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Multilevel Solvers for Unstructured Surface Meshes

Aksoylu, Burak and Khodakovsky, Andrei and Schröder, Peter (2005) Multilevel Solvers for Unstructured Surface Meshes. SIAM Journal on Scientific Computing, 26 (4). pp. 1146-1165. ISSN 1064-8275. doi:10.1137/S1064827503430138.

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Parameterization of unstructured surface meshes is of fundamental importance in many applications of digital geometry processing. Such parameterization approaches give rise to large and exceedingly ill-conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies. Since the underlying meshes are very fine to begin with, such multilevel preconditioners require mesh coarsening to build an appropriate hierarchy. In this paper we consider several strategies for the construction of hierarchies using ideas from mesh simplification algorithms used in the computer graphics literature. We introduce two novel hierarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner.

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Schröder, Peter0000-0002-0323-7674
Additional Information:© 2005 Society for Industrial and Applied Mathematics. Received by the editors June 17, 2003; accepted for publication (in revised form) April 14, 2004; published electronically March 11, 2005. This work was supported in part by NSF (DMS-0220905, DMS-0138458, ACI-0219979), the DOE (W-7405-ENG-48/B341492), nVidia, the Center for Integrated Multiscale Modeling and Simulation, Alias|Wavefront, Pixar, Microsoft, and the Packard Foundation. The authors would like to thank M. Holst for providing FEtk, S. Bond for his help on the components of the preconditioner code, and I. Guskov for parts of the parameterization and coarsening code. We would also like to thank them for many enlightening discussions. The David head model is courtesy of the Digital Michelangelo Project at Stanford University. The Igea and skull models are courtesy of Cyberware, Inc., and Headus, Inc., respectively.
Subject Keywords:multilevel preconditioning, multigrid, hierarchical basis multigrid, Bramble–Pasciak–Xu, computer graphics, unstructured surface mesh, surface parameterization, harmonic weights, mean value weights, mesh coarsening
Issue or Number:4
Record Number:CaltechAUTHORS:AKSsiamjsc05
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:433
Deposited By: Archive Administrator
Deposited On:18 Jun 2005
Last Modified:08 Nov 2021 19:02

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