High-order explicit local time-stepping methods for damped wave equations

Details High-order explicit local time-stepping methods for damped wave equations High-order explicit local time-stepping methods for damped wave equations

2011-09-21

arxiv.org/abs/1109.4480v1

Mathematics

Numerical Analysis

23 pages, 11 figures

Scientific paper

Locally refined meshes impose severe stability constraints on explicit time-stepping methods for the numerical simulation of time dependent wave phenomena. Local time-stepping methods overcome that bottleneck by using smaller time-steps precisely where the smallest elements in the mesh are located. Starting from classical Adams-Bashforth multi-step methods, local time-stepping methods of arbitrarily high order of accuracy are derived for damped wave equations. When combined with a finite element discretization in space with an essentially diagonal mass matrix, the resulting time-marching schemes are fully explicit and thus inherently parallel. Numerical experiments with continuous and discontinuous Galerkin finite element discretizations validate the theory and illustrate the usefulness of these local time-stepping methods.

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