hp-Finite element simulation of three-dimensional eddy current problems on multiply connected domains

This work considers the accurate and efficient finite element simulation of three-dimensional eddy current problems. We review the application of H and A based formulations for multiply connected domains for the cases where the conductor has a handle and/or a hole. We focus on an hierarchical hp-fin...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2010-12, Vol.199 (49-52), p.3386-3401
Main Authors: Ledger, P.D., Zaglmayr, S.
Format: Article
Language:English
Subjects:
Applied classical electromagnetism
Computer simulation
Discretization
Eddy current problems
Eddy currents
Efficient preconditioning
Electromagnetic wave propagation, radiowave propagation
Electromagnetism
electron and ion optics
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
hp-Finite elements
Mathematical analysis
Mathematical models
Multiply connected domains
Physics
Preconditioning
Series (mathematics)
Splitting
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Summary:This work considers the accurate and efficient finite element simulation of three-dimensional eddy current problems. We review the application of H and A based formulations for multiply connected domains for the cases where the conductor has a handle and/or a hole. We focus on an hierarchical hp-finite element discretization of the A based formulation that is gauged by regularization. Based on an explicit kernel splitting of the underlying hp-finite element basis, we present a novel preconditioning technique for eddy current problems. We demonstrate its validity on multiply connected domains and include a series of numerical examples to show the effectiveness of the proposed approach.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2010.07.010