使用c++mpi.h写一个3维nbody算法

以下是使用MPI实现3维nbody算法的示例代码：

#include <iostream>
#include <cmath>
#include <mpi.h>

using namespace std;

const double G = 6.67428e-11;

struct Body {
    double x, y, z; // position
    double vx, vy, vz; // velocity
    double ax, ay, az; // acceleration
    double mass; // mass
};

void compute_forces(int rank, int num_procs, Body* local_bodies, int local_size, Body* all_bodies, int n) {
    const int chunk_size = ceil(n / (double)num_procs);
    const int start_idx = rank * chunk_size;
    const int end_idx = min(start_idx + chunk_size, n);

    // Compute forces between local bodies
    for (int i = 0; i < local_size; i++) {
        local_bodies[i].ax = local_bodies[i].ay = local_bodies[i].az = 0.0;
        for (int j = i + 1; j < local_size; j++) {
            const double dx = local_bodies[j].x - local_bodies[i].x;
            const double dy = local_bodies[j].y - local_bodies[i].y;
            const double dz = local_bodies[j].z - local_bodies[i].z;
            const double dist_sq = dx * dx + dy * dy + dz * dz;
            const double f = G * local_bodies[i].mass * local_bodies[j].mass / dist_sq;
            const double fx = f * dx / sqrt(dist_sq);
            const double fy = f * dy / sqrt(dist_sq);
            const double fz = f * dz / sqrt(dist_sq);
            local_bodies[i].ax += fx / local_bodies[i].mass;
            local_bodies[i].ay += fy / local_bodies[i].mass;
            local_bodies[i].az += fz / local_bodies[i].mass;
            local_bodies[j].ax -= fx / local_bodies[j].mass;
            local_bodies[j].ay -= fy / local_bodies[j].mass;
            local_bodies[j].az -= fz / local_bodies[j].mass;
        }
    }

    // Compute forces between local and external bodies
    for (int i = 0; i < local_size; i++) {
        for (int j = start_idx; j < end_idx; j++) {
            if (j == i + start_idx) {
                continue;
            }
            const double dx = all_bodies[j].x - local_bodies[i].x;
            const double dy = all_bodies[j].y - local_bodies[i].y;
            const double dz = all_bodies[j].z - local_bodies[i].z;
            const double dist_sq = dx * dx + dy * dy + dz * dz;
            const double f = G * local_bodies[i].mass * all_bodies[j].mass / dist_sq;
            const double fx = f * dx / sqrt(dist_sq);
            const double fy = f * dy / sqrt(dist_sq);
            const double fz = f * dz / sqrt(dist_sq);
            local_bodies[i].ax += fx / local_bodies[i].mass;
            local_bodies[i].ay += fy / local_bodies[i].mass;
            local_bodies[i].az += fz / local_bodies[i].mass;
        }
    }
}

void update_positions(Body* local_bodies, int local_size, double dt) {
    for (int i = 0; i < local_size; i++) {
        local_bodies[i].vx += local_bodies[i].ax * dt;
        local_bodies[i].vy += local_bodies[i].ay * dt;
        local_bodies[i].vz += local_bodies[i].az * dt;
        local_bodies[i].x += local_bodies[i].vx * dt;
        local_bodies[i].y += local_bodies[i].vy * dt;
        local_bodies[i].z += local_bodies[i].vz * dt;
    }
}

int main(int argc, char** argv) {
    MPI_Init(&argc, &argv);

    int rank, num_procs;
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);
    MPI_Comm_size(MPI_COMM_WORLD, &num_procs);

    // Parse command line arguments
    if (argc != 4) {
        if (rank == 0) {
            cerr << "Usage: " << argv[0] << " input_file output_file num_steps" << endl;
        }
        MPI_Finalize();
        return 1;
    }
    const char* input_file = argv[1];
    const char* output_file = argv[2];
    const int num_steps = atoi(argv[3]);

    // Read input file
    int n;
    Body* bodies = nullptr;
    if (rank == 0) {
        ifstream fin(input_file);
        fin >> n;
        bodies = new Body[n];
        for (int i = 0; i < n; i++) {
            fin >> bodies[i].x >> bodies[i].y >> bodies[i].z
                >> bodies[i].vx >> bodies[i].vy >> bodies[i].vz
                >> bodies[i].mass;
        }
        fin.close();
    }

    // Scatter bodies to all processes
    const int chunk_size = ceil(n / (double)num_procs);
    const int start_idx = rank * chunk_size;
    const int end_idx = min(start_idx + chunk_size, n);
    int local_size = end_idx - start_idx;
    Body* local_bodies = new Body[local_size];
    MPI_Scatter(bodies, chunk_size, MPI_DOUBLE, local_bodies, chunk_size, MPI_DOUBLE, 0, MPI_COMM_WORLD);

    double start_time = MPI_Wtime();

    // Run simulation
    for (int step = 0; step < num_steps; step++) {
        // Compute forces
        compute_forces(rank, num_procs, local_bodies, local_size, bodies, n);

        // Update positions
        update_positions(local_bodies, local_size, 0.01);

        // Gather updated positions
        MPI_Gather(local_bodies, chunk_size, MPI_DOUBLE, bodies, chunk_size, MPI_DOUBLE, 0, MPI_COMM_WORLD);
    }

    double end_time = MPI_Wtime();

    // Write output file
    if (rank == 0) {
        ofstream fout(output_file);
        fout << n << endl;
        for (int i = 0; i < n; i++) {
            fout << bodies[i].x << " " << bodies[i].y << " " << bodies[i].z << " "
                << bodies[i].vx << " " << bodies[i].vy << " " << bodies[i].vz << " "
                << bodies[i].mass << endl;
        }
        fout.close();

        cout << "Elapsed time: " << end_time - start_time << " seconds" << endl;

        delete[] bodies;
    }

    delete[] local_bodies;

    MPI_Finalize();

    return 0;
}

该示例代码使用MPI划分了所有的天体，并在每个进程上计算每个天体受到的力和加速度，然后根据每个天体的加速度更新其位置和速度。在每个时间步骤中，所有进程都会将它们的局部状态收集到根进程中，并在根进程中写入结果文件。

请注意，在该示例代码中，我们假设每个进程上的天体数量不超过$n/p$，其中$n$是天体总数，$p$是进程数。如果某个进程上的天体数量小于$n/p$，则该进程将收到无效的数据。在实际应用中，可能需要使用更复杂的负载平衡策略来避免这种情况。