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