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A third order
finite volume WENO scheme for Maxwell's equations on
tetrahedral meshes
Marina Kotovshchikova, Dmitry K. Firsov and Shiu Hong Lui |
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Vol. 13 (2018), No. 1, 87–106
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 65M08, 78M12
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Milestones
Received: 9 March 2017
Revised: 3 January 2018
Accepted: 7 January 2018
Published: 17 February 2018
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Authors |
| Marina Kotovshchikova | |
| Department of Mathematics University of Manitoba Winnipeg, Manitoba Canada |
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| Dmitry K. Firsov | |
| San Jose, CA United States |
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| Shiu Hong Lui | |
| Department of Mathematics University of Manitoba Winnipeg, Manitoba Canada |
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