A Multigrid Algorithm for an Elliptic Problem with a Perturbed Boundary Condition
KAUST Grant NumberKUS-C1-016-04
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AbstractWe 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.
CitationBonito A, Pasciak JE (2013) A Multigrid Algorithm for an Elliptic Problem with a Perturbed Boundary Condition. Springer Proceedings in Mathematics & Statistics: 69–79. Available: http://dx.doi.org/10.1007/978-1-4614-7172-1_4.
SponsorsThis 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.
PublisherSpringer Science + Business Media
JournalNumerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications