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
This is a preview of subscription content, access via your institution.
Unable to display preview. Download preview PDF.
Editors and Affiliations
Rights and permissions
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Heinlein, A., Klawonn, A., Kühn, M.J. (2020). Local Spectra of Adaptive Domain Decomposition Methods. In: , et al. Domain Decomposition Methods in Science and Engineering XXV. DD 2018. Lecture Notes in Computational Science and Engineering, vol 138. Springer, Cham. https://doi.org/10.1007/978-3-030-56750-7_18
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-56749-1
Online ISBN: 978-3-030-56750-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)