diff --git a/examples/multipole-moments-accuracy.ipynb b/examples/multipole-moments-accuracy.ipynb new file mode 100644 index 0000000..a91261e --- /dev/null +++ b/examples/multipole-moments-accuracy.ipynb @@ -0,0 +1,404 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "729cda97", + "metadata": {}, + "source": [ + "# Accuracy Comparison\n", + "\n", + "In this notebook, we'll compare the accuracy of approximate results from\n", + "the multipole expansion of various orders with some analytic result.\n", + "\n", + "In particular, we will use the Gaussian unit charge distribution\n", + "\n", + "$$\n", + "\\rho({\\bf r}) = \\frac{\\exp\\left(-|{\\bf r}|^2 / \\sigma^2\\right)}{\\pi^{3/2}\\sigma^3}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "b33ceb28", + "metadata": {}, + "source": [ + "which is known to generate the electrostatic potential\n", + "\n", + "$$\n", + "\\Phi({\\bf r}) = \\frac{{\\rm erf}\\left(|{\\bf r}|/\\sigma\\right)}{|{\\bf r}|}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "579071b7", + "metadata": {}, + "source": [ + "Set up a numerical box containing the charge distribution:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "002955d2", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy.special import erf\n", + "\n", + "N = 101\n", + "x = y = z = np.linspace(-10, 10, N)\n", + "X, Y, Z = np.meshgrid(x, y, z, indexing=\"ij\")\n", + "\n", + "R = np.sqrt(X**2 + Y**2 + Z**2)\n", + "R[R==0] = 0.00001 # cut off singularity\n", + "\n", + "sig = 1.5\n", + "\n", + "# charge distribution\n", + "rho = np.exp(-R**2 / sig**2) / (np.pi**1.5 * sig**3)\n", + "\n", + "# exact potential for comparison\n", + "def phi_ex(r, sigma):\n", + " return erf(r/sigma) / r\n" + ] + }, + { + "cell_type": "markdown", + "id": "8e8cd99c", + "metadata": {}, + "source": [ + "Now prepare the multipole expansion up to high order. Specifically use the version 0.4.0 of *multipoles*:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "53caa4b7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Defaulting to user installation because normal site-packages is not writeable\n", + "Requirement already satisfied: multipoles==0.4.0 in /Users/mbaer/Library/Python/3.9/lib/python/site-packages (0.4.0)\n", + "Requirement already satisfied: numpy in /Users/mbaer/Library/Python/3.9/lib/python/site-packages (from multipoles==0.4.0) (1.24.1)\n", + "Requirement already satisfied: scipy in /Users/mbaer/Library/Python/3.9/lib/python/site-packages (from multipoles==0.4.0) (1.9.3)\n" + ] + } + ], + "source": [ + "! pip install multipoles==0.4.0" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "3ef5c80f", + "metadata": {}, + "outputs": [], + "source": [ + "from multipoles import MultipoleExpansion\n", + "\n", + "mpe = MultipoleExpansion({'discrete': False, 'rho': rho, 'xyz': (X, Y, Z)}, l_max=8)" + ] + }, + { + "cell_type": "markdown", + "id": "335a89ef", + "metadata": {}, + "source": [ + "Now compare the far-away solutions with the exact solution:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "1fd3a351", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'error in multipole expansion up to order l_max')" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "rr = np.logspace(np.log10(3), np.log10(100), 50)\n", + "\n", + "for l_max in range(5):\n", + " phi = np.array([mpe(r, 0, 0, l_max=l_max) for r in rr])\n", + " err = np.abs(phi - phi_ex(rr, sig))\n", + " plt.loglog(rr, err, \"-o\", label=f\"lmax={l_max}\")\n", + " \n", + "plt.legend()\n", + "plt.xlabel(\"x\")\n", + "plt.grid()\n", + "plt.ylabel(\"error in multipole expansion up to order l_max\")" + ] + }, + { + "cell_type": "markdown", + "id": "f830b4ed", + "metadata": {}, + "source": [ + "All curves are on top of each other, so the monopole was sufficient for superb accuracy. That's not surprising,\n", + "since we have a radially symmetric charge distribution. \n", + "\n", + "Let's shift the charge distribution and see what happens. We now have\n", + "\n", + "$$\n", + "\\rho({\\bf r}) = \\frac{\\exp\\left(-|{\\bf r}-{\\bf R}|^2 / \\sigma^2\\right)}{\\pi^{3/2}\\sigma^3}\n", + "$$\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "18a14ede", + "metadata": {}, + "source": [ + "and \n", + "\n", + "$$\n", + "\\Phi({\\bf r}) = \\frac{{\\rm erf}\\left(|{\\bf r}-{\\bf R}|/\\sigma\\right)}{|{\\bf r}-{\\bf R}|}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "2515ce4a", + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "# shift along diagonal by 1 in x-direction:\n", + "R = np.sqrt((X-1)**2 + Y**2 + Z**2)\n", + "\n", + "rho = np.exp(-R**2 / sig**2) / (np.pi**1.5 * sig**3)\n", + "\n", + "mpe = MultipoleExpansion({'discrete': False, 'rho': rho, 'xyz': (X, Y, Z)}, l_max=8)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "c44a35d0", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for l_max in range(4):\n", + " \n", + " phi = np.array([mpe(r, 0, 0, l_max=l_max) for r in rr])\n", + " err = np.abs(phi - phi_ex(rr-1, sig))\n", + " plt.loglog(rr, err, \"-o\", label=f\"lmax={l_max}\")\n", + " \n", + "plt.legend()\n", + "plt.xlabel(\"x\")\n", + "plt.ylabel(\"error in multipole expansion up to order l_max\")\n", + "plt.grid()" + ] + }, + { + "cell_type": "markdown", + "id": "e823fff9", + "metadata": {}, + "source": [ + "All right. That's as expected. Now let's add a few Gaussian charge distributions so that we obtain more\n", + "non-zero multipole moments:" + ] + }, + { + "cell_type": "markdown", + "id": "1d549f5b", + "metadata": {}, + "source": [ + "$$\n", + "\\rho({\\bf r}) = \\sum_i \\frac{Q_i\\exp\\left(-|{\\bf r}-{\\bf R_i}|^2 / \\sigma^2\\right)}{\\pi^{3/2}\\sigma^3}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "87fca45d", + "metadata": {}, + "source": [ + "with corresponding exact potential" + ] + }, + { + "cell_type": "markdown", + "id": "65f4d637", + "metadata": {}, + "source": [ + "$$\n", + "\\Phi({\\bf r}) =\\sum_i Q_i \\frac{{\\rm erf}\\left(|{\\bf r}-{\\bf R_i}|/\\sigma\\right)}{|{\\bf r}-{\\bf R_i}|}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "3ee11098", + "metadata": {}, + "outputs": [], + "source": [ + "Q = [1, -0.5, -1.5, 0.75]\n", + "pos = np.array(\n", + " [(0, 0, 0), (1, 0, 0), (0, 1, 0), (-1, -1, -0.5)]\n", + ")\n", + "\n", + "rho = np.zeros_like(X)\n", + "num_charges, _ = pos.shape\n", + "XYZ = X, Y, Z\n", + "\n", + "phi_ex = np.zeros_like(rho)\n", + "\n", + "for i in range(num_charges):\n", + " xyz_i = pos[i, :]\n", + " R = np.sqrt(sum((XYZ[k] - xyz_i[k])**2 for k in range(3)))\n", + " rho += Q[i] * np.exp(-R**2 / sig**2) / (np.pi**1.5 * sig**3)\n", + "\n", + "mpe = MultipoleExpansion({'discrete': False, 'rho': rho, 'xyz': (X, Y, Z)}, l_max=8)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "7ae4180f", + "metadata": {}, + "outputs": [], + "source": [ + "def phi_ex_xyz(x, y, z, xyz0, Q):\n", + " \"\"\"The exact value of the potential for comparison.\"\"\"\n", + " num_charges, _ = xyz0.shape\n", + " phi = 0\n", + " for i in range(num_charges):\n", + " r = np.sqrt((x-xyz0[i, 0])**2 + (y-xyz0[i, 1])**2 + (z-xyz0[i, 2])**2)\n", + " phi += Q[i] * erf(r/sig) / r\n", + " return phi" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "242b926d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for l_max in range(9):\n", + " phi = mpe(rr, 0, 0, l_max=l_max)\n", + " err = np.abs(phi - phi_ex_xyz(rr, 0, 0, pos, Q))\n", + " plt.loglog(rr, err, \"-o\", label=f\"lmax={l_max}\")\n", + " \n", + "plt.legend()\n", + "plt.xlabel(\"x\")\n", + "plt.ylabel(\"error in multipole expansion up to order l_max\")\n", + "plt.grid()" + ] + }, + { + "cell_type": "markdown", + "id": "b9a3dbd6", + "metadata": {}, + "source": [ + "Now we finally see get contributions from higher multipole moments. As expected, the more\n", + "moments we take into accounts, the smaller the error. Apparently, for our charge distribution,\n", + "calculating up to the octupole ($l_{max}=3$) should be sufficient for the most applications." + ] + } + ], + "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": "3.9.6" + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}