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 #include <ceed.h> 23 24 #ifndef __CUDACC__ 25 # include <math.h> 26 #endif 27 28 // ***************************************************************************** 29 // This QFunction sets up the geometric factors required for integration and 30 // coordinate transformations when reference coordinates have a different 31 // dimension than the one of physical coordinates 32 // 33 // Reference (parent) 2D coordinates: X \in [-1, 1]^2 34 // 35 // Global 3D physical coordinates given by the mesh: xx \in [-R, R]^3 36 // with R radius of the sphere 37 // 38 // Local 3D physical coordinates on the 2D manifold: x \in [-l, l]^3 39 // with l half edge of the cube inscribed in the sphere 40 // 41 // Change of coordinates matrix computed by the library: 42 // (physical 3D coords relative to reference 2D coords) 43 // dxx_j/dX_i (indicial notation) [3 * 2] 44 // 45 // Change of coordinates x (on the 2D manifold) relative to xx (phyisical 3D): 46 // dx_i/dxx_j (indicial notation) [3 * 3] 47 // 48 // Change of coordinates x (on the 2D manifold) relative to X (reference 2D): 49 // (by chain rule) 50 // dx_i/dX_j [3 * 2] = dx_i/dxx_k [3 * 3] * dxx_k/dX_j [3 * 2] 51 // 52 // modJ is given by the magnitude of the cross product of the columns of dx_i/dX_j 53 // 54 // The quadrature data is stored in the array qdata. 55 // 56 // We require the determinant of the Jacobian to properly compute integrals of 57 // the form: int( u v ) 58 // 59 // Qdata: modJ * w 60 // 61 // ***************************************************************************** 62 63 // ***************************************************************************** 64 CEED_QFUNCTION(SetupMassGeo)(void *ctx, const CeedInt Q, 65 const CeedScalar *const *in, 66 CeedScalar *const *out) { 67 // Inputs 68 const CeedScalar *X = in[0], *J = in[1], *w = in[2]; 69 // Outputs 70 CeedScalar *qdata = out[0]; 71 72 // Quadrature Point Loop 73 CeedPragmaSIMD 74 for (CeedInt i=0; i<Q; i++) { 75 // Read global Cartesian coordinates 76 const CeedScalar xx[3] = {X[i+0*Q], 77 X[i+1*Q], 78 X[i+2*Q] 79 }; 80 81 // Read dxxdX Jacobian entries, stored as 82 // 0 3 83 // 1 4 84 // 2 5 85 const CeedScalar dxxdX[3][2] = {{J[i+Q*0], 86 J[i+Q*3]}, 87 {J[i+Q*1], 88 J[i+Q*4]}, 89 {J[i+Q*2], 90 J[i+Q*5]} 91 }; 92 93 // Setup 94 // x = xx (xx^T xx)^{-1/2} 95 // dx/dxx = I (xx^T xx)^{-1/2} - xx xx^T (xx^T xx)^{-3/2} 96 const CeedScalar modxxsq = xx[0]*xx[0]+xx[1]*xx[1]+xx[2]*xx[2]; 97 CeedScalar xxsq[3][3]; 98 for (int j=0; j<3; j++) 99 for (int k=0; k<3; k++) 100 xxsq[j][k] = xx[j]*xx[k] / (sqrt(modxxsq) * modxxsq); 101 102 const CeedScalar dxdxx[3][3] = {{1./sqrt(modxxsq) - xxsq[0][0], 103 -xxsq[0][1], 104 -xxsq[0][2]}, 105 {-xxsq[1][0], 106 1./sqrt(modxxsq) - xxsq[1][1], 107 -xxsq[1][2]}, 108 {-xxsq[2][0], 109 -xxsq[2][1], 110 1./sqrt(modxxsq) - xxsq[2][2]} 111 }; 112 113 CeedScalar dxdX[3][2]; 114 for (int j=0; j<3; j++) 115 for (int k=0; k<2; k++) { 116 dxdX[j][k] = 0; 117 for (int l=0; l<3; l++) 118 dxdX[j][k] += dxdxx[j][l]*dxxdX[l][k]; 119 } 120 121 // J is given by the cross product of the columns of dxdX 122 const CeedScalar J[3] = {dxdX[1][0]*dxdX[2][1] - dxdX[2][0]*dxdX[1][1], 123 dxdX[2][0]*dxdX[0][1] - dxdX[0][0]*dxdX[2][1], 124 dxdX[0][0]*dxdX[1][1] - dxdX[1][0]*dxdX[0][1] 125 }; 126 127 // Use the magnitude of J as our detJ (volume scaling factor) 128 const CeedScalar modJ = sqrt(J[0]*J[0]+J[1]*J[1]+J[2]*J[2]); 129 130 // Interp-to-Interp qdata 131 qdata[i+Q*0] = modJ * w[i]; 132 } // End of Quadrature Point Loop 133 134 return 0; 135 } 136 137 // ***************************************************************************** 138 // This QFunction sets up the rhs and true solution for the problem 139 // ***************************************************************************** 140 141 // ----------------------------------------------------------------------------- 142 CEED_QFUNCTION(SetupMassRhs)(void *ctx, const CeedInt Q, 143 const CeedScalar *const *in, 144 CeedScalar *const *out) { 145 // Inputs 146 const CeedScalar *X = in[0], *qdata = in[1]; 147 // Outputs 148 CeedScalar *true_soln = out[0], *rhs = out[1]; 149 150 // Context 151 const CeedScalar *context = (const CeedScalar*)ctx; 152 const CeedScalar R = context[0]; 153 154 // Quadrature Point Loop 155 CeedPragmaSIMD 156 for (CeedInt i=0; i<Q; i++) { 157 // Compute latitude 158 const CeedScalar theta = asin(X[i+2*Q] / R); 159 160 // Use absolute value of latitute for true solution 161 true_soln[i] = fabs(theta); 162 163 rhs[i] = qdata[i] * true_soln[i]; 164 } // End of Quadrature Point Loop 165 166 return 0; 167 } 168 169 // ***************************************************************************** 170 // This QFunction applies the mass operator for a scalar field. 171 // 172 // Inputs: 173 // u - Input vector at quadrature points 174 // qdata - Geometric factors 175 // 176 // Output: 177 // v - Output vector (test functions) at quadrature points 178 // 179 // ***************************************************************************** 180 181 // ----------------------------------------------------------------------------- 182 CEED_QFUNCTION(Mass)(void *ctx, const CeedInt Q, 183 const CeedScalar *const *in, CeedScalar *const *out) { 184 // Inputs 185 const CeedScalar *u = in[0], *qdata = in[1]; 186 // Outputs 187 CeedScalar *v = out[0]; 188 189 // Quadrature Point Loop 190 CeedPragmaSIMD 191 for (CeedInt i=0; i<Q; i++) 192 v[i] = qdata[i] * u[i]; 193 194 return 0; 195 } 196 // ----------------------------------------------------------------------------- 197 198 #endif // bp1sphere_h 199