Absorbing boundary conditions for the Helmholtz equation using Gauss-Legendre quadrature reduced integrations

We introduce a new class of absorbing boundary conditions (ABCs) for the Helmholtz equation. The proposed ABCs are obtained by using \(L\) discrete layers and the \(Q_N\) Lagrange finite element in conjunction with the \(N\)-point Gauss-Legendre quadrature reduced integration rule in a specific form...

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Bibliographic Details
Published in:arXiv.org 2024-05
Main Author: Sagiyama, Koki
Format: Article
Language:English
Subjects:
Boundary conditions
Helmholtz equations
Perfectly matched layers
Quadratures
Online Access:Get full text
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Summary:We introduce a new class of absorbing boundary conditions (ABCs) for the Helmholtz equation. The proposed ABCs are obtained by using \(L\) discrete layers and the \(Q_N\) Lagrange finite element in conjunction with the \(N\)-point Gauss-Legendre quadrature reduced integration rule in a specific formulation of perfectly matched layers. The proposed ABCs are classified by a tuple \((L,N)\), and achieve reflection error of order \(O(R^{2LN})\) for some \(R
ISSN:2331-8422