ArbiLoMod: Local Solution Spaces by Random Training in Electrodynamics
This work addresses the need for efficient re-simulation in computational electromagnetics, but the analysis is limited to 2D and non-coercive problems.
ArbiLoMod enables quick re-simulation after localized changes in finite element models without solving the full model, using a localized reduced basis method. Numerical analysis for 2D time-harmonic Maxwell's equations shows the method's effectiveness.
The simulation method ArbiLoMod has the goal to provide 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).