Causal-Path Local Time-Stepping in the Discontinuous Galerkin Method for Maxwell’s equations

Díaz Angulo, Luis Manuel; Álvarez González, Jesús; Teixeira, Fernando; Rubio Bretones, Amelia Consuelo; González García, Salvador

doi:j.jcp.2013.09.010

a1_causalpath_jcp14_NOAGRAD.pdf (11.86Mb)

Identificadores

URI: http://hdl.handle.net/10481/50151

DOI: j.jcp.2013.09.010

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Materia

Causal Path

Local Time-Stepping

LTS

Discontinuous Galerkin Methods

Maxwell's equations

DGTD

Date

2014

Referencia bibliográfica

Diaz Angulo, Luis; et. al. Causal-Path Local Time-Stepping in the Discontinuous Galerkin Method for Maxwell’s equations. Journal of Computational Physics, vol. 256, pp. 678-695, 2014 [http://hdl.handle.net/10481/50151]

Sponsorship

The work described in this paper and the research leading to these results have re- ceived funding from the European Community's Seventh Framework Programme FP7/2007- 2013, under grant agreement no 205294 (HIRF SE project), and from the Spanish Na- tional Projects TEC2010-20841-C04-04, CSD2008-00068, and the Junta de Andalucia Project P09-TIC-5327. The work of FLT has been supported by U.S. NSF under grants 0925272 and 1305838.

Abstract

We introduce a novel local time-stepping technique for marching-in-time algorithms. The technique is denoted as Causal-Path Local Time-Stepping (CPLTS) and it is ap- plied for two time integration techniques: fourth order low{storage explicit Runge{Kutta (LSERK4) and second order Leapfrog (LF2). The CPLTS method is applied to evolve Maxwell's curl equations using a Discontinuous Galerkin (DG) scheme for the spatial discretization. Numerical results for LF2 and LSERK4 are compared with analytical so- lutions and the Montseny's LF2 technique. The results show that the CPLTS technique improves the dispersive and dissipative properties of LF2-LTS scheme.

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