Variants of an explicit kernel-split panel-based Nyström discretization scheme for Helmholtz boundary value problems

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Abstract

The incorporation of analytical kernel information is exploited in the construction of Nyström discretization schemes for integral equations modeling planar Helmholtz boundary value problems. Splittings of kernels and matrices, coarse and fine grids, high-order polynomial interpolation, product integration performed on the fly, and iterative solution are some of the numerical techniques used to seek rapid and stable convergence of computed fields in the entire computational domain.
Original languageEnglish
Pages (from-to)691-708
JournalAdvances in Computational Mathematics
Volume41
Issue number3
DOIs
Publication statusPublished - 2015

Subject classification (UKÄ)

  • Computational Mathematics

Keywords

  • high-order quadrature
  • singular kernel
  • Helmholtz equation
  • Nyström discretization
  • integral equation

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