High order Nyström methods for transmission problems for Helmholtz equation

Document Type

Syllabus

Publication Date

1-1-2016

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.

Identifier

85031905435 (Scopus)

Publication Title

Sema Simai Springer Series

External Full Text Location

https://doi.org/10.1007/978-3-319-32013-7_15

e-ISSN

2199305X

ISSN

21993041

First Page

261

Last Page

285

Volume

8

Grant

MTM2011-22741

Fund Ref

Ministerio de Economía y Competitividad

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