A Nested Dissection Approach for Sparse Matrix Partitioning

We consider how to partition and distribute sparse matrices among processors to reduce communication cost in sparse matrix computations, in particular, sparse matrix-vector multiplication. We consider 2d distributions, where the distribution is not constrained to just rows or columns. We present a new model and an algorithm based on vertex separators and nested dissection. Preliminary numerical results for sparse matrices from real applications indicate the new method performs consistently better than traditional 1d partitioning and is often also better than current 2d methods.