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