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/types.h> 12 #ifndef CEED_RUNNING_JIT_PASS 13 #include <math.h> 14 #endif 15 16 // ----------------------------------------------------------------------------- 17 // This QFunction sets up the geometric factors required for integration and coordinate transformations when reference coordinates have a different 18 // dimension than the one of physical coordinates 19 // 20 // Reference (parent) 2D coordinates: X \in [-1, 1]^2 21 // 22 // Global 3D physical coordinates given by the mesh: xx \in [-R, R]^3 with R radius of the sphere 23 // 24 // Local 3D physical coordinates on the 2D manifold: x \in [-l, l]^3 with l half edge of the cube inscribed in the sphere 25 // 26 // Change of coordinates matrix computed by the library: 27 // (physical 3D coords relative to reference 2D coords) 28 // dxx_j/dX_i (indicial notation) [3 * 2] 29 // 30 // Change of coordinates x (on the 2D manifold) relative to xx (phyisical 3D): 31 // dx_i/dxx_j (indicial notation) [3 * 3] 32 // 33 // Change of coordinates x (on the 2D manifold) relative to X (reference 2D): 34 // (by chain rule) 35 // dx_i/dX_j [3 * 2] = dx_i/dxx_k [3 * 3] * dxx_k/dX_j [3 * 2] 36 // 37 // mod_J is given by the magnitude of the cross product of the columns of dx_i/dX_j 38 // 39 // The quadrature data is stored in the array q_data. 40 // 41 // We require the determinant of the Jacobian to properly compute integrals of the form: int( u v ) 42 // 43 // Qdata: mod_J * w 44 // ----------------------------------------------------------------------------- 45 CEED_QFUNCTION(SetupMassGeo)(void *ctx, const CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 46 // Inputs 47 const CeedScalar *X = in[0], *J = in[1], *w = in[2]; 48 // Outputs 49 CeedScalar *q_data = out[0]; 50 51 // Quadrature Point Loop 52 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 53 // Read global Cartesian coordinates 54 const CeedScalar xx[3] = {X[i + 0 * Q], X[i + 1 * Q], X[i + 2 * Q]}; 55 56 // Read dxxdX Jacobian entries, stored as 57 // 0 3 58 // 1 4 59 // 2 5 60 const CeedScalar dxxdX[3][2] = { 61 {J[i + Q * 0], J[i + Q * 3]}, 62 {J[i + Q * 1], J[i + Q * 4]}, 63 {J[i + Q * 2], J[i + Q * 5]} 64 }; 65 66 // Setup 67 // x = xx (xx^T xx)^{-1/2} 68 // dx/dxx = I (xx^T xx)^{-1/2} - xx xx^T (xx^T xx)^{-3/2} 69 const CeedScalar mod_xx_sq = xx[0] * xx[0] + xx[1] * xx[1] + xx[2] * xx[2]; 70 CeedScalar xx_sq[3][3]; 71 for (int j = 0; j < 3; j++) { 72 for (int k = 0; k < 3; k++) xx_sq[j][k] = xx[j] * xx[k] / (sqrt(mod_xx_sq) * mod_xx_sq); 73 } 74 75 const CeedScalar dxdxx[3][3] = { 76 {1. / sqrt(mod_xx_sq) - xx_sq[0][0], -xx_sq[0][1], -xx_sq[0][2] }, 77 {-xx_sq[1][0], 1. / sqrt(mod_xx_sq) - xx_sq[1][1], -xx_sq[1][2] }, 78 {-xx_sq[2][0], -xx_sq[2][1], 1. / sqrt(mod_xx_sq) - xx_sq[2][2]} 79 }; 80 81 CeedScalar dxdX[3][2]; 82 for (int j = 0; j < 3; j++) { 83 for (int k = 0; k < 2; k++) { 84 dxdX[j][k] = 0; 85 for (int l = 0; l < 3; l++) dxdX[j][k] += dxdxx[j][l] * dxxdX[l][k]; 86 } 87 } 88 89 // J is given by the cross product of the columns of dxdX 90 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], 91 dxdX[0][0] * dxdX[1][1] - dxdX[1][0] * dxdX[0][1]}; 92 93 // Use the magnitude of J as our detJ (volume scaling factor) 94 const CeedScalar mod_J = sqrt(J[0] * J[0] + J[1] * J[1] + J[2] * J[2]); 95 96 // Interp-to-Interp q_data 97 q_data[i + Q * 0] = mod_J * w[i]; 98 } // End of Quadrature Point Loop 99 100 return 0; 101 } 102 103 // ----------------------------------------------------------------------------- 104 // This QFunction sets up the rhs and true solution for the problem 105 // ----------------------------------------------------------------------------- 106 CEED_QFUNCTION(SetupMassRhs)(void *ctx, const CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 107 // Inputs 108 const CeedScalar *X = in[0], *q_data = in[1]; 109 // Outputs 110 CeedScalar *true_soln = out[0], *rhs = out[1]; 111 112 // Context 113 const CeedScalar *context = (const CeedScalar *)ctx; 114 const CeedScalar R = context[0]; 115 116 // Quadrature Point Loop 117 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 118 // Compute latitude 119 const CeedScalar theta = asin(X[i + 2 * Q] / R); 120 121 // Use absolute value of latitude for true solution 122 true_soln[i] = fabs(theta); 123 124 rhs[i] = q_data[i] * true_soln[i]; 125 } // End of Quadrature Point Loop 126 127 return 0; 128 } 129 130 // ----------------------------------------------------------------------------- 131 // This QFunction applies the mass operator for a scalar field. 132 // 133 // Inputs: 134 // u - Input vector at quadrature points 135 // q_data - Geometric factors 136 // 137 // Output: 138 // v - Output vector (test functions) at quadrature points 139 // ----------------------------------------------------------------------------- 140 CEED_QFUNCTION(Mass)(void *ctx, const CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 141 // Inputs 142 const CeedScalar *u = in[0], *q_data = in[1]; 143 // Outputs 144 CeedScalar *v = out[0]; 145 146 // Quadrature Point Loop 147 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) v[i] = q_data[i] * u[i]; 148 149 return 0; 150 } 151 // ----------------------------------------------------------------------------- 152