ArbiLoMod: Local Solution Spaces by Random Training in Electrodynamics

Buhr A, Engwer C, Ohlberger M, Rave S

Zusammenfassung

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 inH(curl).