MPI topology for arbitrary domains - mpi

Question

I have a rectangular domain 3 x 2 as shown in figure (a). Using MPI Cartesian topology, I can identify the 4 neighbors (-1 means NULL) of each cell as demonstrated below
Figure: Rectangular and arbitrary domain
#include <mpi.h>
#include <stdio.h>
#include <stdlib.h>
int main(int argc, char** argv) {
int rank, size;
int top = 0, right = 1, bottom = 2, left = 3;
int neighbors[4], dimSize[2] = {3, 2};
int usePeriods[2] = {0, 0}, newCoords[2];
MPI_Comm cartComm = MPI_COMM_WORLD;
MPI_Init(&argc, &argv);
MPI_Comm_rank(MPI_COMM_WORLD, &rank);
MPI_Comm_size(MPI_COMM_WORLD, &size);
if (size != 6) {
if (rank == 0)
printf("Please Launch with ONLY 6 processes \n");
MPI_Finalize();
exit(0);
}
// Create a carthesian communicator
MPI_Cart_create(MPI_COMM_WORLD, 2, dimSize, usePeriods, 1, &cartComm);
// Obtain the 2D coordinates in the new communicator
MPI_Cart_coords(cartComm, rank, 2, newCoords);
// Obtain the direct neighbor ranks
MPI_Cart_shift(cartComm, 0, 1, neighbors + left, neighbors + right);
MPI_Cart_shift(cartComm, 1, 1, neighbors + top, neighbors + bottom);
printf("Rank: %d \t Neighbors(top, right, bottom, left): %2d, %2d, %2d, %2d \n", rank, neighbors[0], neighbors[1], neighbors[2], neighbors[3]);
MPI_Finalize();
return 0;
}
Results:
Rank: 0 Neighbors(top, right, bottom, left): -1, 2, 1, -1
Rank: 1 Neighbors(top, right, bottom, left): 0, 3, -1, -1
Rank: 2 Neighbors(top, right, bottom, left): -1, 4, 3, 0
Rank: 3 Neighbors(top, right, bottom, left): 2, 5, -1, 1
Rank: 4 Neighbors(top, right, bottom, left): -1, -1, 5, 2
Rank: 5 Neighbors(top, right, bottom, left): 4, -1, -1, 3
My question: Is there a way that uses MPI to identify these neighbors for non-rectangular domain as shown in figure (b). Here, we assume no periodic neighbors. Now, I can only think of implementing a similar Cartesian topology approach for 3x3 (figure c):
mpirun -np 9 ./run_cartesian
Next, remove NULL cells (gray color) and reorder the ranks from 0-5. Save result to a file, then load the file (using root) and scatter the corresponding neighbors to each processor.
mpirun -np 6 ./run_load_scatter
Any suggestion for better ways to do this? Thanks.