| Issue |
ESAIM: M2AN
Volume 54, Number 6, November-December 2020
|
|
|---|---|---|
| Page(s) | 1975 - 2009 | |
| DOI | https://doi.org/10.1051/m2an/2020017 | |
| Published online | 12 October 2020 | |
Research Article
High-order Galerkin method for Helmholtz and Laplace problems on multiple open arcs
1
Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Santiago, Chile
2
School of Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile
* Corresponding author: carlos.jerez@uai.cl
Received:
23
July
2019
Accepted:
11
March
2020
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.
Mathematics Subject Classification: 65R20 / 65N22 / 65N35 / 65N38
Key words: Boundary integral equations / spectral methods / wave scattering problems / screens problems / non-Lipschitz domains
© EDP Sciences, SMAI 2020
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