Runge-Kutta Based Explicit Local Time-Stepping Methods for Wave Propagation

Grote, Marcus and Mehlin, Michaela and Mitkova, Teodora. (2014) Runge-Kutta Based Explicit Local Time-Stepping Methods for Wave Propagation. Preprints Fachbereich Mathematik, 2014 (05).

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Locally refined meshes severely impede the efficiency of explicit Runge-Kutta (RK) methods for the simulation of time-dependent wave phenomena. By taking smaller time-steps precisely where the smallest elements are located, local time-stepping (LTS) methods overcome the bottleneck caused by the stringent stability constraint of but a few small elements in the mesh. Starting from classical or low-storage explicit RK methods, explicit LTS methods of arbitrarily high accuracy are derived. When combined with an essentially diagonal finite element mass matrix, the resulting time-marching schemes retain the high accuracy, stability, and efficiency of the original RK methods while circumventing the geometry-induced stiffness. Numerical experiments with continuous and discontinuous Galerkin finite element discretizations corroborate the expected rates of convergence and illustrate the usefulness of these LTS-RK methods.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Numerik (Grote)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Grote, Marcus J. and Mehlin, Michaela and Mitkova, Teodora
Item Type:Preprint
Publisher:Universität Basel
Last Modified:12 May 2019 22:49
Deposited On:28 Mar 2019 09:52

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