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.readthedocs.io/)." 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 "## CeedOperator\n", 37 "\n", 38 "Here we show some basic examples to illustrate the `libceed.Operator` class. In libCEED, a `libceed.Operator` defines the finite/spectral element operator associated to a `libceed.QFunction` (see [the API documentation](https://libceed.readthedocs.io/en/latest/libCEEDapi.html#finite-element-operator-decomposition))." 39 ] 40 }, 41 { 42 "cell_type": "markdown", 43 "metadata": {}, 44 "source": [ 45 "* In the following example, we create and apply a CeedOperator for the mass matrix in 1D. By applying this operator to a vector of 1's, we compute the length of this 1D domain, similar to Ex1-Volume in the [tutorial-6-shell tutorial](./tutorial-6-shell.ipynb)" 46 ] 47 }, 48 { 49 "cell_type": "code", 50 "execution_count": null, 51 "metadata": {}, 52 "outputs": [], 53 "source": [ 54 "import libceed\n", 55 "import numpy as np\n", 56 "\n", 57 "ceed = libceed.Ceed()\n", 58 "\n", 59 "nelem = 15\n", 60 "p = 5\n", 61 "q = 8\n", 62 "nx = nelem + 1\n", 63 "nu = nelem*(p-1) + 1\n", 64 "\n", 65 "# Vectors\n", 66 "x = ceed.Vector(nx)\n", 67 "x_array = np.zeros(nx)\n", 68 "for i in range(nx):\n", 69 " x_array[i] = i / (nx - 1.0)\n", 70 "x.set_array(x_array, cmode=libceed.USE_POINTER)\n", 71 "\n", 72 "qdata = ceed.Vector(nelem*q)\n", 73 "u = ceed.Vector(nu)\n", 74 "v = ceed.Vector(nu)\n", 75 "\n", 76 "# Restrictions\n", 77 "indx = np.zeros(nx*2, dtype=\"int32\")\n", 78 "for i in range(nx):\n", 79 " indx[2*i+0] = i\n", 80 " indx[2*i+1] = i+1\n", 81 "rx = ceed.ElemRestriction(nelem, 2, 1, 1, nx, indx, cmode=libceed.USE_POINTER)\n", 82 "\n", 83 "indu = np.zeros(nelem*p, dtype=\"int32\")\n", 84 "for i in range(nelem):\n", 85 " for j in range(p):\n", 86 " indu[p*i+j] = i*(p-1) + j\n", 87 "ru = ceed.ElemRestriction(nelem, p, 1, 1, nu, indu, cmode=libceed.USE_POINTER)\n", 88 "strides = np.array([1, q, q], dtype=\"int32\")\n", 89 "rui = ceed.StridedElemRestriction(nelem, q, 1, q*nelem, strides)\n", 90 "\n", 91 "# Bases\n", 92 "bx = ceed.BasisTensorH1Lagrange(1, 1, 2, q, libceed.GAUSS)\n", 93 "bu = ceed.BasisTensorH1Lagrange(1, 1, p, q, libceed.GAUSS)\n", 94 "\n", 95 "# QFunctions\n", 96 "qf_setup = ceed.QFunctionByName(\"Mass1DBuild\")\n", 97 "qf_mass = ceed.QFunctionByName(\"MassApply\")\n", 98 "\n", 99 "# Setup operator\n", 100 "op_setup = ceed.Operator(qf_setup)\n", 101 "op_setup.set_field(\"dx\", rx, bx, libceed.VECTOR_ACTIVE)\n", 102 "op_setup.set_field(\"weights\", libceed.ELEMRESTRICTION_NONE, bx,\n", 103 " libceed.VECTOR_NONE)\n", 104 "op_setup.set_field(\"qdata\", rui, libceed.BASIS_COLLOCATED,\n", 105 " libceed.VECTOR_ACTIVE)\n", 106 "op_setup.check()\n", 107 "print('Setup operator: ', op_setup)\n", 108 "\n", 109 "# Mass operator\n", 110 "op_mass = ceed.Operator(qf_mass)\n", 111 "op_mass.set_field(\"u\", ru, bu, libceed.VECTOR_ACTIVE)\n", 112 "op_mass.set_field(\"qdata\", rui, libceed.BASIS_COLLOCATED, qdata)\n", 113 "op_mass.set_field(\"v\", ru, bu, libceed.VECTOR_ACTIVE)\n", 114 "op_mass.check()\n", 115 "print('Mass operator: ', op_mass)\n", 116 "\n", 117 "# Setup\n", 118 "op_setup.apply(x, qdata)\n", 119 "\n", 120 "# Apply mass matrix\n", 121 "u.set_value(1)\n", 122 "op_mass.apply(u, v)\n", 123 "\n", 124 "# Check\n", 125 "with v.array_read() as v_array:\n", 126 " print('The length of the domain is l = %4.2f'%np.sum(v_array))" 127 ] 128 } 129 ], 130 "metadata": { 131 "kernelspec": { 132 "display_name": "Python 3", 133 "language": "python", 134 "name": "python3" 135 }, 136 "language_info": { 137 "codemirror_mode": { 138 "name": "ipython", 139 "version": 3 140 }, 141 "file_extension": ".py", 142 "mimetype": "text/x-python", 143 "name": "python", 144 "nbconvert_exporter": "python", 145 "pygments_lexer": "ipython3", 146 "version": "3.8.5" 147 } 148 }, 149 "nbformat": 4, 150 "nbformat_minor": 4 151} 152