1 // Copyright (c) 2017-2022, 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 #ifndef bp1sphere_h 12 #define bp1sphere_h 13 14 #include <ceed.h> 15 #include <math.h> 16 17 // ----------------------------------------------------------------------------- 18 // This QFunction sets up the geometric factors required for integration and 19 // coordinate transformations when reference coordinates have a different 20 // dimension than the one of physical coordinates 21 // 22 // Reference (parent) 2D coordinates: X \in [-1, 1]^2 23 // 24 // Global 3D physical coordinates given by the mesh: xx \in [-R, R]^3 25 // with R radius of the sphere 26 // 27 // Local 3D physical coordinates on the 2D manifold: x \in [-l, l]^3 28 // with l half edge of the cube inscribed in the sphere 29 // 30 // Change of coordinates matrix computed by the library: 31 // (physical 3D coords relative to reference 2D coords) 32 // dxx_j/dX_i (indicial notation) [3 * 2] 33 // 34 // Change of coordinates x (on the 2D manifold) relative to xx (phyisical 3D): 35 // dx_i/dxx_j (indicial notation) [3 * 3] 36 // 37 // Change of coordinates x (on the 2D manifold) relative to X (reference 2D): 38 // (by chain rule) 39 // dx_i/dX_j [3 * 2] = dx_i/dxx_k [3 * 3] * dxx_k/dX_j [3 * 2] 40 // 41 // mod_J is given by the magnitude of the cross product of the columns of dx_i/dX_j 42 // 43 // The quadrature data is stored in the array q_data. 44 // 45 // We require the determinant of the Jacobian to properly compute integrals of 46 // the form: int( u v ) 47 // 48 // Qdata: mod_J * w 49 // 50 // ----------------------------------------------------------------------------- 51 CEED_QFUNCTION(SetupMassGeo)(void *ctx, const CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 52 // Inputs 53 const CeedScalar *X = in[0], *J = in[1], *w = in[2]; 54 // Outputs 55 CeedScalar *q_data = out[0]; 56 57 // Quadrature Point Loop 58 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 59 // Read global Cartesian coordinates 60 const CeedScalar xx[3] = {X[i + 0 * Q], X[i + 1 * Q], X[i + 2 * Q]}; 61 62 // Read dxxdX Jacobian entries, stored as 63 // 0 3 64 // 1 4 65 // 2 5 66 const CeedScalar dxxdX[3][2] = { 67 {J[i + Q * 0], J[i + Q * 3]}, 68 {J[i + Q * 1], J[i + Q * 4]}, 69 {J[i + Q * 2], J[i + Q * 5]} 70 }; 71 72 // Setup 73 // x = xx (xx^T xx)^{-1/2} 74 // dx/dxx = I (xx^T xx)^{-1/2} - xx xx^T (xx^T xx)^{-3/2} 75 const CeedScalar mod_xx_sq = xx[0] * xx[0] + xx[1] * xx[1] + xx[2] * xx[2]; 76 CeedScalar xx_sq[3][3]; 77 for (int j = 0; j < 3; j++) { 78 for (int k = 0; k < 3; k++) xx_sq[j][k] = xx[j] * xx[k] / (sqrt(mod_xx_sq) * mod_xx_sq); 79 } 80 81 const CeedScalar dxdxx[3][3] = { 82 {1. / sqrt(mod_xx_sq) - xx_sq[0][0], -xx_sq[0][1], -xx_sq[0][2] }, 83 {-xx_sq[1][0], 1. / sqrt(mod_xx_sq) - xx_sq[1][1], -xx_sq[1][2] }, 84 {-xx_sq[2][0], -xx_sq[2][1], 1. / sqrt(mod_xx_sq) - xx_sq[2][2]} 85 }; 86 87 CeedScalar dxdX[3][2]; 88 for (int j = 0; j < 3; j++) { 89 for (int k = 0; k < 2; k++) { 90 dxdX[j][k] = 0; 91 for (int l = 0; l < 3; l++) dxdX[j][k] += dxdxx[j][l] * dxxdX[l][k]; 92 } 93 } 94 95 // J is given by the cross product of the columns of dxdX 96 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], 97 dxdX[0][0] * dxdX[1][1] - dxdX[1][0] * dxdX[0][1]}; 98 99 // Use the magnitude of J as our detJ (volume scaling factor) 100 const CeedScalar mod_J = sqrt(J[0] * J[0] + J[1] * J[1] + J[2] * J[2]); 101 102 // Interp-to-Interp q_data 103 q_data[i + Q * 0] = mod_J * w[i]; 104 } // End of Quadrature Point Loop 105 106 return 0; 107 } 108 109 // ----------------------------------------------------------------------------- 110 // This QFunction sets up the rhs and true solution for the problem 111 // ----------------------------------------------------------------------------- 112 CEED_QFUNCTION(SetupMassRhs)(void *ctx, const CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 113 // Inputs 114 const CeedScalar *X = in[0], *q_data = in[1]; 115 // Outputs 116 CeedScalar *true_soln = out[0], *rhs = out[1]; 117 118 // Context 119 const CeedScalar *context = (const CeedScalar *)ctx; 120 const CeedScalar R = context[0]; 121 122 // Quadrature Point Loop 123 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 124 // Compute latitude 125 const CeedScalar theta = asin(X[i + 2 * Q] / R); 126 127 // Use absolute value of latitude for true solution 128 true_soln[i] = fabs(theta); 129 130 rhs[i] = q_data[i] * true_soln[i]; 131 } // End of Quadrature Point Loop 132 133 return 0; 134 } 135 136 // ----------------------------------------------------------------------------- 137 // This QFunction applies the mass operator for a scalar field. 138 // 139 // Inputs: 140 // u - Input vector at quadrature points 141 // q_data - Geometric factors 142 // 143 // Output: 144 // v - Output vector (test functions) at quadrature points 145 // 146 // ----------------------------------------------------------------------------- 147 CEED_QFUNCTION(Mass)(void *ctx, const CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 148 // Inputs 149 const CeedScalar *u = in[0], *q_data = in[1]; 150 // Outputs 151 CeedScalar *v = out[0]; 152 153 // Quadrature Point Loop 154 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) v[i] = q_data[i] * u[i]; 155 156 return 0; 157 } 158 // ----------------------------------------------------------------------------- 159 160 #endif // bp1sphere_h 161