20515 グリッド援用による改良型確率有限要素法(大規模数値解析(3),OS11 大規模数値解析)

概要

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When variables of FEM have stochastic terms, SFEM can be used to solve the problem. In SFEM, if every element has a stochastic material property, we need to solve number of elements of linear systems Ax=b. The systems have the same symmetric positive definite matrix A and different right-hand sides b. SFEM is adaptive to distributed environment because these systems can be solved asynchronously and distributively. There are many other problems which has numbers of systems Ax=b with the same coefficient matrix A and different right-hand sides b. So some modified methods of solving such systems have been suggested. For example in conjugate gradient method, the Krylov subspace generated from the first system can be recycled thanks to orthogonal projections in subsequent systems. In this paper, we will promote a grid enhanced SFEM with a modified conjugate gradient method.
社団法人日本機械学会の論文
2006-03-09