基于 MPI/OpenMP 混合编程的大规模多体（N-Body）问题仿真实验

完整代码：

#include <iostream>
#include <ctime>
#include <mpi.h>
#include <omp.h>
#include <cstdlib>
#include <iomanip>
#include <Windows.h>
#include <cmath>
#include <algorithm>

using namespace std;
const long double G = 6.67 * pow(10, -11);
const int STAR_NUM = 32;
const int THREAD_NUM = 4;
const long int TIME_STEP = 3600;
const int MAX_PROCESS = 128;

struct Star
{
    long double x, y, z; // Position
    long double vx, vy, vz; // Speed
    long double ax, ay, az; // Acceleration
    long double nax, nay, naz; // Acceleration of next iteration
    long double m; // Mass
};

Star stars[STAR_NUM];
Star temp[STAR_NUM];
Star buffer[STAR_NUM];

void updateNextAcceration(Star& a, Star& b) {
    long double dx = a.x - b.x;
    long double dy = a.y - b.y;
    long double dz = a.z - b.z;
    long double r2 = pow(dx, 2) + pow(dy, 2) + pow(dz, 2);
    long double A = G * a.m / r2;
    long double r = sqrt(r2);
    long double k = A / r;
    b.nax += k * dx;
    b.nay += k * dy;
    b.naz += k * dz;
}

void updateAcceration(Star& star) {
    star.ax = star.nax;
    star.ay = star.nay;
    star.az = star.naz;
    star.nax = 0;
    star.nay = 0;
    star.naz = 0;
}

void updateSpeed(Star& star) {
    star.vx += star.ax * TIME_STEP;
    star.vy += star.ay * TIME_STEP;
    star.vz += star.az * TIME_STEP;
}

void updatePosition(Star& star) {
    star.x += star.vx * TIME_STEP;
    star.y += star.vy * TIME_STEP;
    star.z += star.vz * TIME_STEP;
}

void print(Star* stars, int num=STAR_NUM) {
    cout << setiosflags(ios::left) << setw(4) << "Num" << setw(16) << "x" << setw(16) << "y" << setw(16) << "z"
        << setw(16) << "Speed x" << setw(16) << "Speed y" << setw(16) << "Speed z"
        << setw(16) << "Acceleration x" << setw(16) << "Acceleration y" << setw(16) << "Acceleration z"
        << setw(16) << "Next a x" << setw(16) << "Next a y" << setw(16) << "Next a z"
        << setw(16) << "Mass" << endl;
    for (int i = 0; i < num; i++) {
        cout << setiosflags(ios::left) << setw(4) << i << setw(16) << stars[i].x << setw(16) << stars[i].y << setw(16) << stars[i].z
            << setw(16) << stars[i].vx << setw(16) << stars[i].vy << setw(16) << stars[i].vz
            << setw(16) << stars[i].ax << setw(16) << stars[i].ay << setw(16) << stars[i].az
            << setw(16) << stars[i].nax << setw(16) << stars[i].nay << setw(16) << stars[i].naz
            << setw(16) << stars[i].m << endl;
    }
}

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

    real_size = min(STAR_NUM, size);
    // 每个进程的工作量
    int part = STAR_NUM / real_size;
    if (part * real_size < STAR_NUM) part++; // 每个进程的工作量已确定
    // 现在要剔除不需要的进程
    size = STAR_NUM / part;
    if (size * part < STAR_NUM) size++; // 进程数已确定

    MPI_Comm COMM_WORLD;
    if (rank < size) {
        MPI_Comm_split(MPI_COMM_WORLD, 1, rank, &COMM_WORLD);
    }else {
        MPI_Comm_split(MPI_COMM_WORLD, MPI_UNDEFINED, rank, &COMM_WORLD);
    }

    MPI_Comm_rank(COMM_WORLD, &rank);
    MPI_Comm_size(COMM_WORLD, &size);
    //int part = STAR_NUM / size;
    //if (part * size < STAR_NUM) part++;

    // Create custome mpi datatype.
    const int nitems = 13;
    int blocklengths[nitems] = { 1,1,1,1, 1,1, 1,1, 1,1, 1,1,1 };
    MPI_Datatype types[nitems] = { MPI_LONG_DOUBLE,MPI_LONG_DOUBLE, MPI_LONG_DOUBLE, MPI_LONG_DOUBLE, MPI_LONG_DOUBLE, MPI_LONG_DOUBLE, MPI_LONG_DOUBLE, MPI_LONG_DOUBLE, MPI_LONG_DOUBLE, MPI_LONG_DOUBLE, MPI_LONG_DOUBLE, MPI_LONG_DOUBLE, MPI_LONG_DOUBLE };
    MPI_Datatype MPI_STAR;
    MPI_Aint offsets[nitems];
    offsets[0] = offsetof(Star, x);
    offsets[1] = offsetof(Star, y);
    offsets[2] = offsetof(Star, z);
    offsets[3] = offsetof(Star, vx);
    offsets[4] = offsetof(Star, vy);
    offsets[5] = offsetof(Star, vz);
    offsets[6] = offsetof(Star, ax);
    offsets[7] = offsetof(Star, ay);
    offsets[8] = offsetof(Star, az);
    offsets[9] = offsetof(Star, nax);
    offsets[10] = offsetof(Star, nay);
    offsets[11] = offsetof(Star, naz);
    offsets[12] = offsetof(Star, m);
    MPI_Type_create_struct(nitems, blocklengths, offsets, types, &MPI_STAR);
    MPI_Type_commit(&MPI_STAR);

    omp_set_num_threads(THREAD_NUM);

    if (rank == 0) {
        cout << "Generating origin data..." << endl;
        srand(time(NULL));
        for (int i = 0; i < STAR_NUM; i++) {
            stars[i].m = pow(10, 21) + ((long double)rand() / (RAND_MAX)) * pow(10, 22);
            stars[i].x = pow(10, 7) + ((long double)rand() / (RAND_MAX)) * pow(10, 8);
            stars[i].y = pow(10, 7) + ((long double)rand() / (RAND_MAX)) * pow(10, 8);
            stars[i].z = pow(10, 7) + ((long double)rand() / (RAND_MAX)) * pow(10, 8);
            stars[i].vx = 0;
            stars[i].vy = 0;
            stars[i].vz = 0;
            stars[i].ax = 0;
            stars[i].ay = 0;
            stars[i].az = 0;
            stars[i].nax = 0;
            stars[i].nay = 0;
            stars[i].naz = 0;
        }
    }

    MPI_Bcast(&stars, STAR_NUM, MPI_STAR, 0, COMM_WORLD);

    int loopstart = part * rank;
    int loopend = min(STAR_NUM, (rank + 1) * part);

    while (true)
    {
        // 利用 OpenMP 加速此循环
#pragma omp parallel for
        for (int i = loopstart; i < loopend; i++) {
            Star* s = &(stars[i]);
            updatePosition(*s);
        }

        // 计算下次的加速度需要来自其他进程的数据
        MPI_Request req;
        //MPI_Ibcast(&stars, STAR_NUM, MPI_STAR, rank, COMM_WORLD, &req);
        //MPI_Gather(&stars, STAR_NUM, MPI_STAR, &temp, STAR_NUM, MPI_STAR, rank, COMM_WORLD);
        int start = part * rank;
        int end = min(part * (rank + 1), STAR_NUM);
        int* displs, * rcounts;     
        displs = (int*)malloc(size * sizeof(int));
        rcounts = (int*)malloc(size * sizeof(int));
        for (int i = 0; i < size; i++) {
            displs[i] = i * part;
            rcounts[i] = end - start;
        }
        //cout << "rank " << rank << "end - start" << end << " - " << start << endl;
        MPI_Gatherv(&stars[start], end - start, MPI_STAR, &temp, rcounts, displs, MPI_STAR, 0, COMM_WORLD);

        MPI_Bcast(&temp, STAR_NUM, MPI_STAR, 0, COMM_WORLD);

        // 现在 temp 中存的是更新后的数据
        for (int i = loopstart; i < loopend; i++) {
            for (int j = 0; j < STAR_NUM; j++) {
                if (i == j) continue;
                updateNextAcceration(temp[j], stars[i]);
            }
        }

        //print(stars);
        for (int i = loopstart; i < loopend; i++) {
            cout << rank<<" "<<setiosflags(ios::left) << setw(4) << i << setw(16) << stars[i].x << setw(16) << stars[i].y << setw(16) << stars[i].z
                << setw(16) << stars[i].vx << setw(16) << stars[i].vy << setw(16) << stars[i].vz
                << setw(16) << stars[i].ax << setw(16) << stars[i].ay << setw(16) << stars[i].az
                << setw(16) << stars[i].nax << setw(16) << stars[i].nay << setw(16) << stars[i].naz
                << setw(16) << stars[i].m << endl;
        }

        // 利用 OpenMP 加速此循环
#pragma omp parallel for
        for (int i = loopstart; i < loopend; i++) {
            Star* s = &(stars[i]);
            updateAcceration(*s);
        }

        // 利用 OpenMP 加速此循环
#pragma omp parallel for
        for (int i = loopstart; i < loopend; i++) {
            Star* s = &(stars[i]);
            updateSpeed(*s);
        }
    }
}

运行截图：