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Computing and Visualization in Science

, Volume 7, Issue 3–4, pp 173–181 | Cite as

2-matrices – Multilevel methods for the approximation of integral operators

  • Steffen BörmEmail author
Regular article

Abstract

Multigrid methods are typically used to solve partial differential equations, i.e., they approximate the inverse of the corresponding partial differential operators. At least for elliptic PDEs, this inverse can be expressed in the form of an integral operator by Green’s theorem.

This implies that multigrid methods approximate certain integral operators, so it is straightforward to look for variants of multigrid methods that can be used to approximate more general integral operators.

2-matrices combine a multigrid-like structure with ideas from panel clustering algorithms in order to provide a very efficient method for discretizing and evaluating the integral operators found, e.g., in boundary element applications.

Keywords

Kernel Function Multigrid Method Discretization Error Cluster Tree Nest Iteration 
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 2004

Authors and Affiliations

  1. 1.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany

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