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Solving the Poisson Problem in 20 minutes with the FEniCS Project - RUES Seminar 23/9/2015
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "slide" | |
| } | |
| }, | |
| "source": [ | |
| "# Solving the Poisson Problem in 20 minutes with the FEniCS Project\n", | |
| "#### Author: Jack S. Hale License: Creative Commons CC BY 3.0\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Introduction\n", | |
| "\n", | |
| "This is a fully featured Python workspace running on a cloud computer in Amazon's facility in Frankfurt. All the software you need is already installed." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "metadata": { | |
| "collapsed": false, | |
| "scrolled": true | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Hello World!\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "print \"Hello World!\"" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "If you have used Mathematica before, you will like that we can interleave our notes, mathematics and code together in one file:\n", | |
| "\n", | |
| "$$a^2 + b^2 = c^2$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "5.0" | |
| ] | |
| }, | |
| "execution_count": 2, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "a = 3.0\n", | |
| "b = 4.0\n", | |
| "csqred = a**2 + b**2\n", | |
| "csqred**(0.5)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Using FEniCS for the first time\n", | |
| "\n", | |
| "### What's the Finite Element Method?\n", | |
| "\n", | |
| "*It uses subdivision of a whole problem domain into simpler parts, called finite elements, and variational methods from the calculus of variations to solve the problem by minimizing an associated error function. Analogous to the idea that connecting many tiny straight lines can approximate a larger circle, FEM encompasses methods for connecting many simple element equations over many small subdomains, named finite elements, to approximate a more complex equation over a larger domain.*\n", | |
| "Source: https://en.wikipedia.org/wiki/Finite_element_method\n", | |
| "\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Mathematical Background\n", | |
| "\n", | |
| "### Step 0\n", | |
| "\n", | |
| "Define your problem on the whiteboard!\n", | |
| "\n", | |
| "I want to solve the following Poisson problem on a two-dimensional domain using the Finite Element Method.\n", | |
| "\n", | |
| "https://en.wikipedia.org/wiki/Weak_formulation#Example_2:_Poisson.27s_equation\n", | |
| "\n", | |
| "Find $u \\in V_h$ such that for all $v \\in V_h$:\n", | |
| "\n", | |
| "$$ \\int_{\\Omega} \\nabla u \\cdot \\nabla v \\; dx= \\int_{\\Omega} f \\cdot v \\; dx$$\n", | |
| "\n", | |
| "$$\\Omega = [0, 1] \\times [0, 1]$$\n", | |
| "\n", | |
| "where:\n", | |
| "\n", | |
| "$$f = 1.0$$\n", | |
| "\n", | |
| "and\n", | |
| "\n", | |
| "$$u = 0 \\; \\mathrm{on} \\; \\Gamma$$\n", | |
| "\n", | |
| "This problem (and many others) fits the following 'general' form of linear weak variational problems:\n", | |
| "\n", | |
| "Find $u \\in V$ such that for all $v \\in V$:\n", | |
| "\n", | |
| "$$a(u, v) = L(v) \\\\\n", | |
| "a(u,v) = \\int_{\\Omega} \\nabla u \\cdot \\nabla v \\; dx \\rightarrow \\mathbf{A} \\in \\mathbb{R}^{n \\times n}\\\\ \n", | |
| "L(v) = \\int_{\\Omega} f \\cdot v \\; dx \\rightarrow \\mathbf{b} \\in \\mathbb{R}^{n}\n", | |
| "$$\n", | |
| "and then we solve the linear system:\n", | |
| "$$\n", | |
| "\\mathbf{A} u = \\mathbf{b}\n", | |
| "$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Implementation with MATLAB\n", | |
| "\n", | |
| "https://www.cs.uaf.edu/~bueler/poissonv2.pdf\n", | |
| "\n", | |
| "```\n", | |
| "function [uh,in]=poissonv2(f,fd,h0,p,t);\n", | |
| "%POISSONV2 Solve Poisson’s equation on a domain D by the FE method:\n", | |
| "%...\n", | |
| "%ELB 10/31/04\n", | |
| "geps=.001*h0; ind=(feval(fd,p) < -geps); % find interior nodes\n", | |
| "p=size(p,1); N=sum(ind); % Np=# of nodes; N=# of interior nodes\n", | |
| "in=zeros(Np,1); in(ind)=(1:N)’; % number the interior nodes\n", | |
| "for j=1:Np, ff(j)=feval(f,p(j,:)); end % eval f once for each node\n", | |
| "% loop over triangles to set up stiffness matrix A and load vector b\n", | |
| "A=sparse(N,N); b=zeros(N,1);\n", | |
| "for n=1:size(t,1)\n", | |
| " j=t(n,1); k=t(n,2); l=t(n,3); vj=in(j); vk=in(k); vl=in(l);\n", | |
| " J=[p(k,1)-p(j,1), p(l,1)-p(j,1); p(k,2)-p(j,2), p(l,2)-p(j,2)];\n", | |
| " ar=abs(det(J))/2; C=ar/12; Q=inv(J’*J); fT=[ff(j) ff(k) ff(l)];\n", | |
| " if vj>0\n", | |
| " A(vj,vj)=A(vj,vj)+ar*sum(sum(Q)); b(vj)=b(vj)+C*fT*[2 1 1]’; end\n", | |
| " if vk>0\n", | |
| " A(vk,vk)=A(vk,vk)+ar*Q(1,1); b(vk)=b(vk)+C*fT*[1 2 1]’; end\n", | |
| " if vl>0\n", | |
| " A(vl,vl)=A(vl,vl)+ar*Q(2,2); b(vl)=b(vl)+C*fT*[1 1 2]’; end\n", | |
| " if vj*vk>0\n", | |
| " A(vj,vk)=A(vj,vk)-ar*sum(Q(:,1)); A(vk,vj)=A(vj,vk); end\n", | |
| " if vj*vl>0\n", | |
| " A(vj,vl)=A(vj,vl)-ar*sum(Q(:,2)); A(vl,vj)=A(vj,vl); end\n", | |
| " if vk*vl>0\n", | |
| " A(vk,vl)=A(vk,vl)+ar*Q(1,2); A(vl,vk)=A(vk,vl); end\n", | |
| " end\n", | |
| "uh=zeros(Np,1); uh(ind)=A\\b; % solve for FE solution\n", | |
| "trimesh(t,p(:,1),p(:,2),uh), axis tight % display\n", | |
| "```" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "notes" | |
| } | |
| }, | |
| "source": [ | |
| "There's nothing wrong with the above script! It works and it will solve the Poisson problem for you.\n", | |
| "\n", | |
| "But:\n", | |
| "* How does it relate to the mathematics above? Will I still know what it does in three years/ten years/fifty years time?\n", | |
| "* Ah, I need to run a problem with 500 million degrees of freedom now on the HPC. MATLAB is no good for that! Can you recode it in C++/MPI/PETSc for me?\n", | |
| "* Oh, I forgot, but actually the material properties vary through the domain.\n", | |
| "\n", | |
| "$$a(u,v) = \\int_{\\Omega} \\kappa(x) \\nabla u \\cdot \\nabla v \\; dx$$\n", | |
| "\n", | |
| "* It's 2110 and everyone is using Quantum computers! You can't code like that and get good performance from a Quantum computer!\n", | |
| "\n", | |
| "Key idea: abstract mathematics from implementation. Key piece of software: The Unified Form Language (UFL) (Logg et al.)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### A better way? Implementation with FEniCS" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "First of all, a bit of Python terminology. DOLFIN is the solving module of the FEniCS Project. It is a `package`, and I want to bring in every function from it." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "from dolfin import *" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Step 1\n", | |
| "\n", | |
| "First of all I'm going to make a mesh $\\mathcal{T}_h$ on the Unit Square:\n", | |
| "\n", | |
| "$$ \\Omega = [0,1]\\times[0,1]$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 4, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "T_h = UnitSquareMesh(30, 30)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Now a little bit more Python. This allows us to plot meshes and functions inline in this script." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "%matplotlib inline\n", | |
| "%run /home/fenics/fenics-matplotlib.py" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 6, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "[<matplotlib.lines.Line2D at 0x7f967194fc90>,\n", | |
| " <matplotlib.lines.Line2D at 0x7f967194fd50>]" | |
| ] | |
| }, | |
| "execution_count": 6, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
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xjmHp0qUWl0RPdpzbK5MCDsRhr1vGGU99d6KqEvn5+czD8DpVCQIMr1uVsLaOYd26dcyb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\n/weEyjY8j8Xt4QAAAABJRU5ErkJggg==\n", | |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7f96765d8b10>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plot(T_h)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Step 2\n", | |
| "Make a Function Space $V_h(\\mathcal{T}_h)$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 7, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "DEBUG:FFC:Reusing form from cache.\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "V_h = FunctionSpace(T_h, \"CG\", 1)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Step 3\n", | |
| "\n", | |
| "Make a Trial Function $u \\in V_h$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 8, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "u = TrialFunction(V_h)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Step 4\n", | |
| "\n", | |
| "Make a Test Function $v \\in V_h$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 9, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "v = TestFunction(V_h)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Step 5\n", | |
| "Define the bilinear form (left hand side)\n", | |
| "$$ a(u, v) = \\int_{\\Omega} \\nabla u \\cdot \\nabla v \\; dx $$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 10, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "a = inner(grad(u), grad(v))*dx" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Step 6\n", | |
| "Define the linear form (right hand side)\n", | |
| "$$ f = 1.0 $$\n", | |
| "$$L(v) = \\int_{\\Omega} f \\cdot v \\; dx$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 11, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "f = Constant(1.0)\n", | |
| "L = inner(f, v)*dx" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Step 7\n", | |
| "Now onto the Dirichlet boundary conditions. This is the trickiest part!\n", | |
| "\n", | |
| "$$ u = 0 \\; \\; \\mathrm{on} \\; \\Gamma$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 12, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "u0 = Constant(0.0)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "A little bit more Python. We define a function `boundary` with `def` that takes two arguments: `x[0]` is the position in our domain along the x-axis, `x[1]` is the position in our domain along the y-axis, `on_boundary` is either `True` or `False` depending on whether we are on the boundary $\\Gamma$." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 13, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "def boundary(x, on_boundary):\n", | |
| " return on_boundary" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "What arguments does DirichletBC take? Good question. Find out by typing: `DirichletBC?<enter>`" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 14, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "bc = DirichletBC(V_h, u0, boundary)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Step 8" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "We nearly have everything we need! Remember, we want to:\n", | |
| "\n", | |
| "Find $u_h \\in V_h$:\n", | |
| "\n", | |
| "So let's make $u_h$." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 15, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "u_h = Function(V_h)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 16, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "DEBUG:FFC:Reusing form from cache.\n", | |
| "DEBUG:FFC:Reusing form from cache.\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "solve(a == L, u_h, bc)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 17, | |
| "metadata": { | |
| "collapsed": false, | |
| "scrolled": true | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "<matplotlib.collections.TriMesh at 0x7f966f1c2650>" | |
| ] | |
| }, | |
| "execution_count": 17, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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dpVxBK4OPJMATzqWtAoQxfsqqPVdgZfAtgWOQFDFoY1Qm6aVPwMDgTKAf1DM4ABJoeBCw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\nvzXwGxez7lrgr/Zf5FmUuysdb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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7f9676602b90>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plot(u_h)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## The complete mathematics and script as a summary:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Find $u \\in V_h$ such that for all $v \\in V_h$:\n", | |
| "\n", | |
| "$$ \\int_{\\Omega} \\nabla u \\cdot \\nabla v \\; dx= \\int_{\\Omega} f \\cdot v \\; dx$$\n", | |
| "\n", | |
| "$$\\Omega = [0, 1] \\times [0, 1]$$\n", | |
| "\n", | |
| "where:\n", | |
| "\n", | |
| "$$f = 1.0$$\n", | |
| "\n", | |
| "and\n", | |
| "\n", | |
| "$$u = 0 \\; \\mathrm{on} \\; \\Gamma$$\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 18, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "DEBUG:FFC:Reusing form from cache.\n", | |
| "DEBUG:FFC:Reusing form from cache.\n", | |
| "DEBUG:FFC:Reusing form from cache.\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "# from dolfin import *\n", | |
| "T_h = UnitSquareMesh(30, 30)\n", | |
| " \n", | |
| "V_h = FunctionSpace(T_h, \"CG\", 1)\n", | |
| "u = TrialFunction(V_h)\n", | |
| "v = TestFunction(V_h)\n", | |
| " \n", | |
| "a = inner(grad(u), grad(v))*dx\n", | |
| "f = Constant(1.0)\n", | |
| "L = inner(f, v)*dx\n", | |
| " \n", | |
| "u0 = Constant(0.0)\n", | |
| "def boundary(x, on_boundary):\n", | |
| " return on_boundary\n", | |
| " \n", | |
| "bc = DirichletBC(V_h, u0, boundary)\n", | |
| " \n", | |
| "u_h = Function(V_h)\n", | |
| "solve(a == L, u_h, bc)\n", | |
| "# plot(u_h)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "source": [ | |
| "## Summary\n", | |
| "\n", | |
| "This really scratches the surface of what you can do with FEniCS. Projects I am involved in now include:\n", | |
| "* Uncertainty quantification for hyperelastic parameter identification *Patrick Farrell, Oxford University*.\n", | |
| "* Inverse hyperelasticity problems in medical imaging *Alex Bilger, Luxembourg*.\n", | |
| "* Solving PDEs arising from non-local continuum theories *Elena Atroschenko, Universidad de Chile*.\n", | |
| "* FEniCS-shells, a UFL-based library for simulating thin structures *Corrado Maurini, Matteo Brunetti, UPMC Paris*.\n", | |
| "* Numerical computing in cloud computing environments with Docker *Garth Wells, Cambridge University, Lizao Li, University of Minnesota*.\n", | |
| "\n", | |
| "\n", | |
| "Some of these projects are very complex and yet come in at under a few thousand lines of code.\n", | |
| "\n", | |
| "In my view, this is a direct result of the expressiveness of the Unified Form Language." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "Python 2", | |
| "language": "python", | |
| "name": "python2" | |
| }, | |
| "language_info": { | |
| "codemirror_mode": { | |
| "name": "ipython", | |
| "version": 2 | |
| }, | |
| "file_extension": ".py", | |
| "mimetype": "text/x-python", | |
| "name": "python", | |
| "nbconvert_exporter": "python", | |
| "pygments_lexer": "ipython2", | |
| "version": "2.7.6" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 0 | |
| } |
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