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