1 // Copyright (c) 2017-2024, Lawrence Livermore National Security, LLC and other CEED contributors. 2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details. 3 // 4 // SPDX-License-Identifier: BSD-2-Clause 5 // 6 // This file is part of CEED: http://github.com/ceed 7 8 /// @file 9 /// libCEED QFunctions for mass operator example for a scalar field on the sphere using PETSc 10 11 #include <ceed.h> 12 #include <math.h> 13 14 // ----------------------------------------------------------------------------- 15 // This QFunction sets up the geometric factors required for integration and coordinate transformations when reference coordinates have a different 16 // dimension than the one of physical coordinates 17 // 18 // Reference (parent) 2D coordinates: X \in [-1, 1]^2 19 // 20 // Global 3D physical coordinates given by the mesh: xx \in [-R, R]^3 with R radius of the sphere 21 // 22 // Local 3D physical coordinates on the 2D manifold: x \in [-l, l]^3 with l half edge of the cube inscribed in the sphere 23 // 24 // Change of coordinates matrix computed by the library: 25 // (physical 3D coords relative to reference 2D coords) 26 // dxx_j/dX_i (indicial notation) [3 * 2] 27 // 28 // Change of coordinates x (on the 2D manifold) relative to xx (phyisical 3D): 29 // dx_i/dxx_j (indicial notation) [3 * 3] 30 // 31 // Change of coordinates x (on the 2D manifold) relative to X (reference 2D): 32 // (by chain rule) 33 // dx_i/dX_j [3 * 2] = dx_i/dxx_k [3 * 3] * dxx_k/dX_j [3 * 2] 34 // 35 // mod_J is given by the magnitude of the cross product of the columns of dx_i/dX_j 36 // 37 // The quadrature data is stored in the array q_data. 38 // 39 // We require the determinant of the Jacobian to properly compute integrals of the form: int( u v ) 40 // 41 // Qdata: mod_J * w 42 // ----------------------------------------------------------------------------- 43 CEED_QFUNCTION(SetupMassGeo)(void *ctx, const CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 44 // Inputs 45 const CeedScalar *X = in[0], *J = in[1], *w = in[2]; 46 // Outputs 47 CeedScalar *q_data = out[0]; 48 49 // Quadrature Point Loop 50 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 51 // Read global Cartesian coordinates 52 const CeedScalar xx[3] = {X[i + 0 * Q], X[i + 1 * Q], X[i + 2 * Q]}; 53 54 // Read dxxdX Jacobian entries, stored as 55 // 0 3 56 // 1 4 57 // 2 5 58 const CeedScalar dxxdX[3][2] = { 59 {J[i + Q * 0], J[i + Q * 3]}, 60 {J[i + Q * 1], J[i + Q * 4]}, 61 {J[i + Q * 2], J[i + Q * 5]} 62 }; 63 64 // Setup 65 // x = xx (xx^T xx)^{-1/2} 66 // dx/dxx = I (xx^T xx)^{-1/2} - xx xx^T (xx^T xx)^{-3/2} 67 const CeedScalar mod_xx_sq = xx[0] * xx[0] + xx[1] * xx[1] + xx[2] * xx[2]; 68 CeedScalar xx_sq[3][3]; 69 for (int j = 0; j < 3; j++) { 70 for (int k = 0; k < 3; k++) xx_sq[j][k] = xx[j] * xx[k] / (sqrt(mod_xx_sq) * mod_xx_sq); 71 } 72 73 const CeedScalar dxdxx[3][3] = { 74 {1. / sqrt(mod_xx_sq) - xx_sq[0][0], -xx_sq[0][1], -xx_sq[0][2] }, 75 {-xx_sq[1][0], 1. / sqrt(mod_xx_sq) - xx_sq[1][1], -xx_sq[1][2] }, 76 {-xx_sq[2][0], -xx_sq[2][1], 1. / sqrt(mod_xx_sq) - xx_sq[2][2]} 77 }; 78 79 CeedScalar dxdX[3][2]; 80 for (int j = 0; j < 3; j++) { 81 for (int k = 0; k < 2; k++) { 82 dxdX[j][k] = 0; 83 for (int l = 0; l < 3; l++) dxdX[j][k] += dxdxx[j][l] * dxxdX[l][k]; 84 } 85 } 86 87 // J is given by the cross product of the columns of dxdX 88 const CeedScalar J[3] = {dxdX[1][0] * dxdX[2][1] - dxdX[2][0] * dxdX[1][1], dxdX[2][0] * dxdX[0][1] - dxdX[0][0] * dxdX[2][1], 89 dxdX[0][0] * dxdX[1][1] - dxdX[1][0] * dxdX[0][1]}; 90 91 // Use the magnitude of J as our detJ (volume scaling factor) 92 const CeedScalar mod_J = sqrt(J[0] * J[0] + J[1] * J[1] + J[2] * J[2]); 93 94 // Interp-to-Interp q_data 95 q_data[i + Q * 0] = mod_J * w[i]; 96 } // End of Quadrature Point Loop 97 98 return 0; 99 } 100 101 // ----------------------------------------------------------------------------- 102 // This QFunction sets up the rhs and true solution for the problem 103 // ----------------------------------------------------------------------------- 104 CEED_QFUNCTION(SetupMassRhs)(void *ctx, const CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 105 // Inputs 106 const CeedScalar *X = in[0], *q_data = in[1]; 107 // Outputs 108 CeedScalar *true_soln = out[0], *rhs = out[1]; 109 110 // Context 111 const CeedScalar *context = (const CeedScalar *)ctx; 112 const CeedScalar R = context[0]; 113 114 // Quadrature Point Loop 115 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 116 // Compute latitude 117 const CeedScalar theta = asin(X[i + 2 * Q] / R); 118 119 // Use absolute value of latitude for true solution 120 true_soln[i] = fabs(theta); 121 122 rhs[i] = q_data[i] * true_soln[i]; 123 } // End of Quadrature Point Loop 124 125 return 0; 126 } 127 128 // ----------------------------------------------------------------------------- 129 // This QFunction applies the mass operator for a scalar field. 130 // 131 // Inputs: 132 // u - Input vector at quadrature points 133 // q_data - Geometric factors 134 // 135 // Output: 136 // v - Output vector (test functions) at quadrature points 137 // ----------------------------------------------------------------------------- 138 CEED_QFUNCTION(Mass)(void *ctx, const CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 139 // Inputs 140 const CeedScalar *u = in[0], *q_data = in[1]; 141 // Outputs 142 CeedScalar *v = out[0]; 143 144 // Quadrature Point Loop 145 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) v[i] = q_data[i] * u[i]; 146 147 return 0; 148 } 149 // ----------------------------------------------------------------------------- 150