Schröder,Multilevel Solvers for Unstructured Surface Meshes

Abstract. 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 strate-gies. Since the underlying meshes are very fine to begin with, such multilevel preconditioners require mesh coarsen-ing 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 hi-erarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner