Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 26, Issue 4, Pages 1146-1165Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S1064827503430138
Keywords
multilevel preconditioning; multigrid; hierarchical basis multigrid; Bramble-Pasciak-Xu; computer graphics; unstructured surface mesh; surface parameterization; harmonic weights; mean value weights; mesh coarsening
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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. ne 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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