319 lines
13 KiB
C
319 lines
13 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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/* 只清零不被主循环覆盖的边界面 */
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{
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/* 高边界：k0=ex3-1 */
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for (int j0 = 0; j0 < ex2; ++j0)
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for (int i0 = 0; i0 < ex1; ++i0) {
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const size_t p = idx_ex(i0, j0, ex3 - 1, ex);
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fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
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fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
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}
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/* 高边界：j0=ex2-1 */
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for (int k0 = 0; k0 < ex3 - 1; ++k0)
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for (int i0 = 0; i0 < ex1; ++i0) {
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const size_t p = idx_ex(i0, ex2 - 1, k0, ex);
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fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
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fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
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}
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/* 高边界：i0=ex1-1 */
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for (int k0 = 0; k0 < ex3 - 1; ++k0)
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for (int j0 = 0; j0 < ex2 - 1; ++j0) {
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const size_t p = idx_ex(ex1 - 1, j0, k0, ex);
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fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
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fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
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}
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/* 低边界：当二阶模板也不可用时，对应 i0/j0/k0=0 面 */
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if (kminF == 1) {
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for (int j0 = 0; j0 < ex2; ++j0)
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for (int i0 = 0; i0 < ex1; ++i0) {
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const size_t p = idx_ex(i0, j0, 0, ex);
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fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
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fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
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}
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}
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if (jminF == 1) {
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for (int k0 = 0; k0 < ex3; ++k0)
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for (int i0 = 0; i0 < ex1; ++i0) {
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const size_t p = idx_ex(i0, 0, k0, ex);
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fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
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fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
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}
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}
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if (iminF == 1) {
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for (int k0 = 0; k0 < ex3; ++k0)
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for (int j0 = 0; j0 < ex2; ++j0) {
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const size_t p = idx_ex(0, j0, k0, ex);
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fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
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fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
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}
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}
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}
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/*
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* 两段式：
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* 1) 二阶可用区域先计算二阶模板
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* 2) 高阶可用区域再覆盖四阶模板
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*/
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const int i2_lo = (iminF > 0) ? iminF : 0;
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const int j2_lo = (jminF > 0) ? jminF : 0;
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const int k2_lo = (kminF > 0) ? kminF : 0;
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const int i2_hi = ex1 - 2;
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const int j2_hi = ex2 - 2;
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const int k2_hi = ex3 - 2;
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const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
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const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
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const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
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const int i4_hi = ex1 - 3;
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const int j4_hi = ex2 - 3;
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const int k4_hi = ex3 - 3;
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if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
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for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
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const int kF = k0 + 1;
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for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
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const int jF = j0 + 1;
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for (int i0 = i2_lo; i0 <= i2_hi; ++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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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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if (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi) {
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for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
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const int kF = k0 + 1;
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for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
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const int jF = j0 + 1;
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for (int i0 = i4_lo; i0 <= i4_hi; ++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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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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{
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const double t_jm2 =
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( fh[idx_fh_F_ord2(iF - 2, jF - 2, kF, ex)]
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-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)]
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- fh[idx_fh_F_ord2(iF + 2, jF - 2, kF, ex)] );
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const double t_jm1 =
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( fh[idx_fh_F_ord2(iF - 2, jF - 1, kF, ex)]
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-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)]
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- fh[idx_fh_F_ord2(iF + 2, jF - 1, kF, ex)] );
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const double t_jp1 =
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( fh[idx_fh_F_ord2(iF - 2, jF + 1, kF, ex)]
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-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)]
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- fh[idx_fh_F_ord2(iF + 2, jF + 1, kF, ex)] );
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const double t_jp2 =
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( fh[idx_fh_F_ord2(iF - 2, jF + 2, kF, ex)]
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-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)]
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- fh[idx_fh_F_ord2(iF + 2, jF + 2, kF, ex)] );
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fxy[p] = Fdxdy * ( t_jm2 - F8 * t_jm1 + F8 * t_jp1 - t_jp2 );
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}
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{
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const double t_km2 =
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( fh[idx_fh_F_ord2(iF - 2, jF, kF - 2, ex)]
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-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)]
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- fh[idx_fh_F_ord2(iF + 2, jF, kF - 2, ex)] );
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const double t_km1 =
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( fh[idx_fh_F_ord2(iF - 2, jF, kF - 1, ex)]
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-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)]
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- fh[idx_fh_F_ord2(iF + 2, jF, kF - 1, ex)] );
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const double t_kp1 =
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( fh[idx_fh_F_ord2(iF - 2, jF, kF + 1, ex)]
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-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)]
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- fh[idx_fh_F_ord2(iF + 2, jF, kF + 1, ex)] );
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const double t_kp2 =
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( fh[idx_fh_F_ord2(iF - 2, jF, kF + 2, ex)]
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-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)]
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- fh[idx_fh_F_ord2(iF + 2, jF, kF + 2, ex)] );
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fxz[p] = Fdxdz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 );
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}
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{
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const double t_km2 =
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( fh[idx_fh_F_ord2(iF, jF - 2, kF - 2, ex)]
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-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)]
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- fh[idx_fh_F_ord2(iF, jF + 2, kF - 2, ex)] );
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const double t_km1 =
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( fh[idx_fh_F_ord2(iF, jF - 2, kF - 1, ex)]
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-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)]
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- fh[idx_fh_F_ord2(iF, jF + 2, kF - 1, ex)] );
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const double t_kp1 =
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( fh[idx_fh_F_ord2(iF, jF - 2, kF + 1, ex)]
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-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)]
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- fh[idx_fh_F_ord2(iF, jF + 2, kF + 1, ex)] );
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const double t_kp2 =
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( fh[idx_fh_F_ord2(iF, jF - 2, kF + 2, ex)]
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-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)]
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- fh[idx_fh_F_ord2(iF, jF + 2, kF + 2, ex)] );
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fyz[p] = Fdydz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 );
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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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