Numerical Methods for Homogenization of Maxwell’s Equations
نویسنده
چکیده
When the wavelength is much larger than the typical scale of the microstructure in a material, it is possible to de£ne effective or homogenized material coef£cients. Two numerical methods for the determination of the homogenized, coef£cients are compared. Numerical examples, where extreme properties of the effective material are achieved in the two dimensional case, are presented.
منابع مشابه
Homogenization of Quasi-static Maxwell's Equations
This paper studies the homogenization of quasi-static and nonlinear Maxwell’s equations in grain-oriented (GO) silicon steel laminations. GO silicon steel laminations have multiple scales and the ratio of the largest scale to the smallest scale can be up to 106. Direct solution of three-dimensional nonlinear Maxwell’s equations is very challenging and unrealistic for large electromagnetic devic...
متن کاملNumerical Homogenization for Indefinite H(curl)-problems
In this paper, we present a numerical homogenization scheme for indefinite, timeharmonic Maxwell’s equations involving potentially rough (rapidly oscillating) coefficients. The method involves an H(curl)-stable, quasi-local operator, which allows for a correction of coarse finite element functions such that order optimal (w.r.t. the mesh size) error estimates are obtained. To that end, we exten...
متن کاملHomogenization of random elliptic systems with an application to Maxwell ’ s equations ∗
We study the homogenization of elliptic systems of equations in divergence form where the coefficients are compositions of periodic functions with a random diffeomorphism with stationary gradient. This is done in the spirit of scalar stochastic homogenization by Blanc, Le Bris and P.-L. Lions. An application of the abstract result is given for Maxwell’s equations in random dissipative bianisotr...
متن کاملOptimized Schwarz Methods for Maxwell’s Equations with Non-zero Electric Conductivity
The study of optimized Schwarz methods for Maxwell’s equations started with the Helmholtz equation, see [2, 3, 4, 11]. For the rot-rot formulation of Maxwell’s equations, optimized Schwarz methods were developed in [1], and for the more general form in [9, 10]. An entire hierarchy of families of optimized Schwarz methods was analyzed in [8], see also [5] for discontinuous Galerkin discretizatio...
متن کاملFinite-Difference Time-Domain Simulation of Light Propagation in 2D Periodic and Quasi-Periodic Photonic Structures
Ultra-short pulse is a promising technology for achieving ultra-high data rate transmission which is required to follow the increased demand of data transport over an optical communication system. Therefore, the propagation of such type of pulses and the effects that it may suffer during its transmission through an optical waveguide has received a great deal of attention in the recent years. We...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004