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