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Numerische Mathematik

, Volume 133, Issue 3, pp 409–442 | Cite as

Approximation of integral operators by Green quadrature and nested cross approximation

  • Steffen BörmEmail author
  • Sven Christophersen
Article

Abstract

We present a fast algorithm that constructs a data-sparse approximation of matrices arising in the context of integral equation methods for elliptic partial differential equations. The new algorithm uses Green’s representation formula in combination with quadrature to obtain a first approximation of the kernel function, and then applies nested cross approximation to obtain a more efficient representation. The resulting \({\mathcal H}^2\)-matrix representation requires \({\mathcal O}(n k)\) units of storage for an \(n\times n\) matrix, where k depends on the prescribed accuracy.

Mathematics Subject Classification

65N38 65N80 65D30 45B05 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of KielKielGermany

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