Publication:
High order Nyström methods for transmission problems for Helmholtz equation

Date

2016

Authors

Director

Publisher

Springer
Acceso abierto / Sarbide irekia
Capítulo de libro / Liburuen kapitulua
Versión aceptada / Onetsi den bertsioa

Project identifier

MINECO//MTM2014-52859-P/ES/recolecta
MICINN//MTM2011-22741/ES/recolecta
MINECO//MTM2014-54388-P/ES/recolecta

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.

Description

Keywords

Helmholtz equation, Transmission problems, Helmholtz boundary, Boundary integral operators, Periodic pseudo-differential operators

Department

Ingeniería Matemática e Informática / Matematika eta Informatika Ingeniaritza

Faculty/School

Degree

Doctorate program

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© Springer International Publishing Switzerland 2016

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