In this paper, we present an additive mullevel Schwarz method for second order elliptic problems in two dimensions, which shows great promise for parallel computers. An alternative linear system, which has the same solution as the finite element equation, is derived. For symmetric, positive elliptic problems, the alternative linear system is solved by using conjugate gradient algorithm with a quite rapid convergent rate. For nonsymmetric or indefinite elliptic problmes, the alternative linear system is solved by using GMRES. and we show that the convergent rate is independent of the number of degrees of freedom and the number of local problems if the subdomains are fine enough. The performance of the our method is illustrated by results of several numerical experiments.
CHU DELIN,HU XIANCHENG. AN ADDITIVE MULTILEVEL SCHWARZ METHOD FOR GENERAL ELLIPTIC PROBLEMS[J]. Acta Mathematicae Applicatae Sinica, 1994, 17(3): 334-346.
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