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

Andrea Bonito; Joseph E. Pasciak

doi:10.1007/978-1-4614-7172-1_4

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

Andrea Bonito, Joseph E. Pasciak

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

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 language	English (US)
Title of host publication	Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications
Publisher	Springer Nature
Pages	69-79
Number of pages	11
ISBN (Print)	9781461471714
DOIs	https://doi.org/10.1007/978-1-4614-7172-1_4
State	Published - May 12 2013
Externally published	Yes

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10.1007/978-1-4614-7172-1_4

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title = "A Multigrid Algorithm for an Elliptic Problem with a Perturbed Boundary Condition",

abstract = "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.",

author = "Andrea Bonito and Pasciak, {Joseph E.}",

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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AU - Pasciak, Joseph E.

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N2 - 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.

AB - 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.

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M3 - Chapter

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EP - 79

BT - Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications

PB - Springer Nature

ER -

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

Abstract

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