ArbiLoMod, a Simulation Technique Designed for Arbitrary Local Modifications

TL;DR

ArbiLoMod is a novel simulation technique that enables rapid updates in finite element models after local modifications by combining domain decomposition, localized model reduction, and error estimation.

Contribution

It introduces a localized model reduction method that efficiently reuses reduced bases after local changes, improving iterative structural optimization workflows.

Findings

Enables fast recomputation after local modifications

Uses localized error indicators for adaptive model updates

Demonstrated on a parameterized structural example

Abstract

Engineers manually optimizing a structure using Finite Element based simulation software often employ an iterative approach where in each iteration they change the structure slightly and resimulate. Standard Finite Element based simulation software is usually not well suited for this workflow, as it restarts in each iteration, even for tiny changes. In settings with complex local microstructure, where a fine mesh is required to capture the geometric detail, localized model reduction can improve this workflow. To this end, we introduce ArbiLoMod, a method which allows fast recomputation after arbitrary local modifications. It employs a domain decomposition and a localized form of the Reduced Basis Method for model order reduction. It assumes that the reduced basis on many of the unchanged domains can be reused after a localized change. The reduced model is adapted when necessary, steered by a localized error indicator. The global error introduced by the model order reduction is controlled by a robust and efficient localized a posteriori error estimator, certifying the quality of the result. We demonstrate ArbiLoMod for a coercive, parameterized example with changing structure.