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


Kocak S., Akay H.

APPLIED MATHEMATICAL MODELLING, cilt.25, ss.873-886, 2001 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 25 Konu: 10
  • Basım Tarihi: 2001
  • Doi Numarası: 10.1016/s0307-904x(01)00019-1
  • Dergi Adı: APPLIED MATHEMATICAL MODELLING
  • Sayfa Sayıları: ss.873-886

Özet

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. (C) 2001 Elsevier Science Inc. All rights reserved.