1 // Copyright (c) 2017, Lawrence Livermore National Security, LLC. Produced at 2 // the Lawrence Livermore National Laboratory. LLNL-CODE-734707. All Rights 3 // reserved. See files LICENSE and NOTICE for details. 4 // 5 // This file is part of CEED, a collection of benchmarks, miniapps, software 6 // libraries and APIs for efficient high-order finite element and spectral 7 // element discretizations for exascale applications. For more information and 8 // source code availability see http://github.com/ceed. 9 // 10 // The CEED research is supported by the Exascale Computing Project 17-SC-20-SC, 11 // a collaborative effort of two U.S. Department of Energy organizations (Office 12 // of Science and the National Nuclear Security Administration) responsible for 13 // the planning and preparation of a capable exascale ecosystem, including 14 // software, applications, hardware, advanced system engineering and early 15 // testbed platforms, in support of the nation's exascale computing imperative. 16 17 /// @file 18 /// libCEED QFunctions for mass operator example for a scalar field on the sphere using PETSc 19 20 #ifndef bp1sphere_h 21 #define bp1sphere_h 22 23 #ifndef __CUDACC__ 24 # include <math.h> 25 #endif 26 27 // ----------------------------------------------------------------------------- 28 // This QFunction sets up the geometric factors required for integration and 29 // coordinate transformations when reference coordinates have a different 30 // dimension than the one of physical coordinates 31 // 32 // Reference (parent) 2D coordinates: X \in [-1, 1]^2 33 // 34 // Global 3D physical coordinates given by the mesh: xx \in [-R, R]^3 35 // with R radius of the sphere 36 // 37 // Local 3D physical coordinates on the 2D manifold: x \in [-l, l]^3 38 // with l half edge of the cube inscribed in the sphere 39 // 40 // Change of coordinates matrix computed by the library: 41 // (physical 3D coords relative to reference 2D coords) 42 // dxx_j/dX_i (indicial notation) [3 * 2] 43 // 44 // Change of coordinates x (on the 2D manifold) relative to xx (phyisical 3D): 45 // dx_i/dxx_j (indicial notation) [3 * 3] 46 // 47 // Change of coordinates x (on the 2D manifold) relative to X (reference 2D): 48 // (by chain rule) 49 // dx_i/dX_j [3 * 2] = dx_i/dxx_k [3 * 3] * dxx_k/dX_j [3 * 2] 50 // 51 // mod_J is given by the magnitude of the cross product of the columns of dx_i/dX_j 52 // 53 // The quadrature data is stored in the array q_data. 54 // 55 // We require the determinant of the Jacobian to properly compute integrals of 56 // the form: int( u v ) 57 // 58 // Qdata: mod_J * w 59 // 60 // ----------------------------------------------------------------------------- 61 CEED_QFUNCTION(SetupMassGeo)(void *ctx, const CeedInt Q, 62 const CeedScalar *const *in, 63 CeedScalar *const *out) { 64 // Inputs 65 const CeedScalar *X = in[0], *J = in[1], *w = in[2]; 66 // Outputs 67 CeedScalar *q_data = out[0]; 68 69 // Quadrature Point Loop 70 CeedPragmaSIMD 71 for (CeedInt i=0; i<Q; i++) { 72 // Read global Cartesian coordinates 73 const CeedScalar xx[3] = {X[i+0*Q], 74 X[i+1*Q], 75 X[i+2*Q] 76 }; 77 78 // Read dxxdX Jacobian entries, stored as 79 // 0 3 80 // 1 4 81 // 2 5 82 const CeedScalar dxxdX[3][2] = {{J[i+Q*0], 83 J[i+Q*3]}, 84 {J[i+Q*1], 85 J[i+Q*4]}, 86 {J[i+Q*2], 87 J[i+Q*5]} 88 }; 89 90 // Setup 91 // x = xx (xx^T xx)^{-1/2} 92 // dx/dxx = I (xx^T xx)^{-1/2} - xx xx^T (xx^T xx)^{-3/2} 93 const CeedScalar mod_xx_sq = xx[0]*xx[0]+xx[1]*xx[1]+xx[2]*xx[2]; 94 CeedScalar xx_sq[3][3]; 95 for (int j=0; j<3; j++) 96 for (int k=0; k<3; k++) 97 xx_sq[j][k] = xx[j]*xx[k] / (sqrt(mod_xx_sq) * mod_xx_sq); 98 99 const CeedScalar dxdxx[3][3] = {{1./sqrt(mod_xx_sq) - xx_sq[0][0], 100 -xx_sq[0][1], 101 -xx_sq[0][2]}, 102 {-xx_sq[1][0], 103 1./sqrt(mod_xx_sq) - xx_sq[1][1], 104 -xx_sq[1][2]}, 105 {-xx_sq[2][0], 106 -xx_sq[2][1], 107 1./sqrt(mod_xx_sq) - xx_sq[2][2]} 108 }; 109 110 CeedScalar dxdX[3][2]; 111 for (int j=0; j<3; j++) 112 for (int k=0; k<2; k++) { 113 dxdX[j][k] = 0; 114 for (int l=0; l<3; l++) 115 dxdX[j][k] += dxdxx[j][l]*dxxdX[l][k]; 116 } 117 118 // J is given by the cross product of the columns of dxdX 119 const CeedScalar J[3] = {dxdX[1][0]*dxdX[2][1] - dxdX[2][0]*dxdX[1][1], 120 dxdX[2][0]*dxdX[0][1] - dxdX[0][0]*dxdX[2][1], 121 dxdX[0][0]*dxdX[1][1] - dxdX[1][0]*dxdX[0][1] 122 }; 123 124 // Use the magnitude of J as our detJ (volume scaling factor) 125 const CeedScalar mod_J = sqrt(J[0]*J[0]+J[1]*J[1]+J[2]*J[2]); 126 127 // Interp-to-Interp q_data 128 q_data[i+Q*0] = mod_J * w[i]; 129 } // End of Quadrature Point Loop 130 131 return 0; 132 } 133 134 // ----------------------------------------------------------------------------- 135 // This QFunction sets up the rhs and true solution for the problem 136 // ----------------------------------------------------------------------------- 137 CEED_QFUNCTION(SetupMassRhs)(void *ctx, const CeedInt Q, 138 const CeedScalar *const *in, 139 CeedScalar *const *out) { 140 // Inputs 141 const CeedScalar *X = in[0], *q_data = in[1]; 142 // Outputs 143 CeedScalar *true_soln = out[0], *rhs = out[1]; 144 145 // Context 146 const CeedScalar *context = (const CeedScalar*)ctx; 147 const CeedScalar R = context[0]; 148 149 // Quadrature Point Loop 150 CeedPragmaSIMD 151 for (CeedInt i=0; i<Q; i++) { 152 // Compute latitude 153 const CeedScalar theta = asin(X[i+2*Q] / R); 154 155 // Use absolute value of latitude for true solution 156 true_soln[i] = fabs(theta); 157 158 rhs[i] = q_data[i] * true_soln[i]; 159 } // End of Quadrature Point Loop 160 161 return 0; 162 } 163 164 // ----------------------------------------------------------------------------- 165 // This QFunction applies the mass operator for a scalar field. 166 // 167 // Inputs: 168 // u - Input vector at quadrature points 169 // q_data - Geometric factors 170 // 171 // Output: 172 // v - Output vector (test functions) at quadrature points 173 // 174 // ----------------------------------------------------------------------------- 175 CEED_QFUNCTION(Mass)(void *ctx, const CeedInt Q, 176 const CeedScalar *const *in, CeedScalar *const *out) { 177 // Inputs 178 const CeedScalar *u = in[0], *q_data = in[1]; 179 // Outputs 180 CeedScalar *v = out[0]; 181 182 // Quadrature Point Loop 183 CeedPragmaSIMD 184 for (CeedInt i=0; i<Q; i++) 185 v[i] = q_data[i] * u[i]; 186 187 return 0; 188 } 189 // ----------------------------------------------------------------------------- 190 191 #endif // bp1sphere_h 192