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- W3048883869 abstract "Abstract We present a spectral numerical scheme for solving Helmholtz and Laplace problems with Dirichlet boundary conditions on an unbounded non-Lipschitz domain $$mathbb {R}^2 backslash overline {Gamma }$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mrow> <mml:mi>ℝ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>∖</mml:mo> <mml:mover> <mml:mrow> <mml:mi>Γ</mml:mi> </mml:mrow> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> , 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. This choice of basis allows for exponential convergence rates under smoothness assumptions. Moreover, by implementing a simple compression algorithm, we are able to efficiently account for large numbers of arcs as well as a wide wavenumber range." @default.
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- W3048883869 date "2020-01-01" @default.
- W3048883869 modified "2023-09-26" @default.
- W3048883869 title "Spectral Galerkin Method for Solving Helmholtz and Laplace Dirichlet Problems on Multiple Open Arcs" @default.
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- W3048883869 doi "https://doi.org/10.1007/978-3-030-39647-3_30" @default.
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