#include "tool.h" void fdderivs(const int ex[3], const double *f, double *fxx, double *fxy, double *fxz, double *fyy, double *fyz, double *fzz, const double *X, const double *Y, const double *Z, double SYM1, double SYM2, double SYM3, int Symmetry, int onoff) { (void)onoff; const int NO_SYMM = 0, EQ_SYMM = 1; const double ZEO = 0.0, ONE = 1.0, TWO = 2.0; const double F1o4 = 2.5e-1; // 1/4 const double F8 = 8.0; const double F16 = 16.0; const double F30 = 30.0; const double F1o12 = ONE / 12.0; const double F1o144 = ONE / 144.0; const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2]; const double dX = X[1] - X[0]; const double dY = Y[1] - Y[0]; const double dZ = Z[1] - Z[0]; const int imaxF = ex1; const int jmaxF = ex2; const int kmaxF = ex3; int iminF = 1, jminF = 1, kminF = 1; if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -1; if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -1; if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -1; const double SoA[3] = { SYM1, SYM2, SYM3 }; /* fh: (ex1+2)*(ex2+2)*(ex3+2) because ord=2 */ const size_t nx = (size_t)ex1 + 2; const size_t ny = (size_t)ex2 + 2; const size_t nz = (size_t)ex3 + 2; const size_t fh_size = nx * ny * nz; static double *fh = NULL; static size_t cap = 0; if (fh_size > cap) { free(fh); fh = (double*)aligned_alloc(64, fh_size * sizeof(double)); cap = fh_size; } // double *fh = (double*)malloc(fh_size * sizeof(double)); if (!fh) return; symmetry_bd(2, ex, f, fh, SoA); /* 系数：按 Fortran 原式 */ const double Sdxdx = ONE / (dX * dX); const double Sdydy = ONE / (dY * dY); const double Sdzdz = ONE / (dZ * dZ); const double Fdxdx = F1o12 / (dX * dX); const double Fdydy = F1o12 / (dY * dY); const double Fdzdz = F1o12 / (dZ * dZ); const double Sdxdy = F1o4 / (dX * dY); const double Sdxdz = F1o4 / (dX * dZ); const double Sdydz = F1o4 / (dY * dZ); const double Fdxdy = F1o144 / (dX * dY); const double Fdxdz = F1o144 / (dX * dZ); const double Fdydz = F1o144 / (dY * dZ); const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3; for (size_t p = 0; p < all; ++p) { fxx[p] = ZEO; fxy[p] = ZEO; fxz[p] = ZEO; fyy[p] = ZEO; fyz[p] = ZEO; fzz[p] = ZEO; } // Match Fortran (ghost_width=3, "for bam comparison") exactly: // only compute when x/y/z all satisfy the same-order stencil at this point. for (int k0 = 0; k0 <= ex3 - 2; ++k0) { const int kF = k0 + 1; for (int j0 = 0; j0 <= ex2 - 2; ++j0) { const int jF = j0 + 1; for (int i0 = 0; i0 <= ex1 - 2; ++i0) { const int iF = i0 + 1; const size_t p = idx_ex(i0, j0, k0, ex); if ((iF + 2 <= imaxF && iF - 2 >= iminF) && (jF + 2 <= jmaxF && jF - 2 >= jminF) && (kF + 2 <= kmaxF && kF - 2 >= kminF)) { fxx[p] = Fdxdx * ( -fh[idx_fh_F_ord2(iF - 2, jF, kF, ex)] + F16 * fh[idx_fh_F_ord2(iF - 1, jF, kF, ex)] - F30 * fh[idx_fh_F_ord2(iF, jF, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF, ex)] + F16 * fh[idx_fh_F_ord2(iF + 1, jF, kF, ex)] ); fyy[p] = Fdydy * ( -fh[idx_fh_F_ord2(iF, jF - 2, kF, ex)] + F16 * fh[idx_fh_F_ord2(iF, jF - 1, kF, ex)] - F30 * fh[idx_fh_F_ord2(iF, jF, kF, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF, ex)] + F16 * fh[idx_fh_F_ord2(iF, jF + 1, kF, ex)] ); fzz[p] = Fdzdz * ( -fh[idx_fh_F_ord2(iF, jF, kF - 2, ex)] + F16 * fh[idx_fh_F_ord2(iF, jF, kF - 1, ex)] - F30 * fh[idx_fh_F_ord2(iF, jF, kF, ex)] - fh[idx_fh_F_ord2(iF, jF, kF + 2, ex)] + F16 * fh[idx_fh_F_ord2(iF, jF, kF + 1, ex)] ); fxy[p] = Fdxdy * ( (fh[idx_fh_F_ord2(iF - 2, jF - 2, kF, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF - 2, kF, ex)] + F8 * fh[idx_fh_F_ord2(iF + 1, jF - 2, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF - 2, kF, ex)]) - F8 * (fh[idx_fh_F_ord2(iF - 2, jF - 1, kF, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)] + F8 * fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF - 1, kF, ex)]) + F8 * (fh[idx_fh_F_ord2(iF - 2, jF + 1, kF, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)] + F8 * fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF + 1, kF, ex)]) - (fh[idx_fh_F_ord2(iF - 2, jF + 2, kF, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF + 2, kF, ex)] + F8 * fh[idx_fh_F_ord2(iF + 1, jF + 2, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF + 2, kF, ex)]) ); fxz[p] = Fdxdz * ( (fh[idx_fh_F_ord2(iF - 2, jF, kF - 2, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF, kF - 2, ex)] + F8 * fh[idx_fh_F_ord2(iF + 1, jF, kF - 2, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF - 2, ex)]) - F8 * (fh[idx_fh_F_ord2(iF - 2, jF, kF - 1, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)] + F8 * fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF - 1, ex)]) + F8 * (fh[idx_fh_F_ord2(iF - 2, jF, kF + 1, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)] + F8 * fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF + 1, ex)]) - (fh[idx_fh_F_ord2(iF - 2, jF, kF + 2, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF, kF + 2, ex)] + F8 * fh[idx_fh_F_ord2(iF + 1, jF, kF + 2, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF + 2, ex)]) ); fyz[p] = Fdydz * ( (fh[idx_fh_F_ord2(iF, jF - 2, kF - 2, ex)] - F8 * fh[idx_fh_F_ord2(iF, jF - 1, kF - 2, ex)] + F8 * fh[idx_fh_F_ord2(iF, jF + 1, kF - 2, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF - 2, ex)]) - F8 * (fh[idx_fh_F_ord2(iF, jF - 2, kF - 1, ex)] - F8 * fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)] + F8 * fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF - 1, ex)]) + F8 * (fh[idx_fh_F_ord2(iF, jF - 2, kF + 1, ex)] - F8 * fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)] + F8 * fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF + 1, ex)]) - (fh[idx_fh_F_ord2(iF, jF - 2, kF + 2, ex)] - F8 * fh[idx_fh_F_ord2(iF, jF - 1, kF + 2, ex)] + F8 * fh[idx_fh_F_ord2(iF, jF + 1, kF + 2, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF + 2, ex)]) ); } else if ((iF + 1 <= imaxF && iF - 1 >= iminF) && (jF + 1 <= jmaxF && jF - 1 >= jminF) && (kF + 1 <= kmaxF && kF - 1 >= kminF)) { fxx[p] = Sdxdx * ( fh[idx_fh_F_ord2(iF - 1, jF, kF, ex)] - TWO * fh[idx_fh_F_ord2(iF, jF, kF, ex)] + fh[idx_fh_F_ord2(iF + 1, jF, kF, ex)] ); fyy[p] = Sdydy * ( fh[idx_fh_F_ord2(iF, jF - 1, kF, ex)] - TWO * fh[idx_fh_F_ord2(iF, jF, kF, ex)] + fh[idx_fh_F_ord2(iF, jF + 1, kF, ex)] ); fzz[p] = Sdzdz * ( fh[idx_fh_F_ord2(iF, jF, kF - 1, ex)] - TWO * fh[idx_fh_F_ord2(iF, jF, kF, ex)] + fh[idx_fh_F_ord2(iF, jF, kF + 1, ex)] ); fxy[p] = Sdxdy * ( fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)] - fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)] - fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)] + fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)] ); fxz[p] = Sdxdz * ( fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)] - fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)] - fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)] + fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)] ); fyz[p] = Sdydz * ( fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)] - fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)] - fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)] + fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)] ); } } } } // free(fh); }