laplace2d.cu

/* Copyright (c) 2012, NVIDIA CORPORATION. All rights reserved.
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#include <math.h>
#include <string.h>
#include <stdlib.h>
#include <stdio.h>
#include <cuda.h>
#include <omp.h>

__global__ void stencil(int imax, int jmax, double *Anew, double *A) {
  __shared__ double local[16*4];
  int i = threadIdx.x + blockIdx.x*blockDim.x; //global
  int j = threadIdx.y + blockIdx.y*blockDim.y; //global
  int tid = threadIdx.x + threadIdx.y * blockDim.x; // row contiguous array. This is the thread id.
  if (i < imax+1 && j < jmax+1 && i>0 && j>0){
    Anew[(j)*(imax+2)+i] = 0.25f * ( A[(j)*(imax+2)+i+1] + A[(j)*(imax+2)+i-1]
        + A[(j-1)*(imax+2)+i] + A[(j+1)*(imax+2)+i]);
    local[tid] = fabs(Anew[(j)*(imax+2)+i]-A[(j)*(imax+2)+i]);
  }
    // error = fmax( error, fabs(Anew[(j)*(imax+2)+i]-A[(j)*(imax+2)+i]));
  for (int d=(blockDim.x*blockDim.y)/2; d>0; d=d/2){
    __syncthreads();
    if (tid < d) local[tid] = fmax(local[tid],local[d+tid]);
  }
  if (tid == 0){
    int bid = blockIdx.x + blockIdx.y*gridDim.x; // row contiguous array. This is the block id.
    error[bid] = local[0];
  }
}

__global__ void copy(int imax, int jmax, double *Anew, double *A) {

  int i = threadIdx.x + blockIdx.x*blockDim.x;
  int j = threadIdx.y + blockIdx.y*blockDim.y;
  if (i < imax+1 && j < jmax+1 && i>0 && j>0)
    A[(j)*(imax+2)+i] = Anew[(j)*(imax+2)+i];
}

int main(int argc, char** argv)
{
    //Size along y
    int jmax = 4094;
    //Size along x
    int imax = 4094;
    int iter_max = 1000;

    const double pi  = 2.0 * asin(1.0);
    const double tol = 1.0e-5;
    double error     = 1.0;

    double *A;
    double *Anew;
    double *y0;

    A    = (double *)malloc((imax+2) * (jmax+2) * sizeof(double));
    Anew = (double *)malloc((imax+2) * (jmax+2) * sizeof(double));
    y0   = (double *)malloc((imax+2) * sizeof(double));

    memset(A, 0, (imax+2) * (jmax+2) * sizeof(double));

    // set boundary conditions
    for (int i = 0; i < imax+2; i++)
      A[(0)*(imax+2)+i]   = 0.0;

    for (int i = 0; i < imax+2; i++)
      A[(jmax+1)*(imax+2)+i] = 0.0;

    for (int j = 0; j < jmax+2; j++)
    {
        y0[j] = sin(pi * j / (jmax+1));
        A[(j)*(imax+2)+0] = y0[j];
    }

    for (int j = 0; j < imax+2; j++)
    {
        y0[j] = sin(pi * j/ (jmax+1));
        A[(j)*(imax+2)+imax+1] = y0[j]*exp(-pi);
    }

    printf("Jacobi relaxation Calculation: %d x %d mesh\n", imax+2, jmax+2);

    double t1 = omp_get_wtime();
    int iter = 0;

    for (int i = 1; i < imax+2; i++)
       Anew[(0)*(imax+2)+i]   = 0.0;

    for (int i = 1; i < imax+2; i++)
       Anew[(jmax+1)*(imax+2)+i] = 0.0;

    for (int j = 1; j < jmax+2; j++)
        Anew[(j)*(imax+2)+0]   = y0[j];

    for (int j = 1; j < jmax+2; j++)
        Anew[(j)*(imax+2)+jmax+1] = y0[j]*expf(-pi);


    double *d_A, *d_Anew, *d_error;
    size_t size = (imax+2)*(jmax+2)*sizeof(double);
    cudaMalloc(&d_A, size);
    cudaMalloc(&d_Anew, size);
    cudaMemcpy(d_A, A, size, cudaMemcpyHostToDevice);
    cudaMemcpy(d_Anew, Anew, size, cudaMemcpyHostToDevice);
    dim3 threads(16,4);
    dim3 blocks((imax+2-1)/16+1, (jmax+2-1)/4+1);
    /*cudaMalloc(&d_error );*/
        
    while ( error > tol && iter < iter_max )
    {
        error = 0.0;
        stencil<<<blocks, threads>>>(imax, jmax, d_Anew, d_A);

        copy<<<blocks, threads>>>(imax, jmax, d_Anew, d_A);
        if(iter % 100 == 0) printf("%5d, %0.6f\n", iter, error);

        iter++;
    }
    cudaMemcpy(A, d_A, size, cudaMemcpyDeviceToHost);

    double runtime = omp_get_wtime()-t1;

    printf(" total: %f s\n", runtime);
}