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.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2020017
Keywords: Boundary integral equations, spectral methods, wave scattering problems, screens problems, non-Lipschitz domains
@article{M2AN_2020__54_6_1975_0,
author = {Jerez-Hanckes, Carlos and Pinto, Jos\'e},
title = {High-order {Galerkin} method for {Helmholtz} and {Laplace} problems on multiple open arcs},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1975--2009},
year = {2020},
publisher = {EDP Sciences},
volume = {54},
number = {6},
doi = {10.1051/m2an/2020017},
mrnumber = {4160326},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2020017/}
}
TY - JOUR AU - Jerez-Hanckes, Carlos AU - Pinto, José TI - High-order Galerkin method for Helmholtz and Laplace problems on multiple open arcs JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2020 SP - 1975 EP - 2009 VL - 54 IS - 6 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2020017/ DO - 10.1051/m2an/2020017 LA - en ID - M2AN_2020__54_6_1975_0 ER -
%0 Journal Article %A Jerez-Hanckes, Carlos %A Pinto, José %T High-order Galerkin method for Helmholtz and Laplace problems on multiple open arcs %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2020 %P 1975-2009 %V 54 %N 6 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2020017/ %R 10.1051/m2an/2020017 %G en %F M2AN_2020__54_6_1975_0
Jerez-Hanckes, Carlos; Pinto, José. High-order Galerkin method for Helmholtz and Laplace problems on multiple open arcs. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 6, pp. 1975-2009. doi: 10.1051/m2an/2020017
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