再帰的求解法による全体方程式の解法について

概要

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The purpose of this paper is to solve a class of a global stiffness equations for Finite-Element Method (FEM). Recursive algorithm is derived that the global stiffness equation is decomposed to decoupled linear algebraic equations with low order. Solutions are constructed by sum of a zero-order solution and an error solution. The solution can be approximated to exact solution with an error solution by repeating calculation of reduced-order error equation. For structural analysis of FEM, there exist difficult cases for calculating by a computational error since the global stiffness matrix contains elements of different order. By using recursive approach, however, it can be solved the global stiffness equation to avoid the computational error. Since the decomposed equation are independently each other the reduced-order equation can be solved by using parallel processing. In order to demonstrate the effectiveness of the recursive approach, a simple numerical example will be shown. The results show that the recursive approach converge with the rate of convergence of accuracy O(ε).
社団法人日本機械学会の論文
1998-03-25