c语言用MPI编程的方式实现对等模式的Jacobi叠代求解拉普拉斯方程,程序输入矩阵为16*16的方阵,边缘元素均为8,中间元素均为0,算法迭代次数为10次
时间: 2024-02-12 09:02:36 浏览: 126
好的,这是一个比较复杂的问题,需要详细说明。以下是一个可能的实现方案,供参考:
```c
#include <stdio.h>
#include <stdlib.h>
#include <mpi.h>
#define N 16
#define ITERATIONS 10
int main (int argc, char *argv[]) {
int rank, size, i, j, k;
int chunk_size, start, end;
double A[N+2][N];
double local_A[N/size+2][N];
MPI_Status status;
MPI_Init (&argc, &argv);
MPI_Comm_rank (MPI_COMM_WORLD, &rank);
MPI_Comm_size (MPI_COMM_WORLD, &size);
chunk_size = N / size;
start = rank * chunk_size;
end = (rank == size-1) ? N : (rank+1) * chunk_size;
// 初始化矩阵(边缘元素均为8,中间元素均为0)
for (i = 0; i < N+2; i++) {
for (j = 0; j < N; j++) {
if (i == 0 || i == N+1 || j == 0 || j == N-1) {
A[i][j] = 8.0;
} else {
A[i][j] = 0.0;
}
}
}
// 将矩阵分配给不同的进程
for (i = start+1; i <= end; i++) {
for (j = 0; j < N; j++) {
local_A[i-start][j] = A[i][j];
}
}
// 迭代求解
for (k = 0; k < ITERATIONS; k++) {
// 向左右进程发送和接收数据
if (rank % 2 == 0) {
if (rank != size - 1) {
MPI_Send (local_A[chunk_size], N, MPI_DOUBLE, rank+1, 0, MPI_COMM_WORLD);
MPI_Recv (local_A[chunk_size+1], N, MPI_DOUBLE, rank+1, 0, MPI_COMM_WORLD, &status);
}
if (rank != 0) {
MPI_Send (local_A[1], N, MPI_DOUBLE, rank-1, 0, MPI_COMM_WORLD);
MPI_Recv (local_A[0], N, MPI_DOUBLE, rank-1, 0, MPI_COMM_WORLD, &status);
}
} else {
if (rank != 0) {
MPI_Recv (local_A[0], N, MPI_DOUBLE, rank-1, 0, MPI_COMM_WORLD, &status);
MPI_Send (local_A[1], N, MPI_DOUBLE, rank-1, 0, MPI_COMM_WORLD);
}
if (rank != size - 1) {
MPI_Recv (local_A[chunk_size+1], N, MPI_DOUBLE, rank+1, 0, MPI_COMM_WORLD, &status);
MPI_Send (local_A[chunk_size], N, MPI_DOUBLE, rank+1, 0, MPI_COMM_WORLD);
}
}
// Jacobi 叠代
for (i = 1; i <= chunk_size; i++) {
for (j = 1; j < N-1; j++) {
local_A[i][j] = 0.25 * (local_A[i-1][j] + local_A[i+1][j] +
local_A[i][j-1] + local_A[i][j+1]);
}
}
// 打印每个进程的矩阵
printf("Rank %d\n", rank);
for (i = 0; i < chunk_size+2; i++) {
for (j = 0; j < N; j++) {
printf("%f ", local_A[i][j]);
}
printf("\n");
}
printf("\n");
}
// 收集每个进程的结果并输出
if (rank == 0) {
double result[N][N];
for (i = 1; i <= chunk_size; i++) {
for (j = 0; j < N; j++) {
result[i-1][j] = local_A[i][j];
}
}
for (i = 1; i < size; i++) {
double temp[N/size][N];
MPI_Recv (temp, N/size*N, MPI_DOUBLE, i, 0, MPI_COMM_WORLD, &status);
for (j = 0; j < N/size; j++) {
for (k = 0; k < N; k++) {
result[i*chunk_size+j][k] = temp[j][k];
}
}
}
printf("Final result:\n");
for (i = 0; i < N; i++) {
for (j = 0; j < N; j++) {
printf("%f ", result[i][j]);
}
printf("\n");
}
} else {
double temp[N/size][N];
for (i = 1; i <= chunk_size; i++) {
for (j = 0; j < N; j++) {
temp[i-1][j] = local_A[i][j];
}
}
MPI_Send (temp, N/size*N, MPI_DOUBLE, 0, 0, MPI_COMM_WORLD);
}
MPI_Finalize ();
return 0;
}
```
这个程序使用了 MPI 编程,并且实现了对等模式的 Jacobi 叠代求解拉普拉斯方程。程序将一个 $16 \times 16$ 的矩阵分配给多个进程,并在每个进程上进行迭代计算。每个进程在每次迭代结束后打印自己的矩阵。最后,程序将每个进程的结果收集到主进程,并输出最终结果。
需要注意的是,由于边界元素需要和相邻进程的元素交换,所以每个进程需要额外存储一行元素,即 `local_A[0][j]` 和 `local_A[chunk_size+1][j]`。在计算时需要注意边界元素的处理。
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