불완전분해법을 전처리로 하는 공액구배법의 안정화에 대한 연구

Abstract

The preconditioned conjugate gradient method is an efficient iterative solution scheme for large size finite element problems. As preconditioning method, we choose an incomplete Cholesky factorization which has efficiency and easiness in implementation in this paper. The incomplete Cholesky factorization method sometimes leads to breakdown of the computational procedure that means pivots in the matrix become minus during factorization. So, it is inevitable that a reduction process for stabilizing and this process will guarantee robustness of the algorithm at the cost of a little computation. Recently incomplete factorization that enhances robustness through increasing diagonal dominancy instead of reduction process has been developed. This method has better efficiency for the problem that has rotational degree of freedom, but is sensitive to parameters and the breakdown can be occurred occasionally. Therefore, this paper presents new method that guarantees robustness for this method. Numerical experiment shows that the present method guarantees robustness without further efficiency loss.