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ArbiLoMod, a Simulation Technique Designed for Arbitrary Local Modifications

arXiv e-prints, Number 1512.07840 - december 2015
Télécharger la publication : 1512.07840v3.pdf [3.6Mo]  
Finite Element based simulation software is often used in engineering workflows to design structures whose behavior can be modeled by partial differential equations. Engineers manually optimizing a structure using 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 this paper, we introduce ArbiLoMod, a method designed for improving this manual, iterative workflow. It 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 rigorous a posteriori error estimator, certifying the quality of the result. As ArbiLoMod is based on the Reduced Basis Method, it inherits its advantages for parameterized problems. We demonstrate ArbiLoMod for a coercive, parameterized example with changing structure.

Références BibTex

@Article{BEOR15,
  author       = {Buhr, A. and Engwer, C. and Ohlberger, M. and Rave, S.},
  title        = {ArbiLoMod, a Simulation Technique Designed for Arbitrary Local Modifications},
  journal      = {arXiv e-prints},
  number       = {1512.07840},
  month        = {december},
  year         = {2015},
  publisher    = {arXiv [math.NA]},
  note         = {http://arxiv.org/abs/1512.07840},
  url          = \{/2015/BEOR15},
}

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