fftw用于等离子体物理中的泊松

Question

我正在尝试解决2D等离子体物理中的泊松问题

根据离散傅立叶变换，我有

然后在解决泊松系统之后我得到了

与 傅立叶系数。

我尝试使用fftw计算E.我有文件poisson.c

#include <complex.h>
#include <fftw3.h>
#include <stdlib.h>
#include <stdio.h>
#include <math.h>

#define PI (double)(3.1415926535897932384626433832795028841971693993751058) //from Wolfram Alpha

#define SQ(var) ((var)*(var))

#define PTS_PER_DIR 32 // power of 2
#define PTS_2D 1024 // PTS_PER_DIR*PTS_PER_DIR

int main()
{
  double rho_in[PTS_2D], ex_out[PTS_2D], ey_out[PTS_2D];
  fftw_complex rho_out[PTS_2D], ex_in[PTS_2D], ey_in[PTS_2D];

  double posX[PTS_PER_DIR], posY[PTS_PER_DIR];
  double lx=2.*PI, ly=2.*PI;
  double dx=lx/(double)(PTS_PER_DIR), dy=ly/(double)(PTS_PER_DIR);

  fftw_plan forward, backward_ex, backward_ey;

  forward=fftw_plan_dft_r2c_2d(PTS_PER_DIR, PTS_PER_DIR, rho_in, rho_out,
                               FFTW_EXHAUSTIVE | FFTW_PRESERVE_INPUT); // need to keep rho in full code
  backward_ex=fftw_plan_dft_c2r_2d(PTS_PER_DIR, PTS_PER_DIR, ex_in, ex_out, FFTW_EXHAUSTIVE);
  backward_ey=fftw_plan_dft_c2r_2d(PTS_PER_DIR, PTS_PER_DIR, ey_in, ey_out, FFTW_EXHAUSTIVE);

  int i1, i2, k1, k2;

  for (i1=0; i1<PTS_PER_DIR; ++i1) {
    posX[i1]=(double)(i1)*dx;
    posY[i1]=(double)(i1)*dy;
  }

  for (i1=0; i1<PTS_PER_DIR; ++i1)
    for (i2=0; i2<PTS_PER_DIR; ++i2)
      rho_in[i1*PTS_PER_DIR+i2]=sin(posY[i2]);

  fftw_execute(forward);

  for (i1=0; i1<PTS_PER_DIR; ++i1) {
    k1=i1;
    if (i1>PTS_PER_DIR/2)
      k1-=PTS_PER_DIR;

    for (i2=0; i2<PTS_PER_DIR; ++i2) {
      k2=i2;
      if (i2>PTS_PER_DIR/2)
        k2-=PTS_PER_DIR;

      if (i1==0 && i2==0) {
        ex_in[0]=0;
        ey_in[0]=0;

        continue;
      }

      ex_in[i1*PTS_PER_DIR+i2]=rho_out[i1*PTS_PER_DIR+i2]*(double)(k1)*I/(2.*PI*lx) /
                           ( SQ((double)(k1)/lx)+SQ((double)(k2)/ly) );
      ey_in[i1*PTS_PER_DIR+i2]=rho_out[i1*PTS_PER_DIR+i2]*(double)(k2)*I/(2.*PI*ly) /
                           ( SQ((double)(k1)/lx)+SQ((double)(k2)/ly) );
    } // for i2
  } // for i1

  fftw_execute(backward_ex);
  fftw_execute(backward_ey);

  for (i1=0; i1<PTS_2D; ++i1) {
    ex_out[i1]/=(double)(PTS_2D);
    ey_out[i1]/=(double)(PTS_2D);
  }

  for (i1=0; i1<PTS_PER_DIR; ++i1) {
    for (i2=0; i2<PTS_PER_DIR; ++i2)
      printf("%lg %lg %lg %lg %lg\n", posX[i1], posY[i2], 
             rho_in[i1*PTS_PER_DIR+i2], ex_out[i1*PTS_PER_DIR+i2], ey_out[i1*PTS_PER_DIR+i2]);
    printf("\n");
  }

  return 0;
}

使用gcc poisson.c -lfftw3 -lm -o poisson编译。

如果输入是 一切正常，但如果输入是 然后它没有，我不明白为什么。

Answer 1

我被fftw3文档上的图片误导了。以下是更正。一个人应该有以下声明

fftw_complex rho_out[PTS_PER_DIR*(PTS_PER_DIR/2+1)],
             ex_in[PTS_PER_DIR*(PTS_PER_DIR/2+1)], ey_in[PTS_PER_DIR*(PTS_PER_DIR/2+1)];

，主循环变为

for (i1=0; i1<PTS_PER_DIR; ++i1) {
  k1=i1;
  if (i1>PTS_PER_DIR/2)
    k1-=PTS_PER_DIR;

  for (i2=0; i2<=PTS_PER_DIR/2; ++i2) {
    k2=i2;

    if (i1==0 && i2==0) {
      ex_in[0]=0;
      ey_in[0]=0;

      continue;
    }

    ex_in[i1*(PTS_PER_DIR/2+1)+i2]=rho_out[i1*(PTS_PER_DIR/2+1)+i2]*(double)(k1)*I/(2.*PI*lx) /
                           ( SQ((double)(k1)/lx)+SQ((double)(k2)/ly) );
    ey_in[i1*(PTS_PER_DIR/2+1)+i2]=rho_out[i1*(PTS_PER_DIR/2+1)+i2]*(double)(k2)*I/(2.*PI*ly) /
                           ( SQ((double)(k1)/lx)+SQ((double)(k2)/ly) );
  } // for i2
} // for i1