mpi并行计算二维波动方程C语言代码

以下是一个简单的使用MPI实现二维波动方程的C语言代码：

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <mpi.h>

#define NX 100
#define NY 100
#define T 1000
#define DT 0.01
#define DX 1.0
#define DY 1.0
#define C 1.0

double** alloc_2d_double(int rows, int cols) {
  double** arr = (double**) malloc(rows * sizeof(double*));
  for (int i = 0; i < rows; i++) {
    arr[i] = (double*) malloc(cols * sizeof(double));
  }
  return arr;
}

void free_2d_double(double** arr, int rows) {
  for (int i = 0; i < rows; i++) {
    free(arr[i]);
  }
  free(arr);
}

int main(int argc, char** argv) {
  int size, rank;
  MPI_Init(&argc, &argv);
  MPI_Comm_size(MPI_COMM_WORLD, &size);
  MPI_Comm_rank(MPI_COMM_WORLD, &rank);

  int nx_local = NX / size;
  int nx_start = rank * nx_local;
  int nx_end = (rank + 1) * nx_local;
  if (rank == size - 1) nx_end = NX;

  double** u = alloc_2d_double(nx_local, NY);
  double** u_new = alloc_2d_double(nx_local, NY);

  // Initialize the array
  for (int i = 0; i < nx_local; i++) {
    for (int j = 0; j < NY; j++) {
      u[i][j] = sin(2 * M_PI * i / NX) * sin(2 * M_PI * j / NY);
    }
  }

  // Time-stepping
  for (int t = 0; t < T; t++) {
    // Send and receive ghost cells
    if (rank > 0) {
      MPI_Send(&u[0][0], NY, MPI_DOUBLE, rank - 1, 0, MPI_COMM_WORLD);
      MPI_Recv(&u[nx_start - 1][0], NY, MPI_DOUBLE, rank - 1, 1, MPI_COMM_WORLD, MPI_STATUS_IGNORE);
    }
    if (rank < size - 1) {
      MPI_Send(&u[nx_local - 1][0], NY, MPI_DOUBLE, rank + 1, 1, MPI_COMM_WORLD);
      MPI_Recv(&u[nx_end][0], NY, MPI_DOUBLE, rank + 1, 0, MPI_COMM_WORLD, MPI_STATUS_IGNORE);
    }

    // Update the array
    for (int i = 1; i < nx_local - 1; i++) {
      for (int j = 1; j < NY - 1; j++) {
        u_new[i][j] = 2.0 * u[i][j] - u[i][j-1] - u[i][j+1]
                      + (C * C * DT * DT / (DX * DX)) * (u[i-1][j] - 2.0 * u[i][j] + u[i+1][j])
                      + (C * C * DT * DT / (DY * DY)) * (u[i][j-1] - 2.0 * u[i][j] + u[i][j+1]);
      }
    }

    // Copy back the result
    for (int i = 1; i < nx_local - 1; i++) {
      for (int j = 0; j < NY; j++) {
        u[i][j] = u_new[i][j];
      }
    }
  }

  free_2d_double(u, nx_local);
  free_2d_double(u_new, nx_local);

  MPI_Finalize();
  return 0;
}

该代码将二维数组划分为多个块，并使用MPI进行通信来更新边界。每个进程都负责一定数量的行。在每个时间步长中，每个进程都需要发送和接收其边界的值以更新其边界。最后，每个进程都复制它的块的结果到主数组中。