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Published in:
2020 | OriginalPaper | Chapter
Local Spectra of Adaptive Domain Decomposition Methods
Authors : Alexander Heinlein, Axel Klawonn, Martin J. Kühn
Published in: Domain Decomposition Methods in Science and Engineering XXV
Publisher: Springer International Publishing
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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