A Multigrid Algorithm for an Elliptic Problem with a Perturbed Boundary Condition

Andrea Bonito, Joseph E. Pasciak

Research output: Chapter in Book/Report/Conference proceedingChapter


We discuss the preconditioning of systems coupling elliptic operators in Ω⊂Rd, d=2,3, with elliptic operators defined on hypersurfaces. These systems arise naturally when physical phenomena are affected by geometric boundary forces, such as the evolution of liquid drops subject to surface tension. The resulting operators are sums of interior and boundary terms weighted by parameters. We investigate the behavior of multigrid algorithms suited to this context and demonstrate numerical results which suggest uniform preconditioning bounds that are level and parameter independent.
Original languageEnglish (US)
Title of host publicationNumerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications
PublisherSpringer Nature
Number of pages11
ISBN (Print)9781461471714
StatePublished - May 12 2013
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: This work was supported in part by award number KUS-C1-016-04 madeby King Abdulla University of Science and Technology (KAUST). It was also supported in part bythe National Science Foundation through Grant DMS-0914977 and DMS-1216551.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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