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