High order Nyström methods for transmission problems for Helmholtz equation

Víctor Domínguez, Catalin Turc

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

Abstract

We present super-algebraic compatible Nyström discretizations for the four Helmholtz boundary operators of Calderón’s calculus on smooth closed curves in 2D. These discretizations are based on appropriate splitting of the kernels combined with very accurate product-quadrature rules for the different singularities that such kernels present. A Fourier based analysis shows that the four discrete operators converge to the continuous ones in appropriate Sobolev norms. This proves that Nyström discretizations of many popular integral equation formulations for Helmholtz equations are stable and convergent. The convergence is actually super-algebraic for smooth solutions.

Original languageEnglish (US)
Title of host publicationSEMA SIMAI Springer Series
PublisherSpringer International Publishing
Pages261-285
Number of pages25
DOIs
StatePublished - 2016

Publication series

NameSEMA SIMAI Springer Series
Volume8
ISSN (Print)2199-3041
ISSN (Electronic)2199-305X

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Numerical Analysis
  • Agricultural and Biological Sciences (miscellaneous)
  • Physics and Astronomy (miscellaneous)
  • Fluid Flow and Transfer Processes
  • Computational Mathematics
  • Industrial and Manufacturing Engineering
  • Applied Mathematics

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