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Efficient Linear System Solvers for Mesh Processing

  • Mario Botsch
  • David Bommes
  • Leif Kobbelt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3604)

Abstract

The use of polygonal mesh representations for freeform geometry enables the formulation of many important geometry processing tasks as the solution of one or several linear systems. As a consequence, the key ingredient for efficient algorithms is a fast procedure to solve linear systems. A large class of standard problems can further be shown to lead more specifically to sparse, symmetric, and positive definite systems, that allow for a numerically robust and efficient solution.

In this paper we discuss and evaluate the use of sparse direct solvers for such kind of systems in geometry processing applications, since in our experiments they turned out to be superior even to highly optimized multigrid methods, but at the same time were considerably easier to use and implement. Although the methods we present are well known in the field of high performance computing, we observed that they are in practice surprisingly rarely applied to geometry processing problems.

Keywords

Multigrid Method Cholesky Factorization Iterative Solver Direct Solver Mesh Processing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Mario Botsch
    • 1
  • David Bommes
    • 1
  • Leif Kobbelt
    • 1
  1. 1.Computer Graphics GroupRWTH Aachen Technical UniversityGermany

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