Parallel Schur complement method for large-scale systems on distributed memory computers

Abstract

The Schur complement method, also known as substructuring technique, was widely used in structural mechanics to solve large-scale systems with limited memory computers for more than three decades [J.S. Przemieniecki, AIAA J. 1 (1963) 138]. Currently, due to developments in computer technology, the available on-board memory has increased considerably. Despite the existence of these high-memory systems, the Schur complement method still finds its applications in structural mechanics through parallel computing. When developing a computer program, the Schur method has a significant book-keeping load in comparison to other parallel algorithms used, e.g., Schwarz alternating domain decomposition method [H.A. Schwarz, Gesammelte Mathematiche Abhandlungen, vol. 2, Springer, Berlin, 1890, p. 133]. This results in memory usage. Although parallel systems are used, global coefficient matrices require a large amount of memory. Therefore, significant memory is reserved for the solution of large-scale systems. In this paper, we present an efficient algorithm for the assemblage and solution of interface equations which facilitates the solution of large-scale systems via the Schur complement method on multiple instruction multiple data (MIMD) distributed memory architectures. In this method, we assemble the subdomain and interface coefficient matrices in such a manner that the memory requirements decrease significantly, resulting in the solution of large-scale systems with reasonable memory usage. The computer program is tested on distributed memory architectures with UNIX, WINDOWS NT, and LINUX operating systems.