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

  • Andrea Bonito
  • Joseph E. Pasciak
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 45)

Abstract

We discuss the preconditioning of systems coupling elliptic operators in \(\Omega \subset {\mathbb{R}}^{d}\), 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.

Keywords

Multigrid Laplace-Beltrami Surface Laplacian Parameter dependent problems 

Notes

Acknowledgements

This work was supported in part by award number KUS-C1-016-04 made by King Abdulla University of Science and Technology (KAUST). It was also supported in part by the National Science Foundation through Grant DMS-0914977 and DMS-1216551.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA

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