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Multi-level local time-stepping methods of Runge-Kutta type forwave equations

Almquist, Martin; Mehlin, Michaela

Abstract: Local mesh refinement significantly in uences the performance of explicit time-stepping methods for numerical wave propagation. Local time-stepping (LTS) methods improve the efficiency by using smaller time-steps precisely where the smallest mesh elements are located, thus permitting a larger time-step in the coarser regions of the mesh without violating the stability condition. However, when the mesh contains nested patches of refinement, any local time-step will be unnecessarily small in some regions. To allow for an appropriate time-step at each level of mesh refinement, multi-level local time-stepping (MLTS) methods have been proposed. Starting from the Runge{Kutta-based LTS methods derived by Grote et al. [17], we propose explicit MLTS methods of arbitrarily high accuracy. Numerical experiments with finite difference and continuous finite element spatial discretizations illustrate the usefulness of the novel MLTS methods and show that they retain the high accuracy and stability of the underlying Runge{Kutta methods.

Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000056570
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-565702
KITopen ID: 1000056570
Verlag KIT, Karlsruhe
Umfang 31 S.
Serie CRC 1173 ; 2016/16
Schlagworte finite element methods, SBP-SAT finite differences, explicit time integration, local time-stepping, multi-level, multirate methods, hyperbolic problems
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