有限要素法における全体剛性マトリクスの再帰的分割処理について

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  • Recursive Decomposed Processing of a Global Stiffness Matrix on Finite Element Method.
  • ユウゲン ヨウソホウ ニ オケル ゼンタイ ゴウセイ マトリクス ノ サイキテ

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The purpose of this paper is to derive a recursive decomposed algorithm in which a global stiffness equation is decomposed to decoupled linear algebraic equations with a low order. Generally the computaional efficiency on a finite element method depends upon solving the global stiffness matrix. Since the decomposed equations are independent of each other, the reduced order equations can be solved using parallel processing. The decomposed algorithm is effective in removing zero elements in the global stiffness matrix composed of a band matrix and a sparse matrix. That is, when a band matrix with zero elements is of a low order, the time complexity is reduced. The objective of the analysis is a truss structure. In order to demonstrate the effectiveness of the proposed recursive decomposed algorithm, a brief example is shown. In this paper, the time complexity, arithmetic complexity and accuracy are compared numerically for the decomposed operation, parallel processing and Cholesky's method, respectively.

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