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, 52 const CeedScalar *const *in, 53 CeedScalar *const *out) { 54 // Inputs 55 const CeedScalar *X = in[0], *J = in[1], *w = in[2]; 56 // Outputs 57 CeedScalar *q_data = out[0]; 58 59 // Quadrature Point Loop 60 CeedPragmaSIMD 61 for (CeedInt i=0; i<Q; i++) { 62 // Read global Cartesian coordinates 63 const CeedScalar xx[3] = {X[i+0*Q], 64 X[i+1*Q], 65 X[i+2*Q] 66 }; 67 68 // Read dxxdX Jacobian entries, stored as 69 // 0 3 70 // 1 4 71 // 2 5 72 const CeedScalar dxxdX[3][2] = {{J[i+Q*0], 73 J[i+Q*3]}, 74 {J[i+Q*1], 75 J[i+Q*4]}, 76 {J[i+Q*2], 77 J[i+Q*5]} 78 }; 79 80 // Setup 81 // x = xx (xx^T xx)^{-1/2} 82 // dx/dxx = I (xx^T xx)^{-1/2} - xx xx^T (xx^T xx)^{-3/2} 83 const CeedScalar mod_xx_sq = xx[0]*xx[0]+xx[1]*xx[1]+xx[2]*xx[2]; 84 CeedScalar xx_sq[3][3]; 85 for (int j=0; j<3; j++) 86 for (int k=0; k<3; k++) 87 xx_sq[j][k] = xx[j]*xx[k] / (sqrt(mod_xx_sq) * mod_xx_sq); 88 89 const CeedScalar dxdxx[3][3] = {{1./sqrt(mod_xx_sq) - xx_sq[0][0], 90 -xx_sq[0][1], 91 -xx_sq[0][2]}, 92 {-xx_sq[1][0], 93 1./sqrt(mod_xx_sq) - xx_sq[1][1], 94 -xx_sq[1][2]}, 95 {-xx_sq[2][0], 96 -xx_sq[2][1], 97 1./sqrt(mod_xx_sq) - xx_sq[2][2]} 98 }; 99 100 CeedScalar dxdX[3][2]; 101 for (int j=0; j<3; j++) 102 for (int k=0; k<2; k++) { 103 dxdX[j][k] = 0; 104 for (int l=0; l<3; l++) 105 dxdX[j][k] += dxdxx[j][l]*dxxdX[l][k]; 106 } 107 108 // J is given by the cross product of the columns of dxdX 109 const CeedScalar J[3] = {dxdX[1][0]*dxdX[2][1] - dxdX[2][0]*dxdX[1][1], 110 dxdX[2][0]*dxdX[0][1] - dxdX[0][0]*dxdX[2][1], 111 dxdX[0][0]*dxdX[1][1] - dxdX[1][0]*dxdX[0][1] 112 }; 113 114 // Use the magnitude of J as our detJ (volume scaling factor) 115 const CeedScalar mod_J = sqrt(J[0]*J[0]+J[1]*J[1]+J[2]*J[2]); 116 117 // Interp-to-Interp q_data 118 q_data[i+Q*0] = mod_J * w[i]; 119 } // End of Quadrature Point Loop 120 121 return 0; 122 } 123 124 // ----------------------------------------------------------------------------- 125 // This QFunction sets up the rhs and true solution for the problem 126 // ----------------------------------------------------------------------------- 127 CEED_QFUNCTION(SetupMassRhs)(void *ctx, const CeedInt Q, 128 const CeedScalar *const *in, 129 CeedScalar *const *out) { 130 // Inputs 131 const CeedScalar *X = in[0], *q_data = in[1]; 132 // Outputs 133 CeedScalar *true_soln = out[0], *rhs = out[1]; 134 135 // Context 136 const CeedScalar *context = (const CeedScalar*)ctx; 137 const CeedScalar R = context[0]; 138 139 // Quadrature Point Loop 140 CeedPragmaSIMD 141 for (CeedInt i=0; i<Q; i++) { 142 // Compute latitude 143 const CeedScalar theta = asin(X[i+2*Q] / R); 144 145 // Use absolute value of latitude for true solution 146 true_soln[i] = fabs(theta); 147 148 rhs[i] = q_data[i] * true_soln[i]; 149 } // End of Quadrature Point Loop 150 151 return 0; 152 } 153 154 // ----------------------------------------------------------------------------- 155 // This QFunction applies the mass operator for a scalar field. 156 // 157 // Inputs: 158 // u - Input vector at quadrature points 159 // q_data - Geometric factors 160 // 161 // Output: 162 // v - Output vector (test functions) at quadrature points 163 // 164 // ----------------------------------------------------------------------------- 165 CEED_QFUNCTION(Mass)(void *ctx, const CeedInt Q, 166 const CeedScalar *const *in, CeedScalar *const *out) { 167 // Inputs 168 const CeedScalar *u = in[0], *q_data = in[1]; 169 // Outputs 170 CeedScalar *v = out[0]; 171 172 // Quadrature Point Loop 173 CeedPragmaSIMD 174 for (CeedInt i=0; i<Q; i++) 175 v[i] = q_data[i] * u[i]; 176 177 return 0; 178 } 179 // ----------------------------------------------------------------------------- 180 181 #endif // bp1sphere_h 182