1{ 2 "cells": [ 3 { 4 "cell_type": "markdown", 5 "metadata": {}, 6 "source": [ 7 "# libCEED for Python examples\n", 8 "\n", 9 "This is a tutorial to illustrate the main feautures of the Python interface for [libCEED](https://github.com/CEED/libCEED/), the low-level API library for efficient high-order discretization methods developed by the co-design [Center for Efficient Exascale Discretizations](https://ceed.exascaleproject.org/) (CEED) of the [Exascale Computing Project](https://www.exascaleproject.org/) (ECP).\n", 10 "\n", 11 "While libCEED's focus is on high-order finite/spectral element method implementations, the approach is mostly algebraic and thus applicable to other discretizations in factored form, as explained in the [user manual](https://libceed.org/)." 12 ] 13 }, 14 { 15 "cell_type": "markdown", 16 "metadata": {}, 17 "source": [ 18 "## Setting up libCEED for Python\n", 19 "\n", 20 "Install libCEED for Python by running" 21 ] 22 }, 23 { 24 "cell_type": "code", 25 "execution_count": null, 26 "metadata": {}, 27 "outputs": [], 28 "source": [ 29 "! python -m pip install libceed" 30 ] 31 }, 32 { 33 "cell_type": "markdown", 34 "metadata": {}, 35 "source": [ 36 "## CeedQFunction\n", 37 "\n", 38 "Here we show some basic examples to illustrate the `libceed.QFunction` class. In libCEED, QFunctions represent the spatial terms of the point-wise functions describing the physics at the quadrature points (see [the API documentation](https://libceed.org/en/latest/libCEEDapi.html#api-description)). As shown in the following sketch, QFunctions (such as the one depicted, which defines the Laplacian) are point-wise functions defined at quadrature points. Hence, QFunctions are independent from element shape, resolution and order.\n", 39 "\n", 40 "![alt text][QFunctionSchematic]\n", 41 "\n", 42 "[QFunctionSchematic]: ./img/QFunctionSketch.svg \"Schematic of point-wise QFunctions, defined at quadrature points, belonging to elements that can have different shape, resolution and order.\"" 43 ] 44 }, 45 { 46 "cell_type": "markdown", 47 "metadata": {}, 48 "source": [ 49 "* In the following example, we create and view two QFunctions (for the setup and apply, respectively, of the mass operator in 1D) from the gallery of available built-in QFunctions in libCEED" 50 ] 51 }, 52 { 53 "cell_type": "code", 54 "execution_count": null, 55 "metadata": {}, 56 "outputs": [], 57 "source": [ 58 "import libceed\n", 59 "import numpy as np\n", 60 "\n", 61 "ceed = libceed.Ceed()\n", 62 "\n", 63 "qf_setup = ceed.QFunctionByName(\"Mass1DBuild\")\n", 64 "qf_mass = ceed.QFunctionByName(\"MassApply\")\n", 65 "\n", 66 "print(qf_setup)\n", 67 "print(qf_mass)" 68 ] 69 }, 70 { 71 "cell_type": "markdown", 72 "metadata": {}, 73 "source": [ 74 "* In the following example, we create and evaluate a built-in identity QFunction." 75 ] 76 }, 77 { 78 "cell_type": "code", 79 "execution_count": null, 80 "metadata": {}, 81 "outputs": [], 82 "source": [ 83 "qf = ceed.IdentityQFunction(1, libceed.EVAL_INTERP, libceed.EVAL_INTERP)\n", 84 "\n", 85 "q = 8\n", 86 "\n", 87 "u_array = np.zeros(q, dtype=\"float64\")\n", 88 "for i in range(q):\n", 89 " u_array[i] = i*i\n", 90 "\n", 91 "u = ceed.Vector(q)\n", 92 "u.set_array(u_array, cmode=libceed.USE_POINTER)\n", 93 "v = ceed.Vector(q)\n", 94 "v.set_value(0)\n", 95 "\n", 96 "inputs = [ u ]\n", 97 "outputs = [ v ]\n", 98 "qf.apply(q, inputs, outputs)\n", 99 "\n", 100 "print('v =', v)" 101 ] 102 }, 103 { 104 "cell_type": "markdown", 105 "metadata": {}, 106 "source": [ 107 "* In the following example, we create and evaluate a QFunction (for the mass operator in 1D) from the gallery of available built-in QFunctions in libCEED." 108 ] 109 }, 110 { 111 "cell_type": "code", 112 "execution_count": null, 113 "metadata": {}, 114 "outputs": [], 115 "source": [ 116 "qf_setup = ceed.QFunctionByName(\"Mass1DBuild\")\n", 117 "qf_mass = ceed.QFunctionByName(\"MassApply\")\n", 118 "\n", 119 "q = 8\n", 120 "\n", 121 "j_array = np.zeros(q, dtype=\"float64\")\n", 122 "w_array = np.zeros(q, dtype=\"float64\")\n", 123 "u_array = np.zeros(q, dtype=\"float64\")\n", 124 "v_true = np.zeros(q, dtype=\"float64\")\n", 125 "for i in range(q):\n", 126 " x = 2.*i/(q-1) - 1\n", 127 " j_array[i] = 1\n", 128 " w_array[i] = 1 - x*x\n", 129 " u_array[i] = 2 + 3*x + 5*x*x\n", 130 " v_true[i] = w_array[i] * u_array[i]\n", 131 "\n", 132 "j = ceed.Vector(q)\n", 133 "j.set_array(j_array, cmode=libceed.USE_POINTER)\n", 134 "w = ceed.Vector(q)\n", 135 "w.set_array(w_array, cmode=libceed.USE_POINTER)\n", 136 "u = ceed.Vector(q)\n", 137 "u.set_array(u_array, cmode=libceed.USE_POINTER)\n", 138 "v = ceed.Vector(q)\n", 139 "v.set_value(0)\n", 140 "qdata = ceed.Vector(q)\n", 141 "qdata.set_value(0)\n", 142 "\n", 143 "inputs = [ j, w ]\n", 144 "outputs = [ qdata ]\n", 145 "qf_setup.apply(q, inputs, outputs)\n", 146 "\n", 147 "inputs = [ w, u ]\n", 148 "outputs = [ v ]\n", 149 "qf_mass.apply(q, inputs, outputs)\n", 150 "\n", 151 "print('v =', v)" 152 ] 153 }, 154 { 155 "cell_type": "markdown", 156 "metadata": {}, 157 "source": [ 158 "* In the following example, we create and evaluate a built-in identity QFunction 3 fields per quadrature point." 159 ] 160 }, 161 { 162 "cell_type": "code", 163 "execution_count": null, 164 "metadata": {}, 165 "outputs": [], 166 "source": [ 167 "fields = 3\n", 168 "\n", 169 "qf = ceed.IdentityQFunction(fields, libceed.EVAL_INTERP, libceed.EVAL_INTERP)\n", 170 "\n", 171 "q = 8\n", 172 "\n", 173 "u_array = np.zeros(q*fields, dtype=\"float64\")\n", 174 "for i in range(q*fields):\n", 175 " u_array[i] = i*i\n", 176 "\n", 177 "u = ceed.Vector(q*fields)\n", 178 "u.set_array(u_array, cmode=libceed.USE_POINTER)\n", 179 "v = ceed.Vector(q*fields)\n", 180 "v.set_value(0)\n", 181 "\n", 182 "inputs = [ u ]\n", 183 "outputs = [ v ]\n", 184 "qf.apply(q, inputs, outputs)\n", 185 "\n", 186 "print('v =', v)" 187 ] 188 } 189 ], 190 "metadata": { 191 "kernelspec": { 192 "display_name": "Python 3", 193 "language": "python", 194 "name": "python3" 195 }, 196 "language_info": { 197 "codemirror_mode": { 198 "name": "ipython", 199 "version": 3 200 }, 201 "file_extension": ".py", 202 "mimetype": "text/x-python", 203 "name": "python", 204 "nbconvert_exporter": "python", 205 "pygments_lexer": "ipython3", 206 "version": "3.8.5" 207 } 208 }, 209 "nbformat": 4, 210 "nbformat_minor": 4 211} 212
