Dynamic levelwise scheduling for sparse matrix factorization on vector computers

In this paper the problem of the efficient implementation of sparse matrix factorization on vector computers is considered. A fine-grain dynamic levelwise scheduling algorithm (DLSA) is proposed. DLSA takes into account the dependences between update operations, thus avoiding the recurrence problem. A simplified version of the algorithm (S-DLSA) can be employed to produce a suboptimal scheduling of the factorization operations. DLSA and S-DLSA are also applicable to all sparse matrix operations resulting in the modification of one-dimensional arrays. The scheduling procedures and the resulting vectorization-oriented numerical factorization have been implemented on a CRAY X-MP2/216 and a CRAY Y-MP8/464 computer. Test cases refer to real-life power systems with up to 12 000 buses. The maximum speed-ups achieved (with respect to a code based on standard sparsity programming) are close to 7 for complex matrices and 13 for real matrices.