2023/08/23 by Koki Sagiyama, Sagiyama, Koki
Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Boundary (topology) #Boundary value problem #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Finite element method #Gauss #Gaussian quadrature #Helmholtz equation #Helmholtz free energy #Legendre polynomials #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Nyström method #Physics #Quadrature (astronomy)
paper · pdf · doi:10.48550/arxiv.2308.12255
openalex publication_date 2023/08/23 · openalex created_date 2023/08/25 · openalex updated_date 2026/07/28
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 QN 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(R2LN) for some R<1. The new ABCs generalise the perfectly matched discrete layers proposed by Guddati and Lim [Int. J. Numer. Meth. Engng 66 (6) (2006) 949-977], including them as type (L,1). An analysis of the proposed ABCs is performed motivated by the work of Ainsworth [J. Comput. Phys. 198 (1) (2004) 106-130]. The new ABCs facilitate numerical implementations of the Helmholtz problem with ABCs if QN finite elements are used in the physical domain as well as give more insight into this field for the further advancement.