject.org/), an open-source framework for numerical solution of PDEs.\n", "Its high-level Python interface `dolfin` is used in the following to define the problem and compute its solution.\n", "The implementation is directly based on the variational formulation derived above.\n", "It is common in the FEM to denote the solution of the problem by $u$ and the test function by $v$.\n", "The definition of the problem in FEniCS is very close to the mathematical formulation of the problem." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "import dolfin\n", "import mshr\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "T = 1/40000 # temporal sampling interval\n", "\n", "\n", "def FEM_wave_equation(mesh, T, N, xs, neumann_bc=True, c=343):\n", " \n", " # define function space\n", " V = dolfin.FunctionSpace(mesh, \"CG\", 1)\n", "\n", " # define previous and second-last solution\n", " u1 = dolfin.interpolate(dolfin.Constant(0.0), V)\n", " u0 = dolfin.interpolate(dolfin.Constant(0.0), V)\n", "\n", " # define boundary conditions\n", " if neumann_bc:\n", " bcs = None\n", " else:\n", " bcs = dolfin.DirichletBC(V, dolfin.Constant(0.), \"on_boundary\")\n", "\n", " # define variational problem\n", " u = dolfin.TrialFunction(V)\n", " v = dolfin.TestFunction(V)\n", "\n", " a = dolfin.inner(u, v) * dolfin.dx + dolfin.Constant(T**2 * c**2) * dolfin.inner(dolfin.nabla_grad(u), dolfin.nabla_grad(v)) * dolfin.dx\n", " L = 2*u1*v * dolfin.dx - u0*v * dolfin.dx\n", "\n", " # compute solution for all time-steps\n", " u = dolfin.Function(V)\n", "\n", " for n in range(N):\n", " A, b = dolfin.assemble_system(a, L, bcs)\n", " # define inhomogenity\n", " if n==0:\n", " delta = dolfin.PointSource(V, xs, 1)\n", " delta.apply(b)\n", " # solve variational problem\n", " dolfin.solve(A, u.vector(), b)\n", " u0.assign(u1)\n", " u1.assign(u)\n", " \n", " return u\n", "\n", "\n", "def plot_soundfield(u):\n", " '''plots solution of FEM-based simulation'''\n", " fig = plt.figure(figsize=(10,10))\n", " fig = dolfin.plot(u)\n", " plt.title(r'$p(\\mathbf{x}, t)$')\n", " plt.xlabel(r'$x$ / m')\n", " plt.ylabel(r'$y$ / m')\n", " plt.colorbar(fig, fraction=0.038, pad=0.04);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sound Field in a Rectangular Room with Sound-Hard Boundaries\n", "\n", "For a first validation of the numerical simulation by the FEM, the solution of the inhomogeneous two-dimensional wave equation for a point source $q(\\mathbf{x}, t) = \\delta(\\mathbf{x}-\\mathbf{x}_s) \\cdot \\delta(t)$ at position $\\mathbf{x}_s = (2,2)$ m is considered for a Dirac shaped excitation in the time-domain. The simulated geometry is a two-dimensional rectangular room with size $4 \\times 4$ meters and sound-hard boundaries (Neumann boundary condition). Note that the free-field solution of the two-dimensional wave equation for a spatio-temporally Dirac shaped excitation is given as\n", "\n", "\\begin{equation}\n", "p(\\mathbf{x}, t) = \\frac{1}{2 \\pi \\sqrt{t^2 - (\\frac{||\\mathbf{x} - \\mathbf{x}_s||}{c})^2}} \\qquad \\text{for } t > \\frac{||\\mathbf{x} - \\mathbf{x}_s||}{c} .\n", "\\end{equation}\n", "\n", "In order to validate the simulation for free-field propagation the timestep $N=150$ and sampling interval $T=\\frac{1}{40000}$ s are chosen such that the incident wave is not reflected by one of the walls. The simulated time $t = N \\cdot T = 3.75$ ms after excitation by the Dirac impulse." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# define geometry and mesh\n", "domain = mshr.Rectangle(dolfin.Point(0, 0), dolfin.Point(4,4))\n", "mesh = mshr.generate_mesh(domain, 200)\n", "\n", "# compute solution\n", "u = FEM_wave_equation(mesh, T, 150, dolfin.Point(2,2), neumann_bc=True)\n", "\n", "# plot sound field\n", "plot_soundfield(u)\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result of the numerical simulation is compared to the theoretical result given above for a line parallel to the y-axis for $y = 2$." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "\n", "# extract simulation results on line\n", "x = np.linspace(0 + 1E-14, 4 - 1E-14, 101)\n", "points = [(x_, 2) for x_ in x]\n", "ux = [u(point) for point in points]\n", "\n", "# compute analytic result on line\n", "px = np.zeros(len(x))\n", "a = (150*T)**2 - (np.sqrt((x-2)**2 + (2-2)**2)/343)**2\n", "px[a>0] = 0.34 * 1/(2*np.pi * np.sqrt(a[a>0]))\n", "\n", "# plot comparison\n", "plt.figure(figsize=(10,5))\n", "plt.plot(x, px, 'k--' , label='analytic solution')\n", "plt.plot(x, ux, label='numeric solution')\n", "plt.xlabel(r'$x$ / m')\n", "plt.ylabel(r'$p(\\mathbf{x}, t)$')\n", "plt.legend()\n", "plt.ylim([0, 50]);\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sound Field in Two Coupled Rectangular Rooms#\n", "\n", "In order to illustrate the procedure for a more complex geometry, the sound field in two coupled rectangular rooms with sound-hard boundaries is computed. First, the geometry of the problem is defined and the mesh is plotted with a low number of elements for ease of illustration." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# define geometry and compute low resolution mesh for illustration\n", "domain = mshr.Rectangle(dolfin.Point(0, 0), dolfin.Point(3,4)) + \\\n", " mshr.Rectangle(dolfin.Point(3, 1.5), dolfin.Point(3.5, 2.5)) + \\\n", " mshr.Rectangle(dolfin.Point(3.5, 0), dolfin.Point(6, 4))\n", "mesh = mshr.generate_mesh(domain, 20)\n", "\n", "dolfin.plot(mesh);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now the problem is defined and solved with FEniCS with a high density mesh. The source position is chosen as $\\mathbf{x}_s = (2,1)$ m and the total number of time-steps as $N=300$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# high resolution mesh for FEM simulation\n", "mesh = mshr.generate_mesh(domain, 150)\n", "\n", "# compute solution\n", "u = FEM_wave_equation(mesh, T, 300, dolfin.Point(2,1), neumann_bc=True)\n", "\n", "# plot sound field\n", "plot_soundfield(u)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Copyright**\n", "\n", "This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebook for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT)." ] } ], "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": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }