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Efficient Linear System Solvers for Mesh Processing

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Mathematics of Surfaces XI

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

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Author information

Authors and Affiliations

  1. Computer Graphics Group, RWTH Aachen Technical University, Germany

    Mario Botsch, David Bommes & Leif Kobbelt

Authors
  1. Mario Botsch
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  2. David Bommes
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  3. Leif Kobbelt
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Editor information

Editors and Affiliations

  1. School of Computer Science, Cardiff University, Cardiff, UK

    Ralph Martin

  2. Department of Computer Science, Loughborough University, LE11 3TU, Leicestershire, UK

    Helmut Bez

  3. Numerical Geometry Ltd., UK

    Malcolm Sabin

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Botsch, M., Bommes, D., Kobbelt, L. (2005). Efficient Linear System Solvers for Mesh Processing. In: Martin, R., Bez, H., Sabin, M. (eds) Mathematics of Surfaces XI. Lecture Notes in Computer Science, vol 3604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537908_5

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  • DOI: https://doi.org/10.1007/11537908_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28225-9

  • Online ISBN: 978-3-540-31835-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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