English
Related papers

Related papers: Well-conditioned boundary integral equation formul…

200 papers

The Navier equation is the governing equation of elastic waves, and computing its solution accurately and rapidly has a wide range of applications in geophysical exploration, materials science, etc. In this paper, we focus on the efficient…

Numerical Analysis · Mathematics 2023-10-19 Jianan Yao , Baoling Xie , Jun Lai

The Calder\'on formulas (i.e., the combination of single-layer and hyper-singular boundary integral operators) have been widely utilized in the process of constructing valid boundary integral equation systems which could possess highly…

Analysis of PDEs · Mathematics 2021-08-26 Liwei Xu , Tao Yin

We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…

Numerical Analysis · Mathematics 2016-05-04 Alex. H. Barnett , Bradley J. Nelson , J. Matthew Mahoney

Fast and accurate resolution of electromagnetic problems via the \ac{BEM} is oftentimes challenged by conditioning issues occurring in three distinct regimes: (i) when the frequency decreases and the discretization density remains constant,…

Computational Physics · Physics 2020-04-22 Alexandre Dély , Adrien Merlini , Simon B. Adrian , Francesco P. Andriulli

This paper proposes a new boundary integral equation (BIE) methodology based on the perfectly matched layer (PML) truncation technique for solving the electromagnetic scattering problems in a multi-layered medium. Instead of using the…

Numerical Analysis · Mathematics 2024-01-30 Gang Bao , Wangtao Lu , Tao Yin , Lu Zhang

In this contribution we analyze the spectral properties of some commonly used boundary integral operators in computational electromagnetics and of their discrete counterparts, highlighting peculiar features of their spectra. In particular,…

Computational Engineering, Finance, and Science · Computer Science 2024-07-15 V. Giunzioni , A. Merlini , F. P. Andriulli

We study frequency domain electromagnetic scattering at a bounded, penetrable, and inhomogeneous obstacle $ \Omega \subset \mathbb{R}^3 $. From the Stratton-Chu integral representation, we derive a new representation formula when constant…

Numerical Analysis · Mathematics 2024-12-17 Ignacio Labarca-Figueroa , Ralf Hiptmair

In this paper, we develop second kind integral formulations for flexural wave scattering problems involving the clamped, supported, and free plate boundary conditions. While the clamped plate problem can be solved with layer potentials…

Numerical Analysis · Mathematics 2025-04-09 Peter Nekrasov , Zhaosen Su , Travis Askham , Jeremy G. Hoskins

Based on the perfectly matched layer (PML) technique, this paper develops a high-accuracy boundary integral equation (BIE) solver for acoustic scattering problems in locally defected layered media in both two and three dimensions. The…

Numerical Analysis · Mathematics 2022-11-03 Wangtao Lu , Liwei Xu , Tao Yin , Lu Zhang

The left-right operator splitting method is studied for the efficient calculation of acoustic fields scattered by arbitrary rough surfaces. Here the governing boundary integral is written as a sum of left- and right-going components, and…

Computational Physics · Physics 2017-08-25 Orsola Rath Spivack , Mark Spivack

We consider the scattering problem on locally perturbed periodic penetrable dielectric layers, which is formulated in terms of the full vector-valued time-harmonic Maxwell's equations. The right-hand side is not assumed to be periodic. At…

Analysis of PDEs · Mathematics 2019-08-23 Alexander Konschin

A robust field-only boundary integral formulation of electromagnetics is derived without the use of surface currents that appear in the Stratton-Chu formulation. For scattering by a perfect electrical conductor (PEC), the components of the…

Computational Physics · Physics 2020-02-19 Qiang Sun , Evert Klaseboer , Alex J. Yuffa , Derek Y. C. Chan

This paper is concerned with the problem of an acoustic wave scattering in a locally perturbed periodic structure. As the total wavefield is non-quasi-periodic, effective truncation techniques are pursued for high-accuracy numerical…

Numerical Analysis · Mathematics 2025-12-16 Wangtao Lu , Kuanrong Shen , Ruming Zhang

In this tutorial paper, we consider the problem of electromagnetic scattering by a bounded two-dimensional dielectric object, and discuss certain interesting properties of the scattered field. Using the electric field integral equation,…

Optics · Physics 2015-07-08 Uday K. Khankhoje , Kushal Shah

We consider the linear quadratic regulator (LQR) for one-dimensional linear evolution partial differential equations (PDEs) on a finite interval in space. The control is applied as an additive forcing term to PDEs. Existing methods for…

Systems and Control · Electrical Eng. & Systems 2025-05-26 Zhexian Li , Athanassios S. Fokas , Ketan Savla

We consider time-harmonic electromagnetic scattering problems on perfectly conducting scatterers with uncertain shape. Thus, the scattered field will also be uncertain. Based on the knowledge of the two-point correlation of the domain…

Numerical Analysis · Mathematics 2019-07-15 Jürgen Dölz

We present a new integral equation for solving the Maxwell scattering problem against a perfect conductor. The very same algorithm also applies to sound-soft as well as sound-hard Helmholtz scattering, and in fact the latter two can be…

Analysis of PDEs · Mathematics 2016-07-05 Andreas Rosén

We propose discretisation of a regularised combined field integral equation (regularised CFIE) only with the Rao-Wilton-Glisson (RWG) basis function. The CFIE is a formulation of integral equations, which avoids the so-called ficticious…

Numerical Analysis · Mathematics 2024-06-13 Kazuki Niino , Shunpei Yamamoto

A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…

Mathematical Physics · Physics 2015-06-02 Anders Andersson , Borje Nilsson , Thomas Biro

This paper is concerned with three-dimensional acoustic wave scattering in two-layer media, where the two homogeneous layers are separated by a locally perturbed plane featuring an axially symmetric perturbation. A fast novel boundary…

Numerical Analysis · Mathematics 2024-12-17 Hangya Wang , Wangtao Lu