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Exterior electromagnetic shaping using wavelet BEM
Author(s) -
Eppler K.,
Harbrecht H.
Publication year - 2005
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.572
Subject(s) - mathematics , lagrange multiplier , galerkin method , mathematical analysis , boundary value problem , wavelet , augmented lagrangian method , boundary (topology) , finite element method , mathematical optimization , computer science , physics , artificial intelligence , thermodynamics
The present paper is devoted to exterior electromagnetic shaping in two dimensions. We model the conductors by regular densities which leads to a finite objective and allows a line‐search. In order to compute the surface pressure we optimize an Augmented Lagrangian by a Newton method using a second‐order approach for the Lagrange multiplier. Since the underlying state function satisfies an exterior boundary value problem, we compute first and second order derivatives of its boundary data by boundary integral equations which are numerically solved by a fast wavelet Galerkin scheme. Numerical results prove that we succeeded in finding a fast and robust algorithm for solving the considered class of problems. Copyright © 2004 John Wiley & Sons, Ltd.