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We investigate the parallel one-level overlapping Schwarz method for solving finite element discretization of high-frequency Helmholtz equations. The resulting linear systems are large, indefinite, ill-conditioned, and complex-valued. We…

Numerical Analysis · Mathematics 2026-02-03 Yan Xie , Shihua Gong , Ivan G. Graham , Euan A. Spence , Chen-Song Zhang

We explain how to use smooth bivariate splines of arbitrary degree to solve the exterior Helmholtz equation based on a Perfectly Matched Layer (PML) technique. In a previous study (cf. [26]), it was shown that bivariate spline functions of…

Numerical Analysis · Mathematics 2018-11-20 Shelvean Kapita , Ming Jun Lai

We propose a pure source transfer domain decomposition method (PSTDDM) for solving the truncated perfectly matched layer (PML) approximation in bounded domain of Helmholtz scattering problem. The method is a modification of the STDDM…

Numerical Analysis · Mathematics 2019-07-08 Yu Du , Haijun Wu

Discrete transparent boundary conditions (DTBC) and the Perfectly Matched Layers (PML) method for the realization of open boundary conditions in quantum device simulations are compared, based on the stationary and time-dependent…

Numerical Analysis · Mathematics 2015-06-18 Jan-Frederik Mennemann , Ansgar Jüngel

A new construction of an absorbing boundary condition for indefinite Helmholtz problems on unbounded domains is presented. This construction is based on a near-best uniform rational interpolant of the inverse square root function on the…

Numerical Analysis · Mathematics 2015-07-23 Vladimir Druskin , Stefan Güttel , Leonid Knizhnerman

The multipole expansion method (MEM) is a spatial discretization technique that is widely used in applications that feature scattering of waves from circular cylinders. Moreover, it also serves as a key component in several other numerical…

Numerical Analysis · Mathematics 2021-06-04 Brian Fitzpatrick , Enzo De Sena , Toon van Waterschoot

For scattering problems of time-harmonic waves, the boundary integral equation (BIE) methods are highly competitive, since they are formulated on lower-dimension boundaries or interfaces, and can automatically satisfy outgoing radiation…

Numerical Analysis · Mathematics 2018-04-24 Wangtao Lu , Ya Yan Lu , Jianliang Qian

This work is focused on the modelling of signal propagations in myelinated axons to characterize the functions of the myelin sheath in the neural structure. Based on reasonable assumptions on the medium properties, we derive a…

Numerical Analysis · Mathematics 2022-12-29 Xue Jiang , Maohui Lyu , Tao Yin , Weiying Zheng

The design of absorbing boundary conditions (ABC) in a numerical simulation is a challenging task. In the best cases, spurious reflections remain for some angles of incidence or at certain wave lengths. In the worst, ABC are not even…

Computational Physics · Physics 2024-09-11 Guillaume Bouchard , Arnaud Beck , Francesco Massimo , Arnd Specka

A cylindrical wave expansion method is developed to obtain the scattering field for an ideal two-dimensional cylindrical invisibility cloak. A near-ideal model of the invisibility cloak is set up to solve the boundary problem at the inner…

Optics · Physics 2007-09-15 Zhichao Ruan , Min Yan , Curtis W. Neff , Min Qiu

We consider approximation of the variable-coefficient Helmholtz equation in the exterior of a Dirichlet obstacle using perfectly-matched-layer (PML) truncation; it is well known that this approximation is exponentially accurate in the PML…

Analysis of PDEs · Mathematics 2024-01-19 Jeffrey Galkowski , David Lafontaine , Euan A. Spence , Jared Wunsch

Achieving exact unidirectional invisibility in a finite frequency band has been an outstanding problem for many years. We offer a simple solution to this problem in two dimensions that is based on our solution to another more basic open…

Quantum Physics · Physics 2019-12-06 Farhang Loran , Ali Mostafazadeh

In this paper, we consider near cloaking for the full Maxwell equations. We extend the recent results, where the quasi-static limit case and the Helmholtz equation are considered, to electromagnetic scattering problems. We construct very…

Analysis of PDEs · Mathematics 2012-12-27 Habib Ammari , Hyeonbae Kang , Hyundae Lee , Mikyoung Lim , Sanghyeon Yu

The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of 2D scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary…

Numerical Analysis · Mathematics 2022-03-15 Anne-Sophie Bonnet-Ben Dhia , Simon N. Chandler-Wilde , Sonia Fliss

We consider the numerical solution of scalar wave equations in domains which are the union of a bounded domain and a finite number of infinite cylindrical waveguides. The aim of this paper is to provide a new convergence analysis of both…

Numerical Analysis · Mathematics 2015-04-01 Thorsten Hohage , Lothar Nannen

Generalized linear mixed models are powerful tools for analyzing clustered data, where the unknown parameters are classically (and most commonly) estimated by the maximum likelihood and restricted maximum likelihood procedures. However,…

Statistics Theory · Mathematics 2023-03-23 Andrea M. Bratsberg , Magne Thoresen , Abhik Ghosh

Miniaturized optical resonators with spatial dimensions of the order of the wavelength of the trapped light offer prospects for a variety of new applications like quantum processing or construction of meta-materials. Light propagation in…

Computational Physics · Physics 2009-05-28 L. Zschiedrich , S. Burger , B. Kettner , F. Schmidt

Kernel approximation with exponentials is useful in many problems with convolution quadrature and particle interactions such as integral-differential equations, molecular dynamics and machine learning. This paper proposes a weighted…

Computational Physics · Physics 2025-05-07 Yuanshen Lin , Zhenli Xu , Yusu Zhang , Qi Zhou

In a graph, a perfect matching cut is an edge cut that is a perfect matching. Perfect Matching Cut (PMC) is the problem of deciding whether a given graph has a perfect matching cut, and is known to be NP-complete. We revisit the problem and…

Discrete Mathematics · Computer Science 2021-07-15 Van Bang Le , Jan Arne Telle

A crucial part of successful wave propagation related inverse problems is an efficient and accurate numerical scheme for solving the seismic wave equations. In particular, the numerical solution to a multi-dimensional Helmholtz equation can…

Numerical Analysis · Mathematics 2021-03-11 Hatef Dastour , Wenyuan Liao