Mathematical Problems in Engineering
Volume 1 (1995), Issue 1, Pages 41-57

A nested decomposition algorithm for parallel computations of very large sparse systems

D. D. Šiljak and A. I. Zečević

School of Engineering, Santa Clara University, Santa Clara 95053, CA, USA

Received 15 June 1994

Copyright © 1995 D. D. Šiljak and A. I. Zečević. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we present a generalization of the balanced border block diagonal (BBD) decomposition algorithm, which was developed for the parallel computation of sparse systems of linear equations. The efficiency of the new procedure is substantially higher, and it extends the applicability of the BBD decomposition to extremely large problems. Examples of the decomposition are provided for matrices as large as 250,000×250,000, and its performance is compared to other sparse decompositions. Applications to the parallel solution of sparse systems are discussed for a variety of engineering problems.