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Numerische Mathematik

, Volume 99, Issue 4, pp 605–643 | Cite as

Approximation of Integral Operators by Variable-Order Interpolation

  • Steffen Börm
  • Maike Löhndorf
  • Jens M. MelenkEmail author
Article

Summary.

We employ a data-sparse, recursive matrix representation, so-called Open image in new window -matrices, for the efficient treatment of discretized integral operators. We obtain this format using local tensor product interpolants of the kernel function and replacing high-order approximations with piecewise lower-order ones. The scheme has optimal, i.e., linear, complexity in the memory requirement and time for the matrix-vector multiplication. We present an error analysis for integral operators of order zero. In particular, we show that the optimal convergence Open image in new window (h) is retained for the classical double layer potential discretized with piecewise constant functions.

Keywords

Double Layer Tensor Product Kernel Function Integral Operator Matrix Representation 
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 2005

Authors and Affiliations

  • Steffen Börm
    • 1
  • Maike Löhndorf
    • 1
  • Jens M. Melenk
    • 2
    Email author
  1. 1.Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstrasse 22–26LeipzigGermany
  2. 2.Department of MathematicsThe University of ReadingUnited Kingdom

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