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Localized Reduced Basis Methods for Time Harmonic Maxwell’s Equations

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reduced basis methods, arbilomod, maxwells equations

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      Abstract

      Localized model order reduction methods have attracted significant attention during the last years. They have favorable parallelization properties and promise to perform well on cloud architectures, which become more and more commonplace. We introduced ArbiLoMod, a localized reduced basis method targeted at the important use case of changing problem definition, wherein the changes are of local nature. This is a common situation in simulation software used by engineers optimizing a CAD model. An especially interesting application is the simulation of electromagnetic fields in printed circuit boards, which is necessary to design high frequency electronics. The simulation of the electromagnetic fields can be done by solving the time-harmonic Maxwell’s equations, which results in a parameterized, inf-sup stable problem which has to be solved for many parameters. In this multi-query setting, the reduced basis method can perform well. Experiments have shown two dimensional time-harmonic Maxwell’s to be amenable to localized model reduction. However, Galerkin projection of an inf-sup stable problem is not guaranteed to be stable. Existing stabilization methods for the reduced basis method involve global computations and are thus not applicable in a localized setting. Replacing the Galerkin projection with the minimization of a localized a posteriori error estimator provides a stable reduction for inf-sup stable projects which retains all the advantageous properties of localized model order reduction. It allows for an offline-online decomposition and requires no global computations in the unreduced space.

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      Affiliations
      [1 ]Institute for Computational and Applied Mathematics, University of Münster, Einsteinstraße 62, 48149 Münster, Germany.
      [* ]Correspondence: andreas@ 123456andreasbuhr.de
      Journal
      ScienceOpen Posters
      ScienceOpen
      27 April 2018
      10.14293/P2199-8442.1.SOP-MATH.FBXFMR.v1
      Copyright © 2018

      This work has been published open access under Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com.

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