Vol. 13, No. 1, 2018

Download this article
Download this article For screen
For printing
Recent Issues
Volume 16, Issue 1
Volume 15, Issue 2
Volume 15, Issue 1
Volume 14, Issue 2
Volume 14, Issue 1
Volume 13, Issue 2
Volume 13, Issue 1
Volume 12, Issue 1
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 1
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 1
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 1
Volume 3, Issue 1
Volume 2, Issue 1
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
Author Index
To Appear
Other MSP Journals
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

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.

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