ArbiLoMod: Local Solution Spaces by Random Training in Electrodynamics

TL;DR

ArbiLoMod is a localized reduced basis method that enables rapid re-simulation of electromagnetic models after localized modifications by efficiently generating and recycling basis vectors without solving the full problem.

Contribution

This paper analyzes the local training algorithm of ArbiLoMod for Maxwell's equations, demonstrating its effectiveness in non-coercive, 2D electromagnetic problems.

Findings

Efficient local basis generation for Maxwell's equations

Effective recycling of basis vectors after localized changes

Potential for rapid re-simulation in electromagnetic modeling

Abstract

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).