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 __CUDACC__ 21 # include <math.h> 22 #endif 23 24 // ***************************************************************************** 25 // This QFunction sets up the geometric factors required for integration and 26 // coordinate transformations when reference coordinates have a different 27 // dimension than the one of physical coordinates 28 // 29 // Reference (parent) 2D coordinates: X \in [-1, 1]^2 30 // 31 // Global 3D physical coordinates given by the mesh: xx \in [-R, R]^3 32 // with R radius of the sphere 33 // 34 // Local 3D physical coordinates on the 2D manifold: x \in [-l, l]^3 35 // with l half edge of the cube inscribed in the sphere 36 // 37 // Change of coordinates matrix computed by the library: 38 // (physical 3D coords relative to reference 2D coords) 39 // dxx_j/dX_i (indicial notation) [3 * 2] 40 // 41 // Change of coordinates x (on the 2D manifold) relative to xx (phyisical 3D): 42 // dx_i/dxx_j (indicial notation) [3 * 3] 43 // 44 // Change of coordinates x (on the 2D manifold) relative to X (reference 2D): 45 // (by chain rule) 46 // dx_i/dX_j [3 * 2] = dx_i/dxx_k [3 * 3] * dxx_k/dX_j [3 * 2] 47 // 48 // modJ is given by the magnitude of the cross product of the columns of dx_i/dX_j 49 // 50 // The quadrature data is stored in the array qdata. 51 // 52 // We require the determinant of the Jacobian to properly compute integrals of 53 // the form: int( u v ) 54 // 55 // Qdata: modJ * w 56 // 57 // ***************************************************************************** 58 59 // ***************************************************************************** 60 CEED_QFUNCTION(SetupMassGeo)(void *ctx, const CeedInt Q, 61 const CeedScalar *const *in, 62 CeedScalar *const *out) { 63 // Inputs 64 const CeedScalar *X = in[0], *J = in[1], *w = in[2]; 65 // Outputs 66 CeedScalar *qdata = out[0]; 67 68 // Quadrature Point Loop 69 CeedPragmaSIMD 70 for (CeedInt i=0; i<Q; i++) { 71 // Read global Cartesian coordinates 72 const CeedScalar xx[3] = {X[i+0*Q], 73 X[i+1*Q], 74 X[i+2*Q] 75 }; 76 77 // Read dxxdX Jacobian entries, stored as 78 // 0 3 79 // 1 4 80 // 2 5 81 const CeedScalar dxxdX[3][2] = {{J[i+Q*0], 82 J[i+Q*3]}, 83 {J[i+Q*1], 84 J[i+Q*4]}, 85 {J[i+Q*2], 86 J[i+Q*5]} 87 }; 88 89 // Setup 90 // x = xx (xx^T xx)^{-1/2} 91 // dx/dxx = I (xx^T xx)^{-1/2} - xx xx^T (xx^T xx)^{-3/2} 92 const CeedScalar modxxsq = xx[0]*xx[0]+xx[1]*xx[1]+xx[2]*xx[2]; 93 CeedScalar xxsq[3][3]; 94 for (int j=0; j<3; j++) 95 for (int k=0; k<3; k++) 96 xxsq[j][k] = xx[j]*xx[k] / (sqrt(modxxsq) * modxxsq); 97 98 const CeedScalar dxdxx[3][3] = {{1./sqrt(modxxsq) - xxsq[0][0], 99 -xxsq[0][1], 100 -xxsq[0][2]}, 101 {-xxsq[1][0], 102 1./sqrt(modxxsq) - xxsq[1][1], 103 -xxsq[1][2]}, 104 {-xxsq[2][0], 105 -xxsq[2][1], 106 1./sqrt(modxxsq) - xxsq[2][2]} 107 }; 108 109 CeedScalar dxdX[3][2]; 110 for (int j=0; j<3; j++) 111 for (int k=0; k<2; k++) { 112 dxdX[j][k] = 0; 113 for (int l=0; l<3; l++) 114 dxdX[j][k] += dxdxx[j][l]*dxxdX[l][k]; 115 } 116 117 // J is given by the cross product of the columns of dxdX 118 const CeedScalar J[3] = {dxdX[1][0]*dxdX[2][1] - dxdX[2][0]*dxdX[1][1], 119 dxdX[2][0]*dxdX[0][1] - dxdX[0][0]*dxdX[2][1], 120 dxdX[0][0]*dxdX[1][1] - dxdX[1][0]*dxdX[0][1] 121 }; 122 123 // Use the magnitude of J as our detJ (volume scaling factor) 124 const CeedScalar modJ = sqrt(J[0]*J[0]+J[1]*J[1]+J[2]*J[2]); 125 126 // Interp-to-Interp qdata 127 qdata[i+Q*0] = modJ * w[i]; 128 } // End of Quadrature Point Loop 129 130 return 0; 131 } 132 133 // ***************************************************************************** 134 // This QFunction sets up the rhs and true solution for the problem 135 // ***************************************************************************** 136 137 // ----------------------------------------------------------------------------- 138 CEED_QFUNCTION(SetupMassRhs)(void *ctx, const CeedInt Q, 139 const CeedScalar *const *in, 140 CeedScalar *const *out) { 141 // Inputs 142 const CeedScalar *X = in[0], *qdata = in[1]; 143 // Outputs 144 CeedScalar *true_soln = out[0], *rhs = out[1]; 145 146 // Context 147 const CeedScalar *context = (const CeedScalar*)ctx; 148 const CeedScalar R = context[0]; 149 150 // Quadrature Point Loop 151 CeedPragmaSIMD 152 for (CeedInt i=0; i<Q; i++) { 153 // Compute latitude 154 const CeedScalar theta = asin(X[i+2*Q] / R); 155 156 // Use absolute value of latitute for true solution 157 true_soln[i] = fabs(theta); 158 159 rhs[i] = qdata[i] * true_soln[i]; 160 } // End of Quadrature Point Loop 161 162 return 0; 163 } 164 165 // ***************************************************************************** 166 // This QFunction applies the mass operator for a scalar field. 167 // 168 // Inputs: 169 // u - Input vector at quadrature points 170 // qdata - Geometric factors 171 // 172 // Output: 173 // v - Output vector (test functions) at quadrature points 174 // 175 // ***************************************************************************** 176 177 // ----------------------------------------------------------------------------- 178 CEED_QFUNCTION(Mass)(void *ctx, const CeedInt Q, 179 const CeedScalar *const *in, CeedScalar *const *out) { 180 // Inputs 181 const CeedScalar *u = in[0], *qdata = in[1]; 182 // Outputs 183 CeedScalar *v = out[0]; 184 185 // Quadrature Point Loop 186 CeedPragmaSIMD 187 for (CeedInt i=0; i<Q; i++) 188 v[i] = qdata[i] * u[i]; 189 190 return 0; 191 } 192 // ----------------------------------------------------------------------------- 193