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Engineers manually optimizing a structure using Finite Element basedsimulation software often employ an iterative approach where in each iterationthey change the structure slightly and resimulate. Standard Finite Elementbased simulation software is usually not well suited for this workflow, as itrestarts in each iteration, even for tiny changes. In settings with complexlocal microstructure, where a fine mesh is required to capture the geometricdetail, localized model reduction can improve this workflow. To this end, weintroduce ArbiLoMod, a method which allows fast recomputation after arbitrarylocal modifications. It employs a domain decomposition and a localized form ofthe Reduced Basis Method for model order reduction. It assumes that the reducedbasis on many of the unchanged domains can be reused after a localized change.The reduced model is adapted when necessary, steered by a localized errorindicator. The global error introduced by the model order reduction iscontrolled 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.

ArbiLoMod, a Simulation Technique Designed for Arbitrary Local Modifications