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Efficient modeling of dispersive materials via time-domain simulations of the Maxwell equations relies on the technique of auxiliary differential equations. In this approach, a material's frequency-dependent permittivity is represented via…

We derive from first principles an accurate homogenized description of periodic metamaterials made of magnetodielectric inclusions, highlighting and overcoming relevant limitations of standard homogenization methods. We obtain closed-form…

Mesoscale and Nanoscale Physics · Physics 2015-05-20 Andrea Alu

The Maxwell equations for the electromagnetic potential, supplemented by the Lorenz gauge condition, are decoupled and solved exactly in de Sitter space-time studied in static spherical coordinates. There is no source besides the…

General Relativity and Quantum Cosmology · Physics 2009-12-17 Donato Bini , Giampiero Esposito , Roberto Valentino Montaquila

In 1994, Moulinec and Suquet introduced an efficient technique for the numerical resolution of the cell problem arising in homogenization of periodic media. The scheme is based on a fixed-point iterative solution to an integral equation of…

Numerical Analysis · Mathematics 2014-11-21 Jaroslav Vondřejc , Jan Zeman , Ivo Marek

Fast Fourier transform (FFT) based methods have turned out to be an effective computational approach for numerical homogenisation. In particular, Fourier-Galerkin methods are computational methods for partial differential equations that are…

Numerical Analysis · Mathematics 2020-04-22 Jaroslav Vondřejc , Dishi Liu , Martin Ladecký , Hermann G. Matthies

We study the time harmonic Maxwell equations in a meta-material consisting of perfect conductors and void space. The meta-material is assumed to be periodic with period $\eta > 0$; we study the behaviour of solutions $(E^{\eta}, H^{\eta})$…

Analysis of PDEs · Mathematics 2017-03-17 Ben Schweizer , Maik Urban

We dedicate this paper to the topological analysis of subwavelength solutions in Floquet metamaterials. This work should be considered as a basis for further investigation on whether topological properties of the bulk materials are linked…

Analysis of PDEs · Mathematics 2022-09-09 Habib Ammari , Thea Kosche

This work deals with the micromechanical study of periodic thermo-diffusive elastic multi-layered materials, which are of interest for the fabrication of solid oxide fuel cells (SOFCs). The focus is on the dynamic regime, that is…

Applied Physics · Physics 2018-11-26 Andrea Bacigalupo , Maria Laura De Bellis , Giorgio Gnecco

We survey finite element methods for approximating the time harmonic Maxwell equations. We concentrate on comparing error estimates for problems with spatially varying coefficients. For the conforming edge finite element methods, such…

Numerical Analysis · Mathematics 2019-10-23 Peter Monk , Yangwen Zhang

We present a formulation for high-order generalized periodicity conditions in the context of a high-order electromechanical theory including flexoelectricity, strain gradient elasticity and gradient dielectricity, with the goal of studying…

Numerical Analysis · Mathematics 2023-11-15 J. Barceló-Mercader , D. Codony , A. Mocci , I. Arias

Maxwell's equations are considered with transparent boundary conditions, for initial conditions and inhomogeneity having support in a bounded, not necessarily convex three-dimensional domain or in a collection of such domains. The numerical…

Numerical Analysis · Mathematics 2020-10-21 Balázs Kovács , Christian Lubich

Using a powerful homogenization technique, one- and two-dimensional graphene metasurfaces are homogenized both at the fundamental frequency (FF) and second harmonic (SH). In both cases, there is excellent agreement between the predictions…

Optics · Physics 2019-05-17 Qun Ren , J. W. You , N. C. Panoiu

This paper extends approach of our joint paper with K\"{a}hler and recent paper of the author, published in 2021, on problems of the static Maxwell system in three dimensional inhomogeneous media. Applied pseudoanalytic function theory…

Analysis of PDEs · Mathematics 2021-08-10 Dmitry Bryukhov

We consider the time-harmonic Maxwell equations with impedance boundary conditions on a bounded Lipschitz domain $\Omega$ with analytic boundary $\Gamma$. We suppose that $\Omega$ consists of multiple subdomains, and that the permeability…

Numerical Analysis · Mathematics 2026-03-19 Jens Markus Melenk , David Wörgötter

We present a general framework for the homogenisation theory of space-time metamaterials. By mapping to a frame co-moving with the space-time modulation, we derive analytical formulae for the effective material parameters for travelling…

Mesoscale and Nanoscale Physics · Physics 2021-07-28 Paloma Arroyo Huidobro , Mario G. Silveirinha , Emanuele Galiffi , J. B. Pendry

Single- and multi-valued solutions of homogeneous Maxwell equations in vacuum are considered, with ''sources'' formed by the (point- or string-like) singularities of the field strengths and, generally, irreducible to any delta-functions'…

Classical Physics · Physics 2007-05-23 Vladimir V. Kassandrov

We discuss the radiation problem of total reflection for a time-harmonic generalized Maxwell system in a non-smooth exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards…

Analysis of PDEs · Mathematics 2011-05-23 Dirk Pauly

This paper develops an efficient Monte Carlo interior penalty discontinuous Galerkin method for electromagnetic wave propagation in random media. This method is based on a multi-modes expansion of the solution to the time-harmonic random…

Numerical Analysis · Mathematics 2018-06-15 Xiaobing Feng , Junshan Lin , Cody Lorton

We present a computational framework for two-scale asymptotic homogenization to determine the intrinsic magnetic permeability of composites. To this end, considering linear magnetostatics, both vector and scalar potential formulations are…

Materials Science · Physics 2023-01-05 Celal Soyarslan , Jos Havinga , Leon Abelmann , Ton van den Boogaard

In this paper, we propose fast solvers for Maxwell's equations in rectangular domains. We first discretize the simplified Maxwell's eigenvalue problems by employing the lowest-order rectangular N\'ed\'elec elements and derive the discrete…

Numerical Analysis · Mathematics 2025-03-14 Lixiu Wang , Lueling Jia , Zijian Cao , Huiyuan Li , Zhimin Zhang