大規模有限要素解析のための高速頑健な並列ソルバCGCG法の開発

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This paper describes a very fast and robust parallel solver for large scale finite element analyses. This algorithm is newly invented as an extension of the parallel CG (Conjugate Gradient) algorithm combined with the domain-decomposition-based CPG (Conjugate Projected Gradient) algorithm. Here a coarse space is defined as the space spanned by an appropriately arranged motion of subdomains, while a fine space is defined as the K-orthogonal complement space of the coarse space, where K is a stiffness matrix. The CPG algorithm with the K-orthogonal projection to the fine space is employed in the space of total degrees of freedom (DOF) of the whole analysis domain. Thus we named this algorithm CGCG (Coarse Grid based CG) method. To demonstrate its practical performance, the algorithm is applied to solve the following two problems : (a) an aluminum wheel of automobile with about 4.8 million DOF mesh, and (b) a long cantilever beam with an aspect ratio of 4 000 subjected to a bending force. For the purpose of comparison, both problems are solved by the following two different parallel solvers : (i) the domain decomposition method (DDM) and (ii) an ordinary parallel CG algorithm. It is clearly shown from the former analysis result that the CGCG solver is superior to the other parallel solvers in terms of computation speed. It is also shown from the latter analysis result that the CGCG solver is far more robust than the other parallel solvers in terms of the number of iterations.
社団法人日本機械学会の論文
2002-07-25

大規模有限要素解析のための高速頑健な並列ソルバCGCG法の開発

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