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2020 A third-order multirate Runge–Kutta scheme for finite volume solution of 3D time-dependent Maxwell's equations
Marina Kotovshchikova, Dmitry K. Firsov, Shiu Hong Lui
Commun. Appl. Math. Comput. Sci. 15(1): 65-87 (2020). DOI: 10.2140/camcos.2020.15.65

Abstract

A third-order multirate time-stepping based on an SSP Runge–Kutta method is applied to solve the three-dimensional Maxwell’s equations on unstructured tetrahedral meshes. This allows for an evolution of the solution on fine and coarse meshes with time steps satisfying a local stability condition to improve the computational efficiency of numerical simulations. Two multirate strategies with flexible time-step ratios are compared for accuracy and efficiency. Numerical experiments with a third-order finite volume discretization are presented to validate the theory. Our results of electromagnetic simulations demonstrate that 1D analysis is also valid for linear conservation laws in 3D. In one of the methods, significant speedup in 3D simulations is achieved without sacrificing third-order accuracy.

Citation

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Marina Kotovshchikova. Dmitry K. Firsov. Shiu Hong Lui. "A third-order multirate Runge–Kutta scheme for finite volume solution of 3D time-dependent Maxwell's equations." Commun. Appl. Math. Comput. Sci. 15 (1) 65 - 87, 2020. https://doi.org/10.2140/camcos.2020.15.65

Information

Received: 28 October 2019; Revised: 25 February 2020; Accepted: 12 April 2020; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07224510
MathSciNet: MR4113784
Digital Object Identifier: 10.2140/camcos.2020.15.65

Subjects:
Primary: 65L06, 65M08, 78M12

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.15 • No. 1 • 2020
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