Spectral galerkin method for solving helmholtz and laplace dirichlet problems on multiple open arcs

Carlos Jerez-Hanckes; José Pinto

doi:10.1007/978-3-030-39647-3_30

Spectral galerkin method for solving helmholtz and laplace dirichlet problems on multiple open arcs

Producción científica: Capítulo del libro/informe/acta de congreso › Contribución a la conferencia › revisión exhaustiva

Resumen

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. 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.

Idioma original	Inglés
Título de la publicación alojada	Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference
Editores	Spencer J. Sherwin, Joaquim Peiró, Peter E. Vincent, David Moxey, Christoph Schwab
Editorial	Springer
Páginas	383-393
Número de páginas	11
ISBN (versión impresa)	9783030396466
DOI	https://doi.org/10.1007/978-3-030-39647-3_30
Estado	Publicada - 2020
Publicado de forma externa	Sí
Evento	12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018 - London, Reino Unido Duración: 9 jul. 2018 → 13 jul. 2018

Serie de la publicación

Nombre	Lecture Notes in Computational Science and Engineering
Volumen	134
ISSN (versión impresa)	1439-7358
ISSN (versión digital)	2197-7100

Conferencia

Conferencia	12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018
País/Territorio	Reino Unido
Ciudad	London
Período	9/07/18 → 13/07/18

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10.1007/978-3-030-39647-3_30

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Jerez-Hanckes, C., & Pinto, J. (2020). Spectral galerkin method for solving helmholtz and laplace dirichlet problems on multiple open arcs. En S. J. Sherwin, J. Peiró, P. E. Vincent, D. Moxey, & C. Schwab (Eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference (pp. 383-393). (Lecture Notes in Computational Science and Engineering; Vol. 134). Springer. https://doi.org/10.1007/978-3-030-39647-3_30

Jerez-Hanckes, Carlos ; Pinto, José. / Spectral galerkin method for solving helmholtz and laplace dirichlet problems on multiple open arcs. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference. editor / Spencer J. Sherwin ; Joaquim Peiró ; Peter E. Vincent ; David Moxey ; Christoph Schwab. Springer, 2020. pp. 383-393 (Lecture Notes in Computational Science and Engineering).

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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. 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.",

author = "Carlos Jerez-Hanckes and Jos{\'e} Pinto",

note = "Publisher Copyright: {\textcopyright} 2020, The Author(s).; 12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018 ; Conference date: 09-07-2018 Through 13-07-2018",

year = "2020",

doi = "10.1007/978-3-030-39647-3_30",

language = "English",

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series = "Lecture Notes in Computational Science and Engineering",

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booktitle = "Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference",

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Jerez-Hanckes, C & Pinto, J 2020, Spectral galerkin method for solving helmholtz and laplace dirichlet problems on multiple open arcs. En SJ Sherwin, J Peiró, PE Vincent, D Moxey & C Schwab (eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference. Lecture Notes in Computational Science and Engineering, vol. 134, Springer, pp. 383-393, 12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018, London, Reino Unido, 9/07/18. https://doi.org/10.1007/978-3-030-39647-3_30

Spectral galerkin method for solving helmholtz and laplace dirichlet problems on multiple open arcs. / Jerez-Hanckes, Carlos ; Pinto, José.
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference. ed. / Spencer J. Sherwin; Joaquim Peiró; Peter E. Vincent; David Moxey; Christoph Schwab. Springer, 2020. p. 383-393 (Lecture Notes in Computational Science and Engineering; Vol. 134).

Producción científica: Capítulo del libro/informe/acta de congreso › Contribución a la conferencia › revisión exhaustiva

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N2 - 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. 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.

AB - 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. 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.

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Jerez-Hanckes C , Pinto J. Spectral galerkin method for solving helmholtz and laplace dirichlet problems on multiple open arcs. En Sherwin SJ, Peiró J, Vincent PE, Moxey D, Schwab C, editores, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference. Springer. 2020. p. 383-393. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-030-39647-3_30

Spectral galerkin method for solving helmholtz and laplace dirichlet problems on multiple open arcs

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