Concurrent Multifrontal Methods: Shared Memory, Cache, and Frontwidth Issues
Robert E. Benner, Gary R. Montry, G.G. Weigand, Iain Duff · The International Journal of High Performance Computing Applications · 1987
Frontal methods are an efficient and pop ular means of Gauss elimination of matrix equations that arise in finite element analysis. Nested dissection of a computa tional domain makes possible high-level parallelism in a widely used frontal algo rithm for unsymmetric systems. A concur rent, highly vectorized, multifrontal, finite element analysis of axisymmetric liquid drop oscillations with 2,210 equations runs on the CRAY X-MP/48 with factors of 1.9 and 2.9 reduction in elapsed time on two and four processors, respectively. On an ELXSI 6400 (which has an additional memory level, local processor cache, ig nored in the algorithm's design for the CRAY), implementation of the same problem initially achieved a speedup of only 1.4 on four processors. Modification of the concurrent algorithm, to take ad vantage of the cache and frontwidth re duction by element reordering, doubled the concurrent speedup on the ELXSI to 2.8 on four processors.