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Domain decomposition methods for wave propagation problems. (English) Zbl 0854.65081

Keyes, David E. (ed.) et al., Domain-based parallelism and problem decomposition methods in computational science and engineering. Philadelphia, PA: SIAM. 21-38 (1995).
This is a short and useful survey article on domain decomposition methods for wave problems. Examples are provided by convective, acoustic, and elastic waves. This is a field in which the present author has been a leader.
The study of the domain decomposition algorithms begins by identifying appropriate interface conditions after the domain has been divided into non-overlapping subregions. Closely related to these are Poincaré-Steklov operators; the proofs of the rapid convergence of various algorithms are based on spectral properties of these operators. There is a large number of references to the literature featuring many papers of the author and his collaborators. There is also a discussion of some numerical experiments.
For the entire collection see [Zbl 0829.00009].

MSC:

65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
35L15 Initial value problems for second-order hyperbolic equations
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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