Computational & Technology Resources
an online resource for computational,
engineering & technology publications
Computational Science, Engineering & Technology Series
SUBSTRUCTURING TECHNIQUES AND DOMAIN DECOMPOSITION METHODS
Edited by: F. Magoulès
A Coarse Grid Conjugate Gradient Method and its Application to Realistic Problems: Fully Iterative Method with Coarse Grid
Allied Engineering Corporation, Tokyo, Japan
H. Akiba, "A Coarse Grid Conjugate Gradient Method and its Application to Realistic Problems: Fully Iterative Method with Coarse Grid", in F. Magoulès, (Editor), "Substructuring Techniques and Domain Decomposition Methods", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 6, pp 137-170, 2010. doi:10.4203/csets.24.6
Keywords: parallel processing, large scale analysis, domain decomposition method, iterative substructuring method, Schwarz framework, Neumann precondition, BDD method, CGCG method, coarse grid problem.
This chapter describes a newly developed coarse grid conjugate gradient (CGCG) method in a context of the domain decomposition method, or the iterative substructuring method. The iterative substructuring method is viewed from the Schwarz framework and the preconditioned conjugate gradient (CG) method. Starting from an elementary explanation, then the Schwartz framework is explained, followed by a description of the well known BDD method as an example of Schwarz framework, and finally the CGCG method is constructed. The CGCG method is implemented in a code called ADVENTURE Cluster (ADVC). As an analysis example, a drop impact analysis of a mobile phone model with 305 million degrees of freedom using ADVC performed on the IBM Blue Gene/L with 8 racks, 8192 nodes, 8192 processes is shown. The analysis yielded a performance of 1.27 TFLOPS.
purchase the full-text of this chapter (price £25)