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 <math.h> 15 16 // ----------------------------------------------------------------------------- 17 // This QFunction sets up the geometric factors required for integration and 18 // 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 24 // with R radius of the sphere 25 // 26 // Local 3D physical coordinates on the 2D manifold: x \in [-l, l]^3 27 // with l half edge of the cube inscribed in the sphere 28 // 29 // Change of coordinates matrix computed by the library: 30 // (physical 3D coords relative to reference 2D coords) 31 // dxx_j/dX_i (indicial notation) [3 * 2] 32 // 33 // Change of coordinates x (on the 2D manifold) relative to xx (phyisical 3D): 34 // dx_i/dxx_j (indicial notation) [3 * 3] 35 // 36 // Change of coordinates x (on the 2D manifold) relative to X (reference 2D): 37 // (by chain rule) 38 // dx_i/dX_j [3 * 2] = dx_i/dxx_k [3 * 3] * dxx_k/dX_j [3 * 2] 39 // 40 // mod_J is given by the magnitude of the cross product of the columns of dx_i/dX_j 41 // 42 // The quadrature data is stored in the array q_data. 43 // 44 // We require the determinant of the Jacobian to properly compute integrals of 45 // the form: int( u v ) 46 // 47 // Qdata: mod_J * w 48 // 49 // ----------------------------------------------------------------------------- 50 CEED_QFUNCTION(SetupMassGeo)(void *ctx, const CeedInt Q, 51 const CeedScalar *const *in, 52 CeedScalar *const *out) { 53 // Inputs 54 const CeedScalar *X = in[0], *J = in[1], *w = in[2]; 55 // Outputs 56 CeedScalar *q_data = out[0]; 57 58 // Quadrature Point Loop 59 CeedPragmaSIMD 60 for (CeedInt i=0; i<Q; i++) { 61 // Read global Cartesian coordinates 62 const CeedScalar xx[3] = {X[i+0*Q], 63 X[i+1*Q], 64 X[i+2*Q] 65 }; 66 67 // Read dxxdX Jacobian entries, stored as 68 // 0 3 69 // 1 4 70 // 2 5 71 const CeedScalar dxxdX[3][2] = {{J[i+Q*0], 72 J[i+Q*3]}, 73 {J[i+Q*1], 74 J[i+Q*4]}, 75 {J[i+Q*2], 76 J[i+Q*5]} 77 }; 78 79 // Setup 80 // x = xx (xx^T xx)^{-1/2} 81 // dx/dxx = I (xx^T xx)^{-1/2} - xx xx^T (xx^T xx)^{-3/2} 82 const CeedScalar mod_xx_sq = xx[0]*xx[0]+xx[1]*xx[1]+xx[2]*xx[2]; 83 CeedScalar xx_sq[3][3]; 84 for (int j=0; j<3; j++) 85 for (int k=0; k<3; k++) 86 xx_sq[j][k] = xx[j]*xx[k] / (sqrt(mod_xx_sq) * mod_xx_sq); 87 88 const CeedScalar dxdxx[3][3] = {{1./sqrt(mod_xx_sq) - xx_sq[0][0], 89 -xx_sq[0][1], 90 -xx_sq[0][2]}, 91 {-xx_sq[1][0], 92 1./sqrt(mod_xx_sq) - xx_sq[1][1], 93 -xx_sq[1][2]}, 94 {-xx_sq[2][0], 95 -xx_sq[2][1], 96 1./sqrt(mod_xx_sq) - xx_sq[2][2]} 97 }; 98 99 CeedScalar dxdX[3][2]; 100 for (int j=0; j<3; j++) 101 for (int k=0; k<2; k++) { 102 dxdX[j][k] = 0; 103 for (int l=0; l<3; l++) 104 dxdX[j][k] += dxdxx[j][l]*dxxdX[l][k]; 105 } 106 107 // J is given by the cross product of the columns of dxdX 108 const CeedScalar J[3] = {dxdX[1][0]*dxdX[2][1] - dxdX[2][0]*dxdX[1][1], 109 dxdX[2][0]*dxdX[0][1] - dxdX[0][0]*dxdX[2][1], 110 dxdX[0][0]*dxdX[1][1] - dxdX[1][0]*dxdX[0][1] 111 }; 112 113 // Use the magnitude of J as our detJ (volume scaling factor) 114 const CeedScalar mod_J = sqrt(J[0]*J[0]+J[1]*J[1]+J[2]*J[2]); 115 116 // Interp-to-Interp q_data 117 q_data[i+Q*0] = mod_J * w[i]; 118 } // End of Quadrature Point Loop 119 120 return 0; 121 } 122 123 // ----------------------------------------------------------------------------- 124 // This QFunction sets up the rhs and true solution for the problem 125 // ----------------------------------------------------------------------------- 126 CEED_QFUNCTION(SetupMassRhs)(void *ctx, const CeedInt Q, 127 const CeedScalar *const *in, 128 CeedScalar *const *out) { 129 // Inputs 130 const CeedScalar *X = in[0], *q_data = in[1]; 131 // Outputs 132 CeedScalar *true_soln = out[0], *rhs = out[1]; 133 134 // Context 135 const CeedScalar *context = (const CeedScalar*)ctx; 136 const CeedScalar R = context[0]; 137 138 // Quadrature Point Loop 139 CeedPragmaSIMD 140 for (CeedInt i=0; i<Q; i++) { 141 // Compute latitude 142 const CeedScalar theta = asin(X[i+2*Q] / R); 143 144 // Use absolute value of latitude for true solution 145 true_soln[i] = fabs(theta); 146 147 rhs[i] = q_data[i] * true_soln[i]; 148 } // End of Quadrature Point Loop 149 150 return 0; 151 } 152 153 // ----------------------------------------------------------------------------- 154 // This QFunction applies the mass operator for a scalar field. 155 // 156 // Inputs: 157 // u - Input vector at quadrature points 158 // q_data - Geometric factors 159 // 160 // Output: 161 // v - Output vector (test functions) at quadrature points 162 // 163 // ----------------------------------------------------------------------------- 164 CEED_QFUNCTION(Mass)(void *ctx, const CeedInt Q, 165 const CeedScalar *const *in, CeedScalar *const *out) { 166 // Inputs 167 const CeedScalar *u = in[0], *q_data = in[1]; 168 // Outputs 169 CeedScalar *v = out[0]; 170 171 // Quadrature Point Loop 172 CeedPragmaSIMD 173 for (CeedInt i=0; i<Q; i++) 174 v[i] = q_data[i] * u[i]; 175 176 return 0; 177 } 178 // ----------------------------------------------------------------------------- 179 180 #endif // bp1sphere_h 181