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Mixed finite elements for electromagnetic analysis

Jog, CS and Nandy, Arup (2014) Mixed finite elements for electromagnetic analysis. In: COMPUTERS & MATHEMATICS WITH APPLICATIONS, 68 (8). pp. 887-902.

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Official URL: http://dx.doi.org/ 10.1016/j.camwa.2014.08.006

Abstract

The occurrence of spurious solutions is a well-known limitation of the standard nodal finite element method when applied to electromagnetic problems. The two commonly used remedies that are used to address this problem are (i) The addition of a penalty term with the penalty factor based on the local dielectric constant, and which reduces to a Helmholtz form on homogeneous domains (regularized formulation); (ii) A formulation based on a vector and a scalar potential. Both these strategies have some shortcomings. The penalty method does not completely get rid of the spurious modes, and both methods are incapable of predicting singular eigenvalues in non-convex domains. Some non-zero spurious eigenvalues are also predicted by these methods on non-convex domains. In this work, we develop mixed finite element formulations which predict the eigenfrequencies (including their multiplicities) accurately, even for nonconvex domains. The main feature of the proposed mixed finite element formulation is that no ad-hoc terms are added to the formulation as in the penalty formulation, and the improvement is achieved purely by an appropriate choice of finite element spaces for the different variables. We show that the formulation works even for inhomogeneous domains where `double noding' is used to enforce the appropriate continuity requirements at an interface. For two-dimensional problems, the shape of the domain can be arbitrary, while for the three-dimensional ones, with our current formulation, only regular domains (which can be nonconvex) can be modeled. Since eigenfrequencies are modeled accurately, these elements also yield accurate results for driven problems. (C) 2014 Elsevier Ltd. All rights reserved.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
Keywords: Maxwell equations; Nodal finite elements; Spurious modes; Mixed finite element formulation
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Depositing User: Id for Latest eprints
Date Deposited: 20 Nov 2014 04:36
Last Modified: 20 Nov 2014 04:36
URI: http://eprints.iisc.ac.in/id/eprint/50305

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