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Symmetric coupling of finite and boundary elements for exterior magnetic field problems
Author(s) -
Kuhn M.,
Steinbach O.
Publication year - 2002
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.286
Subject(s) - mathematics , finite element method , discretization , bounded function , galerkin method , scalar (mathematics) , domain (mathematical analysis) , mathematical analysis , boundary value problem , coupling (piping) , iterative method , boundary (topology) , mathematical optimization , geometry , physics , mechanical engineering , engineering , thermodynamics
We consider a coupled finite element (fe)–boundary element (be) approach for three‐dimensional magnetic field problems. The formulation is based on a vector potential in a bounded domain (fe) and a scalar potential in an unbounded domain (be). We describe a coupled variational problem yielding a unique solution where the constraints in the trial spaces are replaced by appropriate side conditions. Then we discuss a Galerkin discretization of the coupled problem and prove a quasi‐optimal error estimate. Finally we discuss an efficient preconditioned iterative solution strategy for the resulting linear system. Copyright © 2002 John Wiley & Sons, Ltd.