ArbiLoMod: Local Solution Spaces by Random Training in Electrodynamics
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The simulation method ArbiLoMod (Buhr et al., SIAM J. Sci. Comput. 2017, accepted) has the goal of providing users of Finite Element based simulation software with quick re-simulation after localized changes to the model under consideration. It generates a Reduced Order Model (ROM) for the full model without ever solving the full model. To this end, a localized variant of the Reduced Basis method is employed, solving only small localized problems in the generation of the reduced basis. The key to quick re-simulation lies in recycling most of the localized basis vectors after a localized model change. In this publication, ArbiLoMod’s local training algorithm is analyzed numerically for the non-coercive problem of time harmonic Maxwell’s equations in 2D, formulated in H(curl).
Andreas Buhr was supported by CST—Computer Simulation Technology AG. Stephan Rave was supported by the German Federal Ministry of Education and Research (BMBF) under contract number 05M13PMA.
- 1.Buhr, A., Engwer, C., Ohlberger, M., Rave, S.: ArbiLoMod, a simulation technique designed for arbitrary local modifications. SIAM J. Sci. Comput. (2017). AcceptedGoogle Scholar
- 4.Chen, Y., Hesthaven, J.S., Maday, Y.: A seamless reduced basis element method for 2D Maxwell’s problem: an introduction. Spectral and High Order Methods for Partial Differential Equations: Selected papers from the ICOSAHOM ’09 Conference, June 22–26, Trondheim, Norway, pp. 141–152. Springer, Berlin (2011)Google Scholar
- 14.Maxwell, J.C.: On physical lines of force. Lond. Edinb. Dublin Philos. Mag. J. Sci. 21(139), 161–175 (1861)Google Scholar
- 15.Milk, R., Rave, S., Schindler, F.: pyMOR-generic algorithms and interfaces for model order reduction. SIAM J. Sci. Comput. 38(5), S194–S216 (2016). doi:10.1137/15M1026614, https://doi.org/10.1137/15M1026614
- 16.Monk, P.: Finite Element Methods for Maxwell’s Equations Oxford University Press, Oxford (2003)Google Scholar