High-order Galerkin method for Helmholtz and Laplace problems on multiple open arcs

Research output: Contribution to journalArticlepeer-review

Abstract

We present a spectral Galerkin numerical scheme for solving Helmholtz and Laplace problems with Dirichlet boundary conditions on a finite collection of open arcs in two-dimensional space. A boundary integral method is employed, giving rise to a first kind Fredholm equation whose variational form is discretized using weighted Chebyshev polynomials. Well-posedness of the discrete problems is established as well as algebraic or even exponential convergence rates depending on the regularities of both arcs and excitations. Our numerical experiments show the robustness of the method with respect to number of arcs and large wavenumber range. Moreover, we present a suitable compression algorithm that further accelerates computational times.

Original languageEnglish
Pages (from-to)1975-2009
Number of pages35
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume54
Issue number6
DOIs
StatePublished - 1 Nov 2020
Externally publishedYes

Keywords

  • Boundary integral equations
  • Non-Lipschitz domains
  • Screens problems
  • Spectral methods
  • Wave scattering problems

Fingerprint

Dive into the research topics of 'High-order Galerkin method for Helmholtz and Laplace problems on multiple open arcs'. Together they form a unique fingerprint.

Cite this