Balanced decompositions of sparse systems for multilevel parallel processing

The objective of this paper is to present a recursive algorithm for permuting sparse matrices into the bordered block diagonal form. An outstanding feature of this algorithm is the resulting balance between the border size and the size of the diagonal blocks, which gives rise to an efficient multilevel scheme for parallel matrix factorization. This scheme is characterized by good load balancing and low interprocessor communications. In addition, it is specifically designed to minimize fill in within the factored matrix in order to preserve the original sparsity. Applications to power transmission systems are presented, together with a discussion of relevant parallelization and sparsity issues