Local Spectra of Adaptive Domain Decomposition Methods

Conference paper (2020)

Authors

A. Heinlein Center for Data and Simulation Science, University of Cologne
A. Klawonn University of Cologne
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Published Date

2020

Language

English

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Abstract

For second order elliptic partial differential equations, such as diffusion or elasticity, with arbitrary and high coefficient jumps, the convergence rate of domain decomposition methods with classical coarse spaces typically deteriorates. One remedy is the use of adaptive coarse spaces, which use eigenfunctions computed from local generalized eigenvalue problems to enrich the standard coarse space; see, e.g., [19, 6, 5, 4, 22, 23, 3, 16, 17, 14, 7, 8, 24, 1, 20, 2, 13, 21, 10, 9, 11]. This typically results in a condition number estimate of the form