Vol. 13, No. 1, 2018

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
A third order finite volume WENO scheme for Maxwell's equations on tetrahedral meshes

Marina Kotovshchikova, Dmitry K. Firsov and Shiu Hong Lui

Vol. 13 (2018), No. 1, 87–106
Abstract

A third order type II WENO finite volume scheme for tetrahedral unstructured meshes is applied to the numerical solution of Maxwell’s equations. Stability and accuracy of the scheme are severely affected by mesh distortions, domain geometries, and material inhomogeneities. The accuracy of the scheme is enhanced by a clever choice of a small parameter in the WENO weights. Also, hybridization with a polynomial scheme is proposed to eliminate unnecessary and costly WENO reconstructions in regions where the solution is smooth. The proposed implementation is applied to several test problems to demonstrate the accuracy and efficiency, as well as usefulness of the scheme to problems with singularities.

Keywords
weighted essentially nonoscillatory (WENO) schemes, finite volume schemes, Maxwell's equations, tetrahedral meshes
Mathematical Subject Classification 2010
Primary: 65M08, 78M12
Milestones
Received: 9 March 2017
Revised: 3 January 2018
Accepted: 7 January 2018
Published: 17 February 2018
Authors
Marina Kotovshchikova
Department of Mathematics
University of Manitoba
Winnipeg, Manitoba
Canada
Dmitry K. Firsov
San Jose, CA
United States
Shiu Hong Lui
Department of Mathematics
University of Manitoba
Winnipeg, Manitoba
Canada