抄録
本論文は,摂動確率有限要素法における摂動項計算の効率化を目的としている.摂動項計算における行列方程式群の係数行列が全て等しいことに着目しSeed Methodを適用し,SFEM向けの実装方法を提案する.Seed MethodはCG法の改良手法であり,多数の行列方程式を解く場合に,部分空間の再利用により計算コストの減少を図る.提案手法によって,摂動項の計算時間を約55%に短縮することができた.
In the calculations of perturbations terms in SFEM, coefficient matrices are always the same. For such kind of problems, a single seed method and its derivations have been reported. The Seed Method is a kind of Krylov Subspace Methods which can reduce computational cost of CG iterations recycling the subspaces produced by one seed system. We applied the Seed Method and implemented in the framework of SFEM. Numerical examples have shown that the total time of calculations of perturbation terms has been reduced to 55%.
