Efficient Linear System Solvers for Mesh Processing

@incollection{citeulike:2601719, 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.}, author = {Botsch, Mario and Bommes, David and Kobbelt, Leif }, citeulike-article-id = {2601719}, doi = {10.1007/11537908\_5}, journal = {Mathematics of Surfaces XI}, keywords = {optimierung, optimization}, pages = {62--83}, posted-at = {2008-03-27 12:37:52}, priority = {2}, title = {Efficient Linear System Solvers for Mesh Processing}, url = {http://dx.doi.org/10.1007/11537908\_5}, year = {2005} }

TY - CHAP ID - citeulike:2601719 L3 - citeulike-article-id:2601719 TI - Efficient Linear System Solvers for Mesh Processing JF - Mathematics of Surfaces XI SP - 62 EP - 83 N2 - 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. KW - optimierung KW - optimization AU - Botsch, Mario AU - Bommes, David AU - Kobbelt, Leif PY - 2005/// UR - http://dx.doi.org/10.1007/11537908_5 ER -