  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.
