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arXiv · 1910.08856

Multiscale-Spectral GFEM and Optimal Oversampling

Ivo Babuska·Robert Lipton·Paul Sinz·Michael Stuebner
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Abstract

In this work we address the Multiscale Spectral Generalized Finite Element Method (MS-GFEM) developed in [I. Babu\v{s}ka and R. Lipton, Multiscale Modeling and Simulation 9 (2011), pp. 373--406]. We outline the numerical implementation of this method and present simulations that demonstrate contrast independent exponential convergence of MS-GFEM solutions. We introduce strategies to reduce the computational cost of generating the optimal oversampled local approximating spaces used here. These strategies retain accuracy while reducing the computational work necessary to generate local bases. Motivated by oversampling we develop a nearly optimal local basis based on a partition of unity on the boundary and the associated A-harmonic extensions.

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Ivo Babuska, Robert Lipton, Paul Sinz, Michael Stuebner. 2019-10-19. Multiscale-Spectral GFEM and Optimal Oversampling. https://doi.org/10.1016/j.cma.2020.112960

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