A geometric multigrid approach to solving the 2D inhomogeneous laplace equation with internal drichlet boundary conditions

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Publication Type Journal Article
School or College College of Engineering
Department Electrical & Computer Engineering
Creator Tasdizen, Tolga; Whitaker, Ross T.
Other Author Grady, Leo
Title A geometric multigrid approach to solving the 2D inhomogeneous laplace equation with internal drichlet boundary conditions
Date 2005
Description The inhomogeneous Laplace (Poisson) equation with internal Dirichlet boundary conditions has recently appeared in several applications to image processing and analysis. Although these approaches have demonstrated quality results, the computational burden of solution demands an efficient solver. Design of an efficient multigrid solver is difficult for these problems due to unpredictable inhomogeneity in the equation coefficients and internal Dirichlet conditions with arbitrary location and value. We present a geometric multigrid approach to solving these systems designed around weighted prolongation/restriction operators and an appropriate system coarsening. This approach is compared against a modified incomplete Cholesky conjugate gradient solver for a range of image sizes. We note that this approach applies equally well to the anisotropic diffusion problem and offers an alternative method to the classic multigrid approach of Acton [1].
Type Text
Publisher Institute of Electrical and Electronics Engineers (IEEE)
First Page 642
Last Page 645
Language eng
Bibliographic Citation Grady, L., Tasdizen, T., & Whitaker, R. (2005). A geometric multigrid approach to solving the 2D inhomogeneous laplace equation with internal drichlet boundary conditions. Proceedings of International Conference on Image Processing (ICIP), 2, 642-5. September.
Rights Management (c) 2005 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Format Medium application/pdf
Format Extent 300,263 bytes
Identifier ir-main,15228
ARK ark:/87278/s6ft948g
Setname ir_uspace
Date Created 2012-06-13
Date Modified 2012-06-13
ID 703821
Reference URL https://collections.lib.utah.edu/ark:/87278/s6ft948g