ArbiLoMod, a Simulation Technique Designed for Arbitrary Local Modifications

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.

32 pages, 14 figures

References in corpus (6)

• pyMOR - Generic Algorithms and Interfaces for Model Order Reduction
• Error control for the localized reduced basis multi-scale method with adaptive on-line enrichment
• A numerically stable a posteriori error estimator for reduced basis approximations of elliptic equations
• An adaptive generalized multiscale discontinuous Galerkin method (GMsDGM) for high-contrast flow problems
• Residual-driven online Generalized Multiscale Finite Element Methods
• ArbiLoMod: Local Solution Spaces by Random Training in Electrodynamics

Cited by in corpus (8)

• Domain-decomposition least-squares Petrov-Galerkin (DD-LSPG) nonlinear model reduction
• Component-wise reduced order model lattice-type structure design
• Randomized Local Model Order Reduction
• A non-conforming dual approach for adaptive Trust-Region Reduced Basis approximation of PDE-constrained optimization
• ArbiLoMod: Local Solution Spaces by Random Training in Electrodynamics
• Localized Reduced Basis Approximation of a Nonlinear Finite Volume Battery Model with Resolved Electrode Geometry
• Exponential Convergence of Online Enrichment in Localized Reduced Basis Methods
• Towards Automatic and Reliable Localized Model Order Reduction