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An explicit multi-level time-step algorithm to model the propagation of interacting acoustic-elastic waves using finite element/finite difference coupled procedures. (English) Zbl 1184.65091

Summary: The present paper discussion is concerned with the development of robust and efficient algorithms to model propagation of interacting acoustic and elastic waves. The paper considers acoustic-elastic, acoustic-acoustic and elastic-elastic partitioned analyses of coupled systems; however, the focus here is the acoustic-elastic coupling considering finite elements and the acoustic-acoustic coupling considering finite elements and finite differences (other coupling procedures can be implemented analogously). One important feature of the algorithms presented is that they allow considering different time-steps for different sub-domains; so it is possible to substantially improve efficiency, accuracy and stability of the central difference time integration algorithm employed here. Three examples, presented at the end of the paper, show the excellent performance of the algorithms developed.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q74 PDEs in connection with mechanics of deformable solids
74S05 Finite element methods applied to problems in solid mechanics
74S25 Spectral and related methods applied to problems in solid mechanics
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