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Identification of nonlinear BH curves based on magnetic field computations and multigrid methods for ill-posed problems

Published online by Cambridge University Press:  17 March 2003

BARBARA KALTENBACHER
Affiliation:
Industrial Mathematics Institute, University of Linz, A-4040 Linz, Austria
MANFRED KALTENBACHER
Affiliation:
Department of Sensor Technology, University of Erlangen D-91056 Erlangen, Germany
STEFAN REITZINGER
Affiliation:
SFB013 Numerical and Symbolic Scientific Computing, University of Linz, A-4040 Linz, Austria

Abstract

Our task is the identification of the reluctivity $\nu\,{=}\,\nu(B)$ in $\vec{H}\,{=}\,\nu(B) \vec{B}$, ($B\,{=}\,|\vec{B}|$) from measurements of the magnetic flux for different excitation currents in a driving coil, in the context of a nonuniform magnetic field distribution. This is a nonlinear inverse problem and ill-posed in the sense of unstable data dependence, whose solution is done numerically by a Newton type iterative scheme, regularized by an appropriate stopping criterion. The computational complexity of this method is determined by the number of necessary forward evaluations, i.e. the number of numerical solutions to the three-dimensional magnetic field problem. We keep the effort minimal by applying a special discretization strategy to the inverse problem, based on multigrid methods for ill-posed problems. Numerical results demonstrate the efficiency of the proposed method.

Type
Research Article
Copyright
2003 Cambridge University Press

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