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On the boundary conditions for the vector potential formulation in electrostatics
Author(s) -
Stark Sebastian,
Semenov Artem S.,
Balke Herbert
Publication year - 2015
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4859
Subject(s) - uniqueness , boundary value problem , consistency (knowledge bases) , mathematics , domain (mathematical analysis) , finite element method , boundary (topology) , social connectedness , nonlinear system , vector potential , mathematical analysis , topology (electrical circuits) , mathematical optimization , physics , geometry , quantum mechanics , psychology , combinatorics , magnetic field , psychotherapist , thermodynamics
Summary The vector potential formulation is a promising solution method for nonlinear electromechanically coupled boundary value problems. However, one of the drawbacks of this formulation is the non‐uniqueness of the (electric) vector potential in three dimensions. The present paper focuses on the Coulomb gauging method to overcome this problem. In particular, the corresponding gauging boundary conditions and their consistency with the physical boundary conditions are examined in detail. Furthermore, certain topological features like cavities and multiply connectedness of the domain of analysis are taken into account. Different variational/weak formulations being appropriate for finite element implementation are described. Finally, the suitability of these formulations is demonstrated in several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.