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Efficient multiple time-stepping algorithms of higher order
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DOI：10.1016/j.jcp.2015.01.018.png)
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摘要
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Multiple time-stepping (MTS) algorithms allow to efficiently integrate large systems of ordinary differential equations, where a few stiff terms restrict the timestep of an otherwise non-stiff system. In this work, we discuss a flexible class of MTS techniques, based on multistep methods. Our approach contains several popular methods as special cases and it allows for the easy construction of novel and efficient higher-order MTS schemes. In addition, we demonstrate how to adapt the stability contour of the non-stiff time-integration to the physical system at hand. This allows significantly larger timesteps when compared to previously known multistep MTS approaches. As an example, we derive novel predictor-corrector (PCMTS) schemes specifically optimized for the time-integration of damped wave equations on locally refined meshes. In a set of numerical experiments, we demonstrate the performance of our scheme on discontinuous Galerkin time-domain (DGTD) simulations of Maxwell's equations. (C) 2015 Elsevier Inc. All rights reserved.
Keyword:
Multiple time-stepping (MTS)
Local time-stepping (LTS)
Multistep methods
Grid-induced stiffness
Exponential integrator
Discontinuous Galerkin time-domain (DGTD)
Maxwell's equations
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3.8
论文数:
1.6W
被引数:
7.4W
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