filename     : /home/mbotsch/dy/ima05/ima05.pdf
entry        : inproceedings
conference   : 11th IMA Conference on the Mathematics of Surfaces, Loughborough, UK, September 5-7, 2005
pages        : 62-83
year         : 2005
month        : 
title        : Efficient Linear System Solvers for Mesh Processing
subtitle     : 
author       : Mario Botsch, David Bommes, Leif Kobbelt
booktitle    : Lecture Notes in Computer Science
ISSN/ISBN    : 3-540-28225-4
editor       : Ralph R. Martin and Helmut E. Bez and Malcolm A. Sabin
publisher    : Springer
publ.place   : 
volume       : 3604
issue        : 
language     : English
keywords     : geometry processing, linear system solvers
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
\emph{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.