Question

I am in the process of mapping this sequential computation to a CUDA computation. This computation is a 2-dimensional Jacobian relaxation on an NxN grid, where N is unknown. N is evenly divisible by 32.

Jacobi(float *a,float *b,int N){
   for (i=1; i<N+1; i++){
      for (j=1; j<N+1; j++) {
         a[i][j]=0.8*(b[i+1][j]+b[i+1][j]+b[i][j+1]+b[i][j+1]);
      }
   }
}

I’m parallelizing the outer two loops, and each thread should compute just one element. The goal is to parallelize it to use a cyclic distribution in the the x and y dimensions. Can some one aid me in implementing a Jacobi_GPU that has the appropriate indexing functions in CUDA that results in the following distribution?

dim3 dimGrid(N/32,N/32);
dim3 dimBlock(32,32);
Jacobi_GPU<<<dimGrid,dimBlock>>>(A,B,N)

Answer 1

forThis is the simple implementation. You can use shared memory optimization for this kernel function

__global__ void jacobi(int* a, const int* b,const int N)
{
  int i= blockIdx.x * blockDim.x + threadIdx.x;
  int j = blockIdx.y * blockDim.y + threadIdx.y;
  if (i<N && j<N)
  {
    a[j*N+i] = 0.8* (2*b[(i+1)+j*N] + 2*b[i+N*(j+1)]);
  }
}