{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# 15 Partial Differential Equations — 2\n", "\n", "## Solving Laplace's or Poisson's equation\n", "\n", "Still solving **Poisson's equation** for the electric potential $\\Phi(\\mathbf{r})$ and the charge density $\\rho(\\mathbf{r})$:\n", "\n", "$$\n", "\\nabla^2 \\Phi(x, y, z) = -4\\pi\\rho(x, y, z)\\\\\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "For a region of space without charges ($\\rho = 0$) this reduces to **Laplace's equation**\n", "\n", "$$\n", "\\nabla^2 \\Phi(x, y, z) = 0\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "General solution by iteration:\n", "$$\n", "\\Phi_{i,j} = \\frac{1}{4}\\Big(\\Phi_{i+1,j} + \\Phi_{i-1,j} + \\Phi_{i,j+1} + \\Phi_{i,j-1}\\Big)\n", " + \\pi\\rho_{i,j} \\Delta^2\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Jacobi method\n", "Do not change $\\Phi_{i,j}$ until a complete sweep has been completed." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "def Laplace_Jacobi_slow(Phi):\n", " # Don't use, very slow AND inefficient\n", " Phi_new = Phi.copy()\n", " Nx, Ny = Phi.shape\n", " for xi in range(1, Nx-1):\n", " for yj in range(1, Ny-1):\n", " Phi_new[xi, yj] = 0.25*(Phi[xi+1, yj] + Phi[xi-1, yj]\n", " + Phi[xi, yj+1] + Phi[xi, yj-1])\n", " Phi[:, :] = Phi_new\n", " return Phi" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fast implementation using numpy array operations (vectorized, run at C speed, not Python speed) (see the [board notes (PDF)](https://github.com/ASU-CompMethodsPhysics-PHY494/PHY494-resources/blob/master/16_PDEs/16_PDEs-2-LectureNotes.pdf) or [local PDF](16_PDEs-2-LectureNotes.pdf) for an explanation for how to set up the numpy array operations that give you a 100-fold speed up over `Laplace_Jacobi_slow()`):" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def Laplace_Jacobi(Phi):\n", " \"\"\"One update in the Jacobi algorithm\"\"\"\n", " Phi[1:-1, 1:-1] = 0.25*(Phi[2:, 1:-1] + Phi[0:-2, 1:-1] + Phi[1:-1, 2:] + Phi[1:-1, 0:-2])\n", " return Phi" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Gauss-Seidel method\n", "Immediately use updated new values for $\\Phi_{i-1, j}$ and $\\Phi_{i, j-1}$ (if starting from $\\Phi_{1, 1}$).\n", "\n", "Leads to *accelerated convergence* and therefore *less round-off error* (but distorts symmetry of boundary conditions... hopefully irrelevant when converged but check!)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def Laplace_Gauss_Seidel(Phi):\n", " \"\"\"One update in the Gauss-Seidel algorithm\"\"\"\n", " Nx, Ny = Phi.shape\n", " for xi in range(1, Nx-1):\n", " for yj in range(1, Ny-1):\n", " Phi[xi, yj] = 0.25*(Phi[xi+1, yj] + Phi[xi-1, yj]\n", " + Phi[xi, yj+1] + Phi[xi, yj-1])\n", " return Phi" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Fast Gauss-Seidel-like\n", "\n", "Divide the lattice into a checkerboard of black and white cells. Update the odd cells first (like Jacobi) but then use the odd cells to update the even ones (Gauss-Seidel-like; see the [board notes (PDF)](https://github.com/ASU-CompMethodsPhysics-PHY494/PHY494-resources/blob/master/16_PDEs/16_PDEs-2-LectureNotes.pdf) or [local PDF](16_PDEs-2-LectureNotes.pdf) ). This leads to faster convergence *and* can be done with numpy array operations." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def Laplace_Gauss_Seidel_odd_even(Phi):\n", " \"\"\"One update in the Gauss-Seidel algorithm on odd or even fields\"\"\"\n", " # odd update (uses old even)\n", " Phi[1:-2:2, 1:-2:2] = 0.25*(Phi[2::2, 1:-2:2] + Phi[0:-2:2, 1:-2:2] + Phi[1:-2:2, 2::2] + Phi[1:-2:2, 0:-2:2])\n", " Phi[2:-1:2, 2:-1:2] = 0.25*(Phi[3::2, 2:-1:2] + Phi[1:-2:2, 2:-1:2] + Phi[2:-1:2, 3::2] + Phi[2:-1:2, 1:-2:2])\n", " \n", " # even update (uses new odd)\n", " Phi[1:-2:2, 2:-1:2] = 0.25*(Phi[2::2, 2:-1:2] + Phi[0:-2:2, 2:-1:2] + Phi[1:-2:2, 3::2] + Phi[1:-2:2, 1:-1:2])\n", " Phi[2:-1:2, 1:-2:2] = 0.25*(Phi[3::2, 1:-2:2] + Phi[1:-2:2, 1:-2:2] + Phi[2:-1:2, 2::2] + Phi[2:-1:2, 0:-2:2])\n", " return Phi" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### *Converged* solution of the wire-in-a-box problem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Solve the box-wire problem and **make sure that the solution is converged to `tol = 1e-3`.**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check convergence with the [_Frobenius Norm_](http://mathworld.wolfram.com/FrobeniusNorm.html):\n", "\n", "$$\n", "||\\mathsf{\\Phi}|| := \\sqrt{\\sum_{i,j}|\\Phi_{ij}|^2}\n", "$$\n", "\n", "which is implemented as [numpy.linalg.norm()](https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.norm.html) when the argument is a matrix." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Interactive plotting (with ipympl):" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# for interactive work\n", "%matplotlib widget" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Only execute the next line if you *don't* want interactive plotting (e.g., when exporting to LaTeX/PDF or html):" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Convience plotting functions. \n", "If you provide a filename then output is only written to a file and figures are close to conserve memory. This allows you to plot files in loops and later assemble them into movies using other programs such as ffmpeg, ImageMagick, mencoder, QuickTime 7, ..." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def plot_contour(Phi, filename=None, zlabel=r\"potential $\\Phi$ (V)\",\n", " cmap=plt.cm.coolwarm):\n", " \"\"\"Plot Phi as a contour plot.\n", " \n", " Arguments\n", " ---------\n", " Phi : 2D array\n", " potential on lattice\n", " filename : string or None, optional (default: None)\n", " If `None` then show the figure and return the axes object.\n", " If a string is given (like \"contour.png\") it will only plot \n", " to the filename and close the figure but return the filename.\n", " cmap : colormap\n", " pick one from matplotlib.cm \n", " \"\"\"\n", " fig = plt.figure(figsize=(5,4))\n", " ax = fig.add_subplot(111)\n", "\n", " x = np.arange(Phi.shape[0])\n", " y = np.arange(Phi.shape[1])\n", " X, Y = np.meshgrid(x, y)\n", " Z = Phi[X, Y]\n", " cset = ax.contourf(X, Y, Z, 20, cmap=cmap)\n", " ax.set_xlabel('X')\n", " ax.set_ylabel('Y')\n", " ax.set_aspect(1)\n", "\n", " cb = fig.colorbar(cset, shrink=0.5, aspect=5)\n", " cb.set_label(zlabel)\n", " \n", " if filename:\n", " fig.savefig(filename)\n", " plt.close(fig)\n", " return filename\n", " else:\n", " return ax\n", " \n", "\n", "def plot_surf(Phi, filename=None, offset=-20, zlabel=r'potential $\\Phi$ (V)',\n", " elevation=40, azimuth=-65, cmap=plt.cm.coolwarm):\n", " \"\"\"Plot Phi as a 3D plot with contour plot underneath.\n", " \n", " Arguments\n", " ---------\n", " Phi : 2D array\n", " potential on lattice\n", " filename : string or None, optional (default: None)\n", " If `None` then show the figure and return the axes object.\n", " If a string is given (like \"contour.png\") it will only plot \n", " to the filename and close the figure but return the filename.\n", " offset : float, optional (default: 20)\n", " position the 2D contour plot by offset along the Z direction\n", " under the minimum Z value\n", " zlabel : string, optional\n", " label for the Z axis and color scale bar\n", " elevation : float, optional\n", " choose elevation for initial viewpoint\n", " azimuth : float, optional\n", " chooze azimuth angle for initial viewpoint\n", " cmap : colormap\n", " pick one from matplotlib.cm\n", " \"\"\"\n", " \n", " x = np.arange(Phi.shape[0])\n", " y = np.arange(Phi.shape[1])\n", " X, Y = np.meshgrid(x, y)\n", " Z = Phi[X, Y]\n", " \n", " fig = plt.figure()\n", " ax = fig.add_subplot(111, projection='3d')\n", " ax.plot_wireframe(X, Y, Z, rstride=2, cstride=2, linewidth=0.5, color=\"gray\")\n", " surf = ax.plot_surface(X, Y, Z, cmap=cmap, alpha=0.6)\n", " cset = ax.contourf(X, Y, Z, 20, zdir='z', offset=offset+Z.min(), cmap=cmap)\n", "\n", " ax.set_xlabel('X')\n", " ax.set_ylabel('Y')\n", " ax.set_zlabel(zlabel)\n", " ax.set_zlim(offset + Z.min(), Z.max())\n", " \n", " ax.view_init(elev=elevation, azim=azimuth)\n", "\n", " cb = fig.colorbar(surf, shrink=0.5, aspect=5)\n", " cb.set_label(zlabel)\n", " \n", " if filename:\n", " fig.savefig(filename)\n", " plt.close(fig)\n", " return filename\n", " else:\n", " return ax" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Wire problem\n", "\n", "Use the fastest Poisson solver that we have at the moment: `Laplace_Gauss_Seidel_odd_even()`" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Laplace_Gauss_Seidel_odd_even converged in 7558 iterations to 0.0009995267090286367\n" ] } ], "source": [ "Max_iter=30000\n", "tol = 1e-3\n", "Nmax = 100\n", "Phi = np.zeros((Nmax, Nmax), dtype=np.float64)\n", "Phi_old = np.zeros_like(Phi)\n", "\n", "# initialize boundaries\n", "# everything starts out zero so nothing special for the grounded wires\n", "Phi[0, :] = 100 # wire at x=0 at 100 V\n", "\n", "for n_iter in range(Max_iter):\n", " Phi_old[:, :] = Phi\n", " Phi = Laplace_Gauss_Seidel_odd_even(Phi)\n", " DeltaPhi = np.linalg.norm(Phi - Phi_old)\n", " if DeltaPhi < tol:\n", " print(\"Laplace_Gauss_Seidel_odd_even converged in {0} iterations to {1}\".format(n_iter+1, DeltaPhi))\n", " break\n", "else:\n", " print(\"Laplace_Gauss_Seidel_odd_even did NOT converge in {0} iterations, DeltaPhi={1}\".format(n_iter+1, DeltaPhi))\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the result and visualy compare to what we had before:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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LiLX40Sn7oTcSPCuqkw1mtrHbMX2SEp8AlGdl+lzgaYIVsnsl3SBpKQkfeCXpCkl3S7p710yhj3ZJLY9FqKzUtdV3zRM+SO9c4NbY238p6X5JPwJ+E3hPl0vcKemd4Un98eseI+k1kjZx9NT+nvIM0/nAi4Drw1WyfaRo6cN/Mdab2frlI8Wuk3Va0S/byftNbvV93rR5wsc8rzCz6dh7bzGzXzez3zCz10eFWwfnATPA5yQ9JekhSY8S3H96CcEtVp9JOp48U2oLsMXM7gpff4EgTLdJWm1mW4f9wKsyWLp/B/sWt78LoNuTS4vg55y6XjQyH41XczupmR0APgl8MlzRnwD2h9ORqeVWmZrZL4AnJa0N39oAPESBD7yKK2IX1KDqurXUuaKZ2UEz29pvkEL+95m+E7g5vH3hUeBtBAF+i6TLgSeAN+c8Bteirgef5MFP33dJ5RqmZnYfsL7Npzbk+XNdM/kpUq5Itd9OWpSiVvSLXoSq49bSYfF7TYuhwKnh4SnJFwla1Go7aR1UfRHKNYuNzK/0tmpJpxEsjh8GBIxIepOZPZT2Wl6ZthjGLqiqHMfnXAN8Gni/mZ1uZv8B+CPg5n4u5GE6oGHfa+or+s4FBj37Q9IfACcAyyS9NTwcZTmwQtJ/STueRoTpoMfwQfEP18ua74RKzreVltagZ3+8GFgA/MfYx3rgmPBzqficqSuN8fFFTE0dGOgavqLfDLGzP/4zBGd/AM9Kugg4J/yyTcC3CVr3Oczs7ZL+HbjOzH4aXve5wIVmdnnaMXmYOufKqNd5pvGzP84A7gGupuXsD0ltz/6I+a/AdyR9CTCCw1Gu6mfAHqY1lOSJpXnybaXNYSPz83oi76SZtbtHPRKd/fFOM7tL0nX0cZynmX1F0v3Ab4VvHalS0/IwdT357VGuhDI7+8PMHgX+16ADasQClHOuXsp49odXpiVUthv3nSupUp394WGao4V7J/OaT3Ku8cp29oeHqXOubzOa3/F83rKTtIdgBX/OpwAzs2Vprudh6pxrJDM7NsvreZg65xov3Ha6BjhyfJmZfTfNNTqu5kv6mqST+x2cy4/vz3cuO5LeDnwX+AbwwfDXD6S9Trdboz4DfFPSH4fPR3HOuTq6mmBf/uNm9pvAmQS7q1Lp2Oab2S2S/gn4E+BuSX9HcOZf9PmPpR6yc86VzwEzOyAJSQvN7OHY/auJ9ZozPUjwiOaFwLHEwtQ55w5rfh3uid4iaTnwZeB2STuBp9JepGOYSjoP+BjBjoIXmZkfxVMS0wdHix6Cc6UgaQS4G/i5mV0o6QPAOzjapr/fzL7W7Rpm9sbwtx+Q9C1gDPh62rF0q0z/GHizmT2Y9qLOOTckVxOcYxq/J/TjZvaRfi5mZt/pdyAdF6DM7JUepM65spJ0IvDbwA19fv/3wl/3SNod+9gjaXfa6/lBJ865qvpr4A+Zu5ZzlaQfSbqp22NLzOwV4a/Hmtmy2MexaXc/gd+0nyvfl+/qbsbm5TWH3/VwaEkXAtvN7B5J58S+7nrgQwTbRD8EfBT4vW4/SNKHzeyPer3Xi1emJVSD1VHnBjVpZutjHxtbPv9y4PWSHgM+D7xG0mfNbJuZzZjZYeBTwFkJfta5bd47P+2APUydc5VjZu8zsxPN7GTgYuBOM7s0PBA68kbggU7XkPQH4Sn7a8NpgejjZ8D9acfkbb5zrk7+UtI6gjb/MeD3u3zt3wP/B/gLZj/yZI+ZpX6ksYdpDWX9/Ke0jyzx5z+5YTKzbxM8hRQze0uK75sGpiW9DXgTcDJhJkrCzP4szTg8TJ1zfZuxeYU+vDEjXwamCZ5w+ky/F/EwdaUxNXVg4Gvs2uEb9VxqJ5rZeYNepBELUKOrxwe+hsbrdZvT1D4/CCypnU9PFz0El6//K+nXB72IV6YDOjw23Ec2+L585zL3CuBtkh4laPOjx5b8RpqLeJi2WDCRfwVa1WfmOFdTqe8pbacRbX6VlO2G/bQr+c5V0BPAK4HLzOxxgtuqjk97Ea9Mc1LUVtKiV1b9tqj+TW9PfWtj4Q7NqA7z758k2N//GuDPgD3AFwlO308s98pU0oikeyV9NXw9Lul2SY+Ev5arFHOF8JV8V6CzzexK4ACAme0Ejkl7kWG0+dF5g5FrgDvMbA1wB7N3HrghqEEl4RpO0iJJ/0/SDyU9KOmD4fv9FGsHw0OmLbzGSvp4qkiuYdrhvMGLgE3h7zcBb8hzDJ0sOr56tzr5Sv7w+W1RpfUM8BozOwNYB5wn6SX0V6z9DfAlYJWkPwe+R7DFNJW850yj8waPjb13vJltBTCzrZJWtftGSVcAVwCsGqlPJVWllXzfRurKyswMiJ55viD8MIJi7Zzw/U0E20y7HqVnZjdLugfYQHBb1BvMbHO372kntzDtct5gIuGRWxsB1i5cYhkPL5VON+xnfY/poCv5RS8+9SuL+VJXjJnDud3x0fU8Uzjy/Kd7gOcDnzCzuyQlKtZarhOdXfpwm/cSy7Myjc4bvABYBCyT9Flgm6TV4X/oamB7jmMoRJkPha7rfKkvPtXOpJmt7/YFZjYDrAufLPolSaf3+bPOZW71en6b97rKbc6003mDBE87vSz8ssuAr+Q1hjrx+dLh8/nSajCzXQTt/HmExRpAr2Ktw3mm94fnmf4o7TiKuGn/WuBcSY8Q/ItwbT8XGT91LNNBwXB2P1XFsOZLvcUPVPEe0yJJWhlWpEhaDLyWoE1PU6z9PfC68HteF35cCLw4LPxSGcpN+y3nDe4gmOhtnG6LT8OYL/UW39XIamBTOG86D7jFzL4q6V+BWyRdTrCz6c2dLhCdZwpcIukMgl1QAP8MNPtw6GXPyb5a7WTYB5w4544ysx8BZ7Z5P3WxJuldBHcO3Rq+9VlJG83sf6a5Tq3CtJ0sjt9LI4/Fp2HPl3qL7/OlSR06VItb4t5OsAtqHwQr+cC/AqnC1A866aEK55h6i+/cQATE/0WYCd9LpfaVaTtF7H7Kc740S36jvmugTwN3SfoSQYheBNyY9iKNDNMqqestUd7iH+Ur+cUys49J+jbBIdEAbzOze9Nex8M0lOa2qE6LT0XcrO8tvnODkbSIYAvqKwkOOBmRtNnMUv2L72E6BN7it3xfiatSl87MzOE6/P/5twRnmP5N+PoS4O/ocltVOx6mXRS9+NSrxa/qXvws5FWV+ip+I60NT5+KfEvSD9NexFfzay5pi+8LT8Xw+dL+SLpJ0nZJD8Te+4Ckn0u6L/y4IOHl7g2P74uuczbwL2nH5GGaUtr50qq0+MNSg5bQlcNnCPbit/q4ma0LP76W8FpnEzzu+TFJjxHcY/rqcJ9+4j36jWvz290WVcY9+Vm0+HWtSr3Fd2b2XUknZ3S5dqGcWq3DdJDdT3nPl3pV6lxXPc8z7eAqSW8F7gbeGz7PqavwiaQDq3WYDks/LX43XpV2VqeqtA7zpYcOHc7r/5Oe55m2cT3wIYIT9z8EfBT4vawH1onPmabgh5v0z6tSlzcz22ZmM2Z2GPgUcNYwf35twnSYJ0YNqluL71VpZ3WqSl32okOhQ28EHuj0tXlofJvfbvEpzXxp1i1+HWVRldZtt1MdWvwiSfocwa6lCUlbgD8FzpG0jqDNfwz4/WGOqVFhOsgBJ1m1+E2rSsve3ntVWk1mdkmbt1MfTpKlRoWpq6a6VaV1MnNoxv9BCtVmzrQIw2zxvSrNXlEh4C1+PdU2TJPcY5p0vrQMLX4veZ0MVXSQelXqqqK2YZq3LKvSYR5okrYqLVKeQeqtqctaY8K0iNP14/Lc8eTtfXV4i19fjQnTJAZt8ctelaZRdJB6VeqqppKr+eOnDn6D/iCHm6Q9Ub/fqrTIRaci1TVI61iVzhw8VMv/rn7UojItw+6nPKrSXry9d00m6TxJP5b0U0nXFD2eWoRpq0FOi4pr1+KXqSpNompB6lWpS0LSCPAJ4HzgNOASSacVOaZahmmrJItPgxy516kq7fdWqKIekudB6irkLOCnZvaomT0LfJ7gEc2FqeSc6aCKPgy6rO19keocpHWuSvfsfPgbd/7D2Xn8hVrU4zzTE4AnY6+3EJyYX5hGhmkSSVv8fqrSbnpVpXWcJ/Ub86vLzDI5pb4P7f6A29BHEdOINr+XYT6FdND2PokqBWnevCqtrS3ASbHXJwJPFTQWwMO0raKq0l58njSdooPU5er7wBpJp0g6BrgYuK3IAdWuzW9dyW9dfGqdL61KVZpHe+9Bmi+vSvNjZockXQV8AxgBbjKzB4scU+3CNA9ZVKUepLN5kLpBhY9yTvo459xVvs3P+ob9QU6IKvKJox6kgTIEqWumyodpGv20+Gmq0k7yrko9SMvFq9Jmyi1MJZ0k6VuSNkt6UNLV4fvjkm6X9Ej4a27lXNqTovKoSj1Ij8o7SMtQlXqQNleelekh4L1m9kLgJcCV4Xava4A7zGwNcEf4upSSVqUepL01IUhds+UWpma21cx+EP5+D7CZYNfCRcCm8Ms2AW/I6md225Pfq8VPUpVm9TgSD9JslSVIvSpttqGs5ks6GTgTuAs43sy2QhC4klZ1+J4rgCsAVo3k80iObpIeaJK2KvUgzU5ZQhQ8SN0QwlTSKPBF4N1mtltKFgThPtyNAGsXLkm9TazbfGlWVWk/7X03dQrSplSj4EHqArmu5ktaQBCkN5vZreHb2yStDj+/Gtie5xgg/cEmaY/Zi+t3ntSDNDkPUldGea7mC7gR2GxmH4t96jbgsvD3lwFfSXPd+Cn7WdxjmnVV2knZg3Rq6oAHaUoepC4uzzb/5cBbgPsl3Re+937gWuAWSZcDTwBvzuKHJT0Qute9pa1VaRbtfRWCNAsepK7JcgtTM/se7Y/JAtiQ18+F2fOl3Vr81qo0SXvvQTpXk0IUPEhde43am5/2UJOkt0IVHaQ+Pzo8HqSuk0aFaVyvqjRpe1/FIPW2vj8epK6b2oVp0hY/rWEFqbf15QtR8CB1vdUiTJMsPsVb/LRVadmC1KvR4fIgdUnUIkwHkaS9T6rOQdrEEAUPUpdcZcO01z2m8Ra/W1XaS9KqtIxBWoUQhXIGqYeoS6uyYdpO2iP3smrv+w1Sr0bLF6LgQer6U6swbSdpVZp1kHo12llZQxQ8SF3/Kh+m7Rafkqzix6vSMgZpEdWoh6hz/at8mEZ6tfjxqjTtQSZZBWlZq9GmzotGPEhdFmoTpu0k2fHUqyodZpB6Sz9cHqIuS5UK0/iJUZ20a/E7VaVVDVIP0cF4iLo8VCpMI9FtUd1u1m9XlXZr7/sN0qpVox6izuWjkmHaKpov7VWVxsWr0iKCtE4hWuYABQ9RNxy1CNNWvarSNEGatq0vU0vf5CoUPETdcNUyTCNRVZplkA6rGvUQ7Z+HqCtC5cO0tcWPqtJ27X1eQdqEEPUAda67yoZp0seUJLmntN8gLUOINjlAwUPUlUdlwzSuU1WapL3vFaT9VKNJQ9Sr0P54gLoyqlyYxk+LSnqwSZIgzaIazTtEPUCdK6/KhWknnarSfoI0bTVa1RD1AHUuO5UM0/h8abt7S7MO0iJC1APUuWqpZJjC7Ba/2wo+HA3SbvOjWYdoWQK07OEJHqCuHiobpjC7Ku3U3rcL0l7V6DBDtIkB6uHp6qjSYQqzdzulDdKk1WivEC06QD08nSteZcJ0/NQxlj1nrO39pfH2vt8gzTtEswzQMoenB6drqsqEadyi4ydYMDExpyrtFKRZhmgRAerh6Vz5VTJM4w6PrZh1c37SIE0TokkDtO7h6cHpXGeVDNOoKo0H6b7FKzoGabcQLTpAyxicHprOpVepMB1dPd5211NrkLarRrMK0TqFp4emc9mpVJhG4lVpFKSdqtEkIZpXgJYhOD0wnRuOyoRptCc/ure0U5B2aulbQ7RbgPYTnkUGpwemc8WrTJhCsIofVaXxIO1UjSYN0DThWURoelg6V36VCtMFE0GQTq1cOytIu4VouwBNGp7DCE4PSufqoTJhOrp6HI1PcGB0Yk6Q7tytrgHaKzzzCE0PSeeapZAwlXQecB0wAtxgZtf2+p5Fx0+w/4S1/GL0+Ty5d+WcEI0HaKfwHDQ0PSCdc50MPUwljQCfAM4FtgDfl3SbmT3U7Vrf2J0AAARlSURBVPsWTEzw0MJ1PLZt2ZEQjQK0NTzThKYHpHMuC0VUpmcBPzWzRwEkfR64COgapnbKWu64b5RHH5kE2gemB6NzrihFhOkJwJOx11uAs1u/SNIVwBXhy2eWvuI/PTCEsWVlApgsehAp+HjzVYXx/lrRA6i6IsK03WGhNucNs43ARgBJd5vZ+rwHlhUfb758vK6M5hXwM7cAJ8Venwg8VcA4nHMuM0WE6feBNZJOkXQMcDFwWwHjcM65zAy9zTezQ5KuAr5BcGvUTWb2YI9v25j/yDLl482Xj9eVjszmTFc655xLqYg23znnasfD1DnnMlDqMJV0nqQfS/qppGuKHk8rSSdJ+pakzZIelHR1+P64pNslPRL+elzRY42TNCLpXklfDV+XdrySlkv6gqSHw/+dX1ry8b4n/LPwgKTPSVpU5vG67JQ2TGPbTs8HTgMukXRasaOa4xDwXjN7IfAS4MpwjNcAd5jZGuCO8HWZXA1sjr0u83ivA75uZi8AziAYdynHK+kE4F3AejM7nWCB9WJKOl6XrdKGKbFtp2b2LBBtOy0NM9tqZj8If7+H4C/6CQTj3BR+2SbgDcWMcC5JJwK/DdwQe7uU45W0DHgVcCOAmT1rZrso6XhD84HFkuYDSwjuoS7zeF1Gyhym7badnlDQWHqSdDJwJnAXcLyZbYUgcIFVxY1sjr8G/hA4HHuvrON9LvA08OlwWuIGSUsp6XjN7OfAR4AngK3AtJl9k5KO12WrzGGaaNtpGUgaBb4IvNvMdhc9nk4kXQhsN7N7ih5LQvOBFwHXm9mZwD5K3CKHc6EXAacAzwGWSrq02FG5YSlzmFZi26mkBQRBerOZ3Rq+vU3S6vDzq4HtRY2vxcuB10t6jGDa5DWSPkt5x7sF2GJmd4Wvv0AQrmUd72uBn5nZ02Z2ELgVeBnlHa/LUJnDtPTbTiWJYD5vs5l9LPap24DLwt9fBnxl2GNrx8zeZ2YnmtnJBP973mlml1Le8f4CeFLS2vCtDQRHNZZyvATt/UskLQn/bGwgmEcv63hdhkq9A0rSBQRzfNG20z8veEizSHoF8M/A/Rydg3w/wbzpLcCvEvwFe7OZleqwVUnnAP/NzC6UtIKSjlfSOoLFsmOAR4G3ERQBZR3vB4HfIbjT417g7cAoJR2vy06pw9Q556qizG2+c85Vhoepc85lwMPUOecy4GHqnHMZ8DB1zrkMeJi6zISnaP1M0nj4+rjwtT/50tWeh6nLjJk9CVwPXBu+dS2w0cweL25Uzg2H32fqMhVur70HuAl4B3BmeOqXc7U29AfquXozs4OS/jvwdeC3PEhdU3ib7/JwPsERdKcXPRDnhsXD1GUq3Et/LsGTB94TnZbkXN15mLrMhCclXU9wrusTwF8RHJbsXO15mLosvQN4wsxuD19/EniBpFcXOCbnhsJX851zLgNemTrnXAY8TJ1zLgMeps45lwEPU+ecy4CHqXPOZcDD1DnnMuBh6pxzGfj/KXa0Us2xcbAAAAAASUVORK5CYII=\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_surf(Phi)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Successive Over Relaxation (SOR)\n", "Accelerate convergence with the scheme\n", "\n", "\\begin{align}\n", "r_{i, j} &= \\Phi_{i,j}^\\text{new} - \\Phi_{i, j}^\\text{old}\\\\\n", "\\Phi_{i,j}^\\text{new} &= \\Phi_{i,j}^\\text{old} + \\omega r_{i,j}\n", "\\end{align}\n", "\n", "where the new solution is computed with the Gauss-Seidel scheme." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Values of $1 \\leq \\omega \\leq 2$ may work well, $\\omega > 2$ can lead to numerical instabilities. Experiment!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solve Wire-in-a-box with SOR " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Run to convergence (tol = 1e-03). Record the number of steps required (and visually check the solution).\n", "* Start with $\\omega = 1$. What should you get?\n", "* Change $\\omega$ and try to get faster convergence? Who can get it to converge in the fewest number of steps?" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SOR converged in 3797 iterations to 0.0009987117944452034\n" ] } ], "source": [ "Max_iter=10000\n", "tol = 1e-3\n", "Nmax = 100\n", "omega = 1.99\n", "\n", "Phi = np.zeros((Nmax, Nmax), dtype=np.float64)\n", "Phi_old = np.zeros_like(Phi)\n", "residual = np.zeros_like(Phi)\n", "\n", "# initialize boundaries\n", "# everything starts out zero so nothing special for the grounded wires\n", "Phi[0, :] = 100 # wire at x=0 at 100 V\n", "\n", "for n_iter in range(Max_iter):\n", " Phi_old[:, :] = Phi\n", " Phi = Laplace_Gauss_Seidel_odd_even(Phi)\n", " residual[:, :] = Phi - Phi_old\n", " DeltaPhi = np.linalg.norm(residual)\n", " if DeltaPhi < tol:\n", " print(\"SOR converged in {0} iterations to {1}\".format(n_iter+1, DeltaPhi))\n", " break\n", " # SOR\n", " Phi[:, :] = Phi_old + omega*residual # = omega*Phi + (1-omega)*Phi_old\n", "else:\n", " print(\"SOR did NOT converge in {0} iterations, DeltaPhi={1}\".format(n_iter+1, DeltaPhi))\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_surf(Phi)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Simple example of Poisson's equation: Wire and charge\n", "Add a positive charge and a negative charge in the box.\n", "\n", "Now we need to solve **Poisson's equation**.\n", "\n", "$$\n", "\\nabla^2 \\Phi(x, y, z) = -4\\pi\\rho(x, y, z)\\\\\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finite difference solution:\n", "$$\n", "\\Phi_{i,j} = \\frac{1}{4}\\Big(\\Phi_{i+1,j} + \\Phi_{i-1,j} + \\Phi_{i,j+1} + \\Phi_{i,j-1}\\Big)\n", " + \\pi\\rho_{i,j} \\Delta^2\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Poisson Solver \n", "Modify the Laplace solvers to now solve Poisson's equation:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "def Poisson_Jacobi(Phi, rho, Delta=1.):\n", " \"\"\"One update in the Jacobi algorithm for Poisson's equation\"\"\" \n", " Phi[1:-1, 1:-1] = 0.25*(Phi[2:, 1:-1] + Phi[0:-2, 1:-1] + Phi[1:-1, 2:] + Phi[1:-1, 0:-2]) \\\n", " + np.pi * Delta**2 * rho[1:-1, 1:-1]\n", " return Phi\n", "\n", "def Poisson_Gauss_Seidel(Phi, rho, Delta=1.):\n", " \"\"\"One update in the Gauss-Seidel algorithm for Poisson's equation\"\"\" \n", " Nx, Ny = Phi.shape\n", " for xi in range(1, Nx-1):\n", " for yj in range(1, Ny-1):\n", " Phi[xi, yj] = 0.25*(Phi[xi+1, yj] + Phi[xi-1, yj]\n", " + Phi[xi, yj+1] + Phi[xi, yj-1]) \\\n", " + np.pi * Delta**2 * rho[xi, yj]\n", " return Phi\n", "\n", "def Poisson_Gauss_Seidel_odd_even(Phi, rho, Delta=1.):\n", " \"\"\"One update in the Gauss-Seidel algorithm on odd or even fields\"\"\"\n", " a = np.pi * Delta**2\n", " # odd update (uses old even)\n", " Phi[1:-2:2, 1:-2:2] = 0.25*(Phi[2::2, 1:-2:2] + Phi[0:-2:2, 1:-2:2] \n", " + Phi[1:-2:2, 2::2] + Phi[1:-2:2, 0:-2:2]) + a * rho[1:-2:2, 1:-2:2]\n", " Phi[2:-1:2, 2:-1:2] = 0.25*(Phi[3::2, 2:-1:2] + Phi[1:-2:2, 2:-1:2] \n", " + Phi[2:-1:2, 3::2] + Phi[2:-1:2, 1:-2:2]) + a * rho[2:-1:2, 2:-1:2]\n", " \n", " # even update (uses new odd)\n", " Phi[1:-2:2, 2:-1:2] = 0.25*(Phi[2::2, 2:-1:2] + Phi[0:-2:2, 2:-1:2] \n", " + Phi[1:-2:2, 3::2] + Phi[1:-2:2, 1:-1:2]) + a * rho[1:-2:2, 2:-1:2]\n", " Phi[2:-1:2, 1:-2:2] = 0.25*(Phi[3::2, 1:-2:2] + Phi[1:-2:2, 1:-2:2] \n", " + Phi[2:-1:2, 2::2] + Phi[2:-1:2, 0:-2:2]) + a * rho[2:-1:2, 1:-2:2]\n", " return Phi" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solve wire with dipole " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Solve the Poisson problem with SOR (as above), but now employing the Poisson solvers (we are using the fastest one that we have):" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SOR converged in 3823 iterations to 0.0009991605868815044\n" ] } ], "source": [ "Nmax = 100\n", "Max_iter = 10000\n", "omega = 1.99\n", "\n", "Phi = np.zeros((Nmax, Nmax), dtype=np.float64)\n", "Phi_old = np.zeros_like(Phi)\n", "rho = np.zeros_like(Phi)\n", "\n", "# initialize boundaries\n", "# everything starts out zero so nothing special for the grounded wires\n", "Phi[:, 0] = 100 # wire at y=0 at 100 V\n", "rho[25:27, 39:41] = 5.0 \n", "rho[75:77, 39:41] = -5.0 \n", "\n", "Delta = 1.0\n", "\n", "for n_iter in range(Max_iter):\n", " Phi_old[:, :] = Phi\n", " Phi = Poisson_Gauss_Seidel_odd_even(Phi, rho, Delta=Delta)\n", " residual[:, :] = Phi - Phi_old\n", " DeltaPhi = np.linalg.norm(residual)\n", " if DeltaPhi < tol:\n", " print(\"SOR converged in {0} iterations to {1}\".format(n_iter+1, DeltaPhi))\n", " break\n", " # SOR\n", " Phi[:, :] = Phi_old + omega*residual # = omega*Phi + (1-omega)*Phi_old\n", "else:\n", " print(\"SOR did NOT converge in {0} iterations, DeltaPhi={1}\".format(n_iter+1, DeltaPhi))\n", "\n", " " ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_surf(Phi, elevation=40, azimuth=20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Charge density \n", "Given a potential $\\Phi$, Poisson's equation gives the charge density:\n", "$$\n", "\\rho(\\mathbf{x}) = -\\frac{1}{4\\pi} \\nabla^2\\Phi(\\mathbf{x})\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Discretized Laplacian\n", "$$\n", "\\nabla^2 \\Phi \\approx \\frac{\\Phi(x+\\Delta x,y) + \\Phi(x-\\Delta x,y) +\\Phi(x,y+\\Delta y) +\\, \\Phi(x,y-\\Delta y) - 4\\Phi(x, y)}{\\Delta^2}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Laplacian in Python " ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "def laplacian2d(f, Delta=1):\n", " \"\"\"Finite difference approximation of Del^2 f.\n", " \n", " Arguments\n", " ---------\n", " f : M x N matrix\n", " Delta : float\n", " \n", " Returns\n", " -------\n", " M x N matrix, boundaries set to 0\n", " \"\"\"\n", " \n", " L = np.zeros_like(f, dtype=np.float64)\n", " L[1:-1, 1:-1] = f[2:, 1:-1] + f[:-2, 1:-1] + f[1:-1, 2:] + f[1:-1, :-2] - 4*f[1:-1, 1:-1]\n", " return L/Delta**2\n", "\n", "def laplacian2dsimple(f, Delta=1):\n", " L = np.zeros_like(f, dtype=np.float64)\n", " for i in range(1, L.shape[0]-1):\n", " for j in range(1, L.shape[1]-1):\n", " L[i, j] = f[i+1, j] + f[i-1, j] + f[i, j+1] + f[i, j-1] - 4*f[i, j] \n", " return L/Delta**2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Testing the implementation of Laplacian \n", "\n", "Making sure that our fancy numpy-version of the Laplacian is producing the same results as the naive implementation with Python loops:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "def test_laplacian2d():\n", " ftest = np.random.random((200, 200))\n", " assert np.allclose(laplacian2d(ftest), laplacian2dsimple(ftest))\n", "\n", "test_laplacian2d()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Charge density from potential" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the charge density from the converged potential\n", "$$\n", "\\rho(x, y) = -\\frac{1}{4\\pi} \\nabla^2 \\Phi(x, y)\n", "$$" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "rhox = - laplacian2d(Phi)/(4*np.pi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Does `rhox` show the charges of $+5$ and $-5$ that we introduced with the charge density $\\rho$?" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-5.0000041867249845\n", "5.000000000000001\n" ] } ], "source": [ "print(rhox.min())\n", "print(rhox.max())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Indeed, the point charges are recovered from the potential." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the charge density:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_contour(rhox, zlabel=r\"charge density $\\rho$\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The position of the point charges are found correctly but the charge on the wire appear to be absent. This is expected because the Laplacian is not defined on the boundary. If you wanted to see the charge on the wire you would need to include it inside the integration domain and also assign a thickness (e.g., one or two grid cells)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The 3D plot shows the \"point\" charges as spikes of the size of one grid cell:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_surf(rhox, zlabel=r\"charge density $\\rho$\", elevation=20, azimuth=20, offset=-3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The position of the point charges are found correctly but the charge on the wire appear to be absent. The problem is that the Laplacian is not defined on the boundary.\n", "\n", "Also, if the charges are only defined on a single grid cell then the 3D visualization is sometimes not able to show it correctly." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "celltoolbar": "Slideshow", "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": "3.6.7" } }, "nbformat": 4, "nbformat_minor": 2 }