@inproceedings{960ac936a2a94c349d0447cb0198ad01,
title = "Spectral galerkin method for solving helmholtz and laplace dirichlet problems on multiple open arcs",
abstract = "We present a spectral numerical scheme for solving Helmholtz and Laplace problems with Dirichlet boundary conditions on an unbounded non-Lipschitz domain R2\Γ, where Γ is a finite collection of open arcs. Through an indirect method, a first kind formulation is derived whose variational form is discretized using weighted Chebyshev polynomials. We show that our discretization basis allows for exponential convergence under smoothness assumptions. We show how a simple preconditioner can be built with successful results and introduce an efficient compression algorithm.",
keywords = "Boundary integral equations, Disjoint domains, Matrix compression, Screens, Spectral methods",
author = "Jos{\'e} Pinto and Carlos Jerez-Hanckes",
note = "Publisher Copyright: copyright {\textcopyright} Crown copyright (2018).All right reserved.; 6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018 ; Conference date: 11-06-2018 Through 15-06-2018",
year = "2020",
language = "English",
series = "Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018",
publisher = "International Centre for Numerical Methods in Engineering, CIMNE",
pages = "1950--1961",
editor = "Roger Owen and {de Borst}, Rene and Jason Reese and Chris Pearce",
booktitle = "Proceedings of the 6th European Conference on Computational Mechanics",
}