{ "cells": [ { "attachments": {}, "cell_type": "markdown", "id": "3df4e493", "metadata": {}, "source": [ "# Boundary Value PDEs" ] }, { "attachments": {}, "cell_type": "markdown", "id": "17835664", "metadata": {}, "source": [ "In this example we will show how CoLA can be used to solve linear and nonlinear boundary value PDEs." ] }, { "attachments": {}, "cell_type": "markdown", "id": "a39ff910", "metadata": {}, "source": [ "## Laplace Equation $\\Delta u = 0$\n", "\n", "For this example we will solve the Laplace equation on an irregularly shaped domain with given boundary conditions using a finite difference discretization." ] }, { "attachments": {}, "cell_type": "markdown", "id": "0c666dd4", "metadata": {}, "source": [ "First lets create a 1000 x 1000 point coordinate mesh." ] }, { "cell_type": "code", "execution_count": 1, "id": "466258d6", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "CUDA backend failed to initialize: Found CUDA version 12000, but JAX was built against version 12020, which is newer. The copy of CUDA that is installed must be at least as new as the version against which JAX was built. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n" ] } ], "source": [ "import numpy as np\n", "import jax.numpy as jnp\n", "import scipy\n", "import jax\n", "\n", "\n", "N=1000\n", "ndims = 2\n", "\n", "xgrid = jnp.linspace(-1,1,N)\n", "xygrid = jnp.stack(jnp.meshgrid(*(ndims*[xgrid])),axis=-1)\n", "dx = xgrid[1]-xgrid[0]\n", "x,y = xygrid.transpose((2,0,1))" ] }, { "attachments": {}, "cell_type": "markdown", "id": "65da3b80", "metadata": {}, "source": [ "With the mesh, lets define the geometry of the PDE domain and boundary conditions. The domain need not be square as shown below. For boundary conditions, we will set them to be $B(x,y) = (x+y)\\cos(2x)$ on the boundary of this domain." ] }, { "cell_type": "code", "execution_count": 2, "id": "5765114d", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.signal import convolve2d\n", "domain = (((x>0)|(y>0))&((y>-.5)|((x-.5)**2+(y+.5)**2<.5**2))) # chosen for example\n", "# reduce the domain by one pixel leave space for the boundary conditions\n", "domain &= ~(convolve2d((~domain).astype(np.float32),jnp.ones((3,3)),mode='same',fillvalue=1)>0)\n", "domain_ids, = domain.reshape(-1).nonzero()\n", "\n", "BCS = jnp.where(domain,jnp.zeros_like(x),(x+y)*jnp.cos(2*x))\n", "\n", "\n", "import matplotlib.pyplot as plt\n", "plt.imshow(domain)\n", "plt.show()\n" ] }, { "attachments": {}, "cell_type": "markdown", "id": "37b31ea7", "metadata": {}, "source": [ "Now we need to define the Laplacian $\\Delta$ as it acts on this discretized domain. \n", "Supposing we have the two dimensional array $v[i,j]$ representing the values on the grid, we can use the centered difference stencil for second derivatives $\\partial_x^2 v(x_i,y_j) = (v[i+1, j] - 2*v[i, j] + v[i-1, j])/h^2$ + O(h^3)$.\n", "\n", "Equivalently, we can write this as a convolution $\\partial_x^2 v(x_i,y_j) =(1/h^2) (\\begin{bmatrix}1& -2 &1\\end{bmatrix} * v)[i,j] + O(h^3)$ where $*$ is the discrete convolution. The discretized 2d Laplacian is therefore\n", "\n", "$Lv = (\\begin{bmatrix}1& -2 &1\\end{bmatrix} * v + \\begin{bmatrix} 1 \\\\ -2 \\\\ 1 \\end{bmatrix} *v)/h^2$. \n", "\n", "From this matrix vector multiply, we can define the linear operator using CoLA." ] }, { "cell_type": "code", "execution_count": 4, "id": "d96a48b5", "metadata": {}, "outputs": [], "source": [ "import cola\n", "from jax import vmap, jit\n", "\n", "def laplacian(x):\n", " x = x.reshape(ndims*(N,)) # unflatten to an ndims-dimensional grid\n", " cderiv = lambda x: jax.scipy.signal.correlate(x,jnp.array([1.,-2,1.])/dx**2,mode='same')\n", " return sum([jnp.apply_along_axis(cderiv,i,x) for i in range(ndims)]).reshape(-1)\n", "\n", "Lfull = cola.ops.LinearOperator(jnp.float32,shape=(N**ndims,N**ndims),matmat=jit(vmap(laplacian,-1,-1)))\n", "Lfull = cola.PSD(Lfull)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "e184db6b", "metadata": {}, "source": [ "Lfull is defined on the full $1000 \\times 1000$ grid rather than our irregularly shaped domain. Restrict it to the domain, we just need to select the indices of the points inside the domain by slicing it, as you would a matrix." ] }, { "cell_type": "code", "execution_count": 5, "id": "a1e772fb", "metadata": {}, "outputs": [], "source": [ "L = Lfull[domain_ids,domain_ids]" ] }, { "attachments": {}, "cell_type": "markdown", "id": "3b69087f", "metadata": {}, "source": [ "Since this would ignore the boundary conditions, we can simply add them in on the right hand side." ] }, { "cell_type": "code", "execution_count": 6, "id": "5f5e9780", "metadata": {}, "outputs": [], "source": [ "RHS = -(Lfull@BCS.reshape(-1))[domain_ids]" ] }, { "attachments": {}, "cell_type": "markdown", "id": "a1fb3b21", "metadata": {}, "source": [ "Finally, let's solve the linear system represented by this discretized laplacian and the boundary conditions\n", "\n", "$Lv = b$\n", "\n", "and annotate that $L$ is a PSD operator to speed up the computation." ] }, { "cell_type": "code", "execution_count": 9, "id": "df413ec9", "metadata": {}, "outputs": [], "source": [ "from cola import Auto\n", "L = cola.PSD(L)\n", "inv = cola.inv(L)\n", "v = inv@RHS" ] }, { "attachments": {}, "cell_type": "markdown", "id": "b6450cfc", "metadata": {}, "source": [ "Though we need to invert a $1000000 \\times 1000000$ sized matrix, the solution is produced very quickly because CoLA never forms the matrix explicitly, and we can visualize the solution below." ] }, { "cell_type": "code", "execution_count": 10, "id": "09aa0cf9", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "out_img = jnp.zeros(domain.shape)\n", "out_img = out_img.at[domain].set(v)\n", "\n", "plt.imshow(out_img,cmap='twilight')\n", "plt.colorbar()\n", "plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "id": "57edf4c9", "metadata": {}, "source": [ "## Nonlinear BVP: Minimal Surface Equation\n", "\n", "In this example we will consider solving the minimal surface equation, and example of a nonlinear boundary value PDE describing the shape of a soap bubble with a fixed boundary.\n", "For the minimal surface, we would like to solve for the height $z$ of the surface at each point $(x,y)$ on the domain, and we make the assumption that the height is single valued.\n", "\n", "The PDE is given by\n", "\n", "$(1+z_x^2)z_{yy} - 2z_x z_y z_{xy} + (1+z_y^2)z_{xx}=0$\n", "\n", " where subscripts denote partial derivatives.\n", "We will solve the PDE on the domain $[-1,1]^2$ with the boundary conditions\n", "\n", "$z(x,\\pm 1) = 1-x^2$ and $z(\\pm 1, y) = 0$." ] }, { "attachments": {}, "cell_type": "markdown", "id": "fd44cef8", "metadata": {}, "source": [ "Before solving, first we will define the mesh and the nonlinear pde constraint." ] }, { "cell_type": "code", "execution_count": 11, "id": "4ad7a1c1", "metadata": {}, "outputs": [], "source": [ "N=50\n", "xgrid = jnp.linspace(-1,1,N)\n", "xygrid = jnp.stack(jnp.meshgrid(xgrid,xgrid),axis=-1)\n", "dx = xgrid[1]-xgrid[0]\n", "\n", "def pde_constraint(z):\n", " deriv = lambda x: jax.scipy.signal.correlate(x,jnp.array([-1/2,0,1/2])/dx,mode='same')\n", " deriv2 = lambda x: jax.scipy.signal.correlate(x,jnp.array([1.,-2,1.])/dx**2,mode='same')\n", " zx,zy = [jnp.apply_along_axis(deriv,i,z) for i in [0,1]]\n", " zxx,zyy = [jnp.apply_along_axis(deriv2,i,z) for i in [0,1]]\n", " zxy = jnp.apply_along_axis(deriv,1,zx)\n", " return (1+zx**2)*zyy-2*zx*zy*zxy+(1+zy**2)*zxx\n", "\n", "x,y = xygrid.transpose((2,0,1))\n", "domain = (jnp.abs(x)<1)&(jnp.abs(y)<1)\n", "boundary_vals = np.zeros_like(x)\n", "boundary_vals[:,0] = 1-y[:,0]**2\n", "boundary_vals[:,-1] = 1-y[:,-1]**2\n", "\n", "@jit\n", "def pde_constraint_on_domain(u):\n", " padded_domain = jnp.zeros(boundary_vals.shape)+boundary_vals\n", " padded_domain = padded_domain.at[domain].set(u.reshape(-1))\n", " padded_domain = pde_constraint(padded_domain)\n", " return padded_domain[domain].reshape(u.shape)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "15a15e1d", "metadata": {}, "source": [ "Now that we have defined the PDE constraint discretized on the domain,\n", "we can now interpret the problem as finding the roots to a nonlinear function\n", "$F(z)=0$ where $F$ is the discretized PDE constraint, and $z$ is a vector representing the heights at the different points on the domain.\n", "\n", "To find the roots, we can employ Newtons method:\n", "\n", "$z \\gets z - J^{-1} F(z)$\n", "\n", "where $J$ is the Jacobian of $z$.\n", "While $J$ will be a large $N^2 \\times N^2$ matrix, with CoLA we can perform this solve efficiently. For this we will use the CoLA [Jacobian](https://CoLA.readthedocs.io/en/latest/package/cola.ops.html#cola.ops.Jacobian) LinearOperator." ] }, { "cell_type": "code", "execution_count": 13, "id": "3c7b5852", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PDE Error: 6.0e+02\n", "PDE Error: 2.4e+02\n", "PDE Error: 2.0e+02\n", "PDE Error: 3.7e+01\n", "PDE Error: 4.0e+00\n", "PDE Error: 2.2e-02\n", "PDE Error: 5.5e-04\n" ] } ], "source": [ "from cola.linalg import GMRES\n", "# Newton Raphson iteration\n", "tol = 3e-3\n", "\n", "z = jnp.zeros_like(x[domain]).reshape(-1) # initial guess\n", "err = np.inf\n", "while err > tol:\n", " F = pde_constraint_on_domain(z)\n", " err = jnp.max(jnp.abs(F))\n", " J = cola.ops.Jacobian(pde_constraint_on_domain,z)\n", " z -= cola.inv(J, alg=GMRES(max_iters=100))@F\n", " print(f\"PDE Error: {err:1.1e}\")" ] }, { "attachments": {}, "cell_type": "markdown", "id": "57725a1b", "metadata": {}, "source": [ "Now let's visualize the results." ] }, { "cell_type": "code", "execution_count": 14, "id": "2226daf8", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "fig = plt.figure()\n", "ax = fig.add_subplot(projection='3d')\n", "img = jnp.zeros(boundary_vals.shape)+boundary_vals\n", "img = img.at[domain].set(z)\n", "ax.plot_surface(x, y, img, cmap=plt.cm.YlGnBu_r)\n", "plt.show()\n", "\n", "plt.imshow(img,cmap='twilight')\n", "plt.colorbar()\n", "plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "id": "a0c3837c", "metadata": {}, "source": [ "We see the minimal surface forms a familiar saddle shape, a solution of negative curvature like other solutions to the minimal surface equation." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 5 }