论文信息 - Multiplicative And Additive Schwarz' Methods: Convergence In The 2-Domain Case

Multiplicative And Additive Schwarz' Methods: Convergence In The 2-Domain Case

We consider the classical Schwarz alternating algorithm and an additive version more suitable for parallel processing. The two methods are compared and analyzed in the case of two domains. We show that the rate of convergence for both methods, can be directly related to a generalized eigenvalue problem, derived from subdomain contributions to the global stiiness matrix. Analytical expressions are given for a model case.

Petter E. Bjørstad

[1] Richard E. Ewing,et al. A preconditioning technique for the efficient solution of problems with local grid refinement , 1988 .

[2] J. S. Przemieniecki. Matrix Structural Analysis of Substructures , 1963 .

[3] JAN MANDELyAbstract. ON THE SPECTRA OF SUMS OF ORTHOGONAL PROJECTIONS WITH APPLICATIONS TO PARALLEL COMPUTING , 1991 .

[4] Tony F. Chan,et al. A domain-decomposed fast Poisson solver on a rectangle , 1985, PPSC.

[5] T. Chan,et al. A Survey of Preconditioners for Domain Decomposition. , 1985 .

[6] Olof B. Widlund,et al. To overlap or not to overlap: a note on a domain decomposition method for elliptic problems , 1989 .

[7] S. McCormick,et al. The fast adaptive composite grid (FAC) method for elliptic equation , 1986 .

[8] J. Pasciak,et al. The Construction of Preconditioners for Elliptic Problems by Substructuring. , 2010 .

[9] Leslie B. Hart,et al. Asynchronous multilevel adaptive methods for solving partial differential equations on multiprocessors - Computational analysis , 1987 .