Multilevel solvers for unstructured surface meshes

被引:33
作者
Aksoylu, B [1 ]
Khodakovsky, A [1 ]
Schröder, P [1 ]
机构
[1] CALTECH, Dept Comp Sci, Pasadena, CA 91125 USA
关键词
multilevel preconditioning; multigrid; hierarchical basis multigrid; Bramble-Pasciak-Xu; computer graphics; unstructured surface mesh; surface parameterization; harmonic weights; mean value weights; mesh coarsening;
D O I
10.1137/S1064827503430138
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:1146 / 1165
页数:20
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