High order Nyström methods for transmission problems for Helmholtz equation

2015/10/22 by Vı́ctor Domínguez, Dominguez, V., Catalin Turc +1
Engineering · Physics and Astronomy · #35J05 #65N38 #65T40 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1510.06682

openalex publication_date 2015/10/22 · openalex created_date 2022/11/28 · openalex updated_date 2026/07/28

Abstract

We present superalgebraic 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 superalgebraic for smooth solutions.

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