MPI中的Jacobi弛豫

Question

1小时前，我提出了一个问题，但问题没有得到很好的回答，所以我重新创建了一个问题。

我得到了C中的Jacobi松弛代码：

while ( error > tol && iter < iter_max ) {
    error = 0.0;

    for( int j = 1; j < n-1; j++)
    {   
        for( int i = 1; i < m-1; i++ )
        {   
            Anew[j][i] = 0.25 * ( A[j][i+1] + A[j][i-1]
                                + A[j-1][i] + A[j+1][i]);
            error = fmax( error, fabs(Anew[j][i] - A[j][i]));
        }
    }

    for( int j = 1; j < n-1; j++)
    {   
        for( int i = 1; i < m-1; i++ )
        {   
            A[j][i] = Anew[j][i];
        }
    }

    if(iter % 100 == 0) printf("%5d, %0.6f\n", iter, error);

    iter++;
}

我做这个的时候：

• 4096x4096阵列
• iter_max = 1000
• 误差= 1.0e-6
• 16芯

我已经用OpenACC并行化了这段代码。现在，我想使用MPI来尝试理解它是如何工作的。但是，对于我所做的第一次实现，我没有很好的结果(新数组的构造并不好)。如何将此代码部分与MPI并行？

Answer 1

下面是我为类似情况编写的代码，您可以使用它作为指南。

do {
  iter++;

  MPI_Irecv(&old[1][0], 1, myHelloVector, nbrs[LEFT], 2, MPI_COMM_WORLD, \
            &requestFourR[LEFT]); 
  MPI_Irecv(&old[1][chunkSize[1]+1], 1, myHelloVector, nbrs[RIGHT], 1, \
            MPI_COMM_WORLD, &requestFourR[RIGHT]); 

  MPI_Irecv(&old[0][1], chunkSize[1], MPI_FLOAT, nbrs[UP], 4, \
            MPI_COMM_WORLD, &requestFourR[UP]);
  MPI_Irecv(&old[chunkSize[0]+1][1], chunkSize[1], MPI_FLOAT, \
            nbrs[DOWN], 3, MPI_COMM_WORLD, &requestFourR[DOWN]);

  MPI_Issend(&old[1][1], 1, myHelloVector, nbrs[LEFT], 1, \
            MPI_COMM_WORLD, &requestFourS[LEFT]);     
  MPI_Issend(&old[1][chunkSize[1]], 1, myHelloVector, nbrs[RIGHT], 2, \
            MPI_COMM_WORLD, &requestFourS[RIGHT]);

  MPI_Issend(&old[1][1], chunkSize[1], MPI_FLOAT, nbrs[UP], 3, \
            MPI_COMM_WORLD, &requestFourS[UP]);
  MPI_Issend(&old[chunkSize[0]][1], chunkSize[1], MPI_FLOAT, nbrs[DOWN], 4, \
            MPI_COMM_WORLD, &requestFourS[DOWN]);

  calImage(old, new, edge, chunkSize[ROWS], chunkSize[COLS]);

  for (itr = 0; itr < 4; itr++) {
    MPI_Waitany(4, &requestFourR[0], &index, &status);
    switch ( index ) {  /* status.MPI_TAG) */
      case 0: /* RIGHT */
              j = 1;
              for (i = 2; i < chunkSize[0]; i++) {
                new[i][j] = 0.25f*(old[i-1][j]+old[i+1][j]+old[i][j-1]+ \
                          old[i][j+1] - edge[i][j]);
              }
              break;
      case 1: /* LEFT */
              j = chunkSize[1];
              for (i = 2; i < chunkSize[0]; i++) {
                new[i][j] = 0.25f*(old[i-1][j]+old[i+1][j]+old[i][j-1]+ \
                          old[i][j+1] - edge[i][j]);
              }
              break;
      case 2: /* DOWN */
              i = 1;
              for (j = 2; j < chunkSize[1]; j++) {
                new[i][j] = 0.25f*(old[i-1][j]+old[i+1][j]+old[i][j-1]+ \
                          old[i][j+1] - edge[i][j]);
              }
              break;
      case 3: /* UP */
              i = chunkSize[0];
              for (j = 2; j < chunkSize[1]; j++) {
                new[i][j] = 0.25f*(old[i-1][j]+old[i+1][j]+old[i][j-1]+ \
                          old[i][j+1] - edge[i][j]);
              }
              break;
    }
  }

  i = 1; j = 1;
  new[i][j] = 0.25f*(old[i-1][j]+old[i+1][j]+old[i][j-1]+old[i][j+1] - \
              edge[i][j]);

  i = 1; j = chunkSize[1];
  new[i][j] = 0.25f*(old[i-1][j]+old[i+1][j]+old[i][j-1]+old[i][j+1] - \
              edge[i][j]);

  i = chunkSize[0]; j = 1;
  new[i][j] = 0.25f*(old[i-1][j]+old[i+1][j]+old[i][j-1]+old[i][j+1] - \
              edge[i][j]);

  i = chunkSize[0]; j = chunkSize[1];
  new[i][j] = 0.25f*(old[i-1][j]+old[i+1][j]+old[i][j-1]+old[i][j+1] - \
              edge[i][j]);

  MPI_Waitall(4, requestFourS, statusS);

  temp = old;
  old = new;
  new = temp;
} while(your_stopping_condition);

calImage()函数正在执行不依赖于晕交换操作的计算。

void calImage(float **image, float **newImage, float **edge, \
          int rows, int cols) {
  int i, j;

  for (i = 2; i < rows; i++) {
    for (j = 2; j < cols; j++) {
      newImage[i][j] = 0.25f * (image[i-1][j] \
                        + image[i+1][j] \
                        + image[i][j-1] \
                        + image[i][j+1] \
                        - edge[i][j]);
    }
  }
}