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 vector field on the sphere using PETSc 19 20 #ifndef bp4sphere_h 21 #define bp4sphere_h 22 23 #ifndef __CUDACC__ 24 # include <math.h> 25 #endif 26 27 // ----------------------------------------------------------------------------- 28 // This QFunction sets up the rhs and true solution for the problem 29 // ----------------------------------------------------------------------------- 30 CEED_QFUNCTION(SetupDiffRhs3)(void *ctx, const CeedInt Q, 31 const CeedScalar *const *in, 32 CeedScalar *const *out) { 33 // Inputs 34 const CeedScalar *X = in[0], *q_data = in[1]; 35 // Outputs 36 CeedScalar *true_soln = out[0], *rhs = out[1]; 37 38 // Context 39 const CeedScalar *context = (const CeedScalar*)ctx; 40 const CeedScalar R = context[0]; 41 42 // Quadrature Point Loop 43 CeedPragmaSIMD 44 for (CeedInt i=0; i<Q; i++) { 45 // Read global Cartesian coordinates 46 CeedScalar x = X[i+Q*0], y = X[i+Q*1], z = X[i+Q*2]; 47 // Normalize quadrature point coordinates to sphere 48 CeedScalar rad = sqrt(x*x + y*y + z*z); 49 x *= R / rad; 50 y *= R / rad; 51 z *= R / rad; 52 // Compute latitude and longitude 53 const CeedScalar theta = asin(z / R); // latitude 54 const CeedScalar lambda = atan2(y, x); // longitude 55 56 // Use absolute value of latitude for true solution 57 // Component 1 58 true_soln[i+0*Q] = sin(lambda) * cos(theta); 59 // Component 2 60 true_soln[i+1*Q] = 2 * true_soln[i+0*Q]; 61 // Component 3 62 true_soln[i+2*Q] = 3 * true_soln[i+0*Q]; 63 64 // Component 1 65 rhs[i+0*Q] = q_data[i+Q*0] * 2 * sin(lambda)*cos(theta) / (R*R); 66 // Component 2 67 rhs[i+1*Q] = 2 * rhs[i+0*Q]; 68 // Component 3 69 rhs[i+2*Q] = 3 * rhs[i+0*Q]; 70 } // End of Quadrature Point Loop 71 72 return 0; 73 } 74 75 // ----------------------------------------------------------------------------- 76 // This QFunction applies the diffusion operator for a vector field of 3 components. 77 // 78 // Inputs: 79 // ug - Input vector Jacobian at quadrature points 80 // q_data - Geometric factors 81 // 82 // Output: 83 // vJ - Output vector (test functions) Jacobian at quadrature points 84 // 85 // ----------------------------------------------------------------------------- 86 CEED_QFUNCTION(Diff3)(void *ctx, const CeedInt Q, 87 const CeedScalar *const *in, CeedScalar *const *out) { 88 const CeedScalar *ug = in[0], *q_data = in[1]; 89 CeedScalar *vJ = out[0]; 90 91 // Quadrature Point Loop 92 CeedPragmaSIMD 93 for (CeedInt i=0; i<Q; i++) { 94 // Read spatial derivatives of u 95 const CeedScalar uJ[3][2] = {{ug[i+(0+0*3)*Q], 96 ug[i+(0+1*3)*Q]}, 97 {ug[i+(1+0*3)*Q], 98 ug[i+(1+1*3)*Q]}, 99 {ug[i+(2+0*3)*Q], 100 ug[i+(2+1*3)*Q]} 101 }; 102 // Read q_data 103 const CeedScalar w_det_J = q_data[i+Q*0]; 104 // -- Grad-to-Grad q_data 105 // ---- dXdx_j,k * dXdx_k,j 106 const CeedScalar dXdxdXdx_T[2][2] = {{q_data[i+Q*1], 107 q_data[i+Q*3]}, 108 {q_data[i+Q*3], 109 q_data[i+Q*2]} 110 }; 111 112 for (int k=0; k<3; k++) // k = component 113 for (int j=0; j<2; j++) // j = direction of vg 114 vJ[i+(k+j*3)*Q] = w_det_J * (uJ[k][0] * dXdxdXdx_T[0][j] + 115 uJ[k][1] * dXdxdXdx_T[1][j]); 116 117 } // End of Quadrature Point Loop 118 119 return 0; 120 } 121 // ----------------------------------------------------------------------------- 122 123 #endif // bp4sphere_h 124