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An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…

Numerical Analysis · Mathematics 2016-05-30 Xue Jiang , Peijun Li , Junliang Lv , Weiying Zheng

An accurate and efficient numerical simulation approach to electromagnetic wave scattering from two-dimensional, randomly rough, penetrable surfaces is presented. The use of the M\"uller equations and an impedance boundary condition for a…

Optics · Physics 2010-06-03 Ingve Simonsen , Alexei A. Maradudin , Tamara A. Leskova

The scattering of electromagnetic waves by three--dimensional periodic structures is important for many problems of crucial scientific and engineering interest. Due to the complexity and three-dimensional nature of these waves, the fast,…

Numerical Analysis · Mathematics 2023-07-31 David P. Nicholls , Liet Vo

In this paper, an efficient and accurate unified approach is proposed to solve transverse magnetic scattering problems by multilayer embedded objects. In the proposed approach, an equivalent current density is derived when the equivalent…

Computational Engineering, Finance, and Science · Computer Science 2020-01-23 Xiaochao Zhou , Zekun Zhu , Shunchuan Yang

Electromagnetic fields in bulk bianisotropic media can be represented using plane waves whose k-vectors can be found using the index of refraction operator method and belong to the Fresnel wave surfaces that fall into one of the 5…

Optics · Physics 2023-02-21 Maxim Durach

It is proved that a convex polyhedral scatterer of impedance type can be uniquely determined by the electric far-field pattern of a non-vanishing incident field. The incoming wave is allowed to bean electromagnetic plane wave, a vector…

Analysis of PDEs · Mathematics 2021-01-22 Guang-Hui Hu , Manmohan Vashisth , Jiaqing Yang

A coupled boundary spectral element method (BSEM) and spectral element method (SEM) formulation for the propagation of small-amplitude water waves over variable bathymetries is presented in this work. The wave model is based on the…

Numerical Analysis · Mathematics 2025-02-04 Antonio Cerrato , Luis Rodríguez-Tembleque , José A. González , M. H. Ferri Aliabadi

The extended boundary condition method can be used to study planewave scattering by an ellipsoid composed of an orthorhombic dielectric-magnetic material whose relative permittivity dyadic is a scalar multiple of its relative permeability…

We apply a new calculation scheme of a finite element method (FEM) for solving an elliptic boundary-value problem describing a quadrupole vibration collective nuclear model with tetrahedral symmetry. We use of shape functions constructed…

This paper is concerned with the analysis of time-harmonic electromagnetic scattering from plasmonic inclusions in the finite frequency regime beyond the quasi-static approximation. The electric permittivity and magnetic permeability in the…

Analysis of PDEs · Mathematics 2019-01-29 Hongjie Li , Shanqiang Li , Hongyu Liu , Xianchao Wang

The T-matrix method is widely used for the calculation of scattering by particles of sizes on the order of the illuminating wavelength. Although the extended boundary condition method (EBCM) is the most commonly used technique for…

Optics · Physics 2007-05-23 T. A. Nieminen , H. Rubinsztein-Dunlop , N. R. Heckenberg

A new proof is given of the existence of the solution to electromagnetic (EM) wave scattering problem for an impedance body of an arbitrary shape. The proof is based on the elliptic systems theory and elliptic estimates for the solutions of…

Mathematical Physics · Physics 2015-03-03 Alexander G. Ramm , Martin Schechter

We extend the Finite-Difference Time-Domain method to treat dispersive magnetic media by incorporating magneto-optical effects through a frequency-dependent permittivity tensor. For benchmarking our method, we consider the light scattering…

In the frame of volume integral equation methods, we introduce an alternative representation of the electromagnetic field scattered by a homogeneous object of arbitrary shape at a given frequency, in terms of a set of modes independent of…

Calculations of the photonic band structure, transmission coefficients, and quality factors of various two-dimensional, periodic and aperiodic, dielectric photonic crystals by using the finite element method (FEM) are reported. The…

Mesoscale and Nanoscale Physics · Physics 2015-06-11 Imanol Andonegui , Angel J. Garcia-Adeva

In this paper, we introduce an alternative representation of the electromagnetic field scattered from a homogeneous sphere coated with a homogeneous layer of uniform thickness. Specifically, we expand the scattered field using a set of…

Optics · Physics 2017-08-02 Mariano Pascale , Giovanni Miano , Carlo Forestiere

The geometric representation at a fixed frequency of the wavevector (or dispersion) surface $\omega(\vec k)$ for lossless, homogeneous dielectric--magnetic uniaxial materials is explored, when the elements of the relative permittivity and…

The scattering of electromagnetic wave by a periodic array of nanowires is calculated by the boundary element method. The method is extended to the infinite grating near the interface between two dielectrics. A special Green function is…

Meromorphic continuation of the scattering operator leads to scattering poles (resonances) in the complex plane. Despite their significance, numerical investigation of scattering poles remains limited. In this paper, we propose and analyze…

Numerical Analysis · Mathematics 2026-03-17 Bo Gong , Takumi Sato , Jiguang Sun , Xinming Wu

Many integral equation-based methods are available for problems of time-harmonic electromagnetic scattering from perfect electric conductors. Among the many challenges that arise in such calculations are the avoidance of spurious…

Numerical Analysis · Mathematics 2025-07-17 Felipe Vico , Leslie Greengard , Michael O'Neil , Manas Rachh