Reducedorder multiscale modeling of nonlinear Em

Authors: M Presho S Ye

Publish Date: 2015/06/05

Volume: 19, Issue: 4, Pages: 921-932

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Abstract

In this paper we consider a class of nonlinear flow problems that are modeled through a timedependent pLaplacian formulation Using an approach that combines the Generalized Multiscale Finite Element Method GMsFEM and Discrete Empirical Interpolation Method DEIM we are able to accurately approximate the nonlinear pLaplacian solutions at a significantly reduced cost In particular GMsFEM allows us to iteratively solve the global problem using a reducedorder model in which a flexible number of multiscale basis functions are used to construct a spectrally enriched coarsegrid solution space The iterative procedure requires a number of nonlinear functional updates that are simultaneously made more cost efficient through implementation of DEIM The combined GMsFEMDEIM approach is shown to be a flexible framework for producing accurate reducedorder descriptions of the nonlinear model for a wide range of parameters and varying levels nonlinearity A number of numerical examples are presented to illustrate the effectiveness of the proposed methodologyThis material is based upon work supported by the US Department of Energy Office of Science Office of Advanced Scientific Computing Research Applied Mathematics program under Award Number DESC0009286 as part of the DiaMonD Multifaceted Mathematics Integrated Capability Center

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