Numerical analysis of nonlinear multiharmonic eddy current problems |
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Authors: | F. Bachinger U. Langer J Schöberl |
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Affiliation: | (1) Spezialforschungsbereich SFB F013 Numerical and Symbolic Scientific Computing, Johannes Kepler University Linz, Austria;(2) Institute for Computational Mathematics, Johannes Kepler University Linz, Austria;(3) Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Austria |
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Abstract: | Summary This work is devoted to non-linear eddy current problems and their numerical treatment by the so-called multiharmonic approach. Since the sources are usually alternating currents, we propose a truncated Fourier series expansion instead of a costly time-stepping scheme. Moreover, we suggest to introduce some regularization parameter that ensures unique solvability not only in the factor space of divergence-free functions, but also in the whole space H(curl). Finally, we provide a rigorous estimate for the total error that is due to the use of truncated Fourier series, the regularization technique and the spatial finite element discretization.This work has been supported by the Austrian Science Fund Fonds zur Förderung der wissenschaftlichen Forschung (FWF) under the grants SFB F013, P 14953 and START Y192. |
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Keywords: | 65M60 65T40 78M10 |
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