We survey finite element methods for approximating the time harmonic Maxwell equations.We concentrate on comparing error estimates problems with spatially varying coefficients.For conforming edge methods, such allow, at least, piecewise smooth coefficients.But Discontinuous Galerkin (DG) state of art analysis is less advanced (we consider three DG families methods: Interior Penalty type, Hybridizable DG, and Trefftz type methods).Nevertheless, offer significant potential advantages compared...

In 1994 Bérenger showed how to construct a perfectly matched absorbing layer for the Maxwell system in rectilinear coordinates. This absorbs waves of any wavelength and frequency without reflection thus can be used artificially terminate domain scattering calculations. this paper we show derive implement curvilinear coordinates (in two space dimensions). We prove that an infinite type solve time harmonic problems. also truncated problem has solution except at discrete set exceptional...

We survey some of the highlights inverse scattering theory as it has developed over last 15 years, with emphasis on uniqueness theorems and reconstruction algorithms for time harmonic acoustic waves. Included in our presentation are numerical experiments using real data examples use methods to detect buried objects.

Journal Article THE INVERSE SCATTERING PROBLEM FOR TIME-HARMONIC ACOUSTIC WAVES IN AN INHOMOGENEOUS MEDIUM Get access DAVID COLTON, COLTON Department of Mathematical Sciences, University DelawareNewark, Delaware 19716, USA Search for other works by this author on: Oxford Academic Google Scholar PETER MONK The Quarterly Mechanics and Applied Mathematics, Volume 41, Issue 1, February 1988, Pages 97–125, https://doi.org/10.1093/qjmam/41.1.97 Published: 01 1988 history Received: 19 January 1987

In a previous paper [SIAM J. Appl. Math. (1985), pp. 1039–1053] we presented new method for determining the shape of an acoustically soft obstacle from knowledge time-harmonic incident wave and far field pattern scattered wave. The given there was based on knowing interval values square number k such that this contained first eigenvalue $\lambda _1 $ interior Dirichlet problem. purpose is to extend methods our earlier treat case when only known single value $k^2 not equal $. addition show...

The interior transmission problem is a boundary value that arises in the scattering of time-harmonic waves by an inhomogeneous medium compact support. associated eigenvalue has important applications qualitative methods inverse theory. In this paper, we first establish optimal conditions for existence eigenvalues spherically stratified and give numerical examples both real complex case. We then propose three finite element computation cases general non-stratified use these to investigate...

The inverse electromagnetic scattering problem for anisotropic media plays a special role in theory due to the fact that (matrix) index of refraction is not uniquely determined from far field pattern scattered even if multi-frequency data are available. In this paper, we describe how transmission eigenvalues can be and used obtain upper lower bounds on norm refraction. Numerical examples will given case when object an infinite cylinder inhomogeneous medium orthotropic.

The use of finite elements to discretize the time dependent Maxwell equations on a bounded domain in three-dimensional space is analyzed. Energy norm error estimates are provided when general element methods used space. In addition, it shown that if some curl conforming due Nédélec used, may also be proved $L^2 $ norm.

The Yee scheme is the principal finite difference method used in computing time domain solutions of Maxwell's equations. On a uniform grid easily seen to be second-order convergent space. This paper shows that also on nonuniform mesh despite fact local truncation error (nodally) only first order.

In this paper we shall analyze a new variational method for approximating the heat equation using continuous finite elements in space and time. special case of linear time reduces to Crank-Nicolson Galerkin with time-averaged data. Using higher-order time, obtain class stepping methods related collocating standard spatial differential equations at Gauss-Legendre points. Again data enters via suitable averages. We present error estimates results some numerical experiments.

In this paper we study, via variational methods, the problem of scattering time harmonic acoustic waves by an unbounded sound soft surface. The boundary $partial D$ is assumed to lie within a finite distance flat plane and incident wave that arising from inhomogeneous term in Helmholtz equation whose support lies some $\partial D$. Via analysis equivalent formulation, provide first proof existence unique solution three-dimensional rough surface for arbitrary number. Our method does not...

In this paper we consider the problem of scattering time-harmonic acoustic waves by a bounded, sound soft obstacle in two and three dimensions, studying dependence on wave number classical formulations problem. The first is standard weak formulation part exterior domain contained large sphere, with an exact Dirichlet-to-Neumann map applied boundary. second as kind boundary integral equation which solution sought combined single- double-layer potential. For variational obtain, case when...

The inverse scattering problem we are considering in this paper is to determine the shape of an obstacle from a knowledge time-harmonic incident field and phase amplitude far pattern scattered wave. A method given which based on determining first eigenfunction unknown which, addition, avoids use integral equations. Numerical examples showing that our proposed both accurate simple use.

A new method for solving the time-domain integral equations of electromagnetic scattering from conductors is introduced. This method, called finite difference delay modeling, appears to be completely stable and accurate when applied arbitrary structures. The temporal discretization used based on differences. Specifically, a mapping Laplace domain z-transform domain, first- second-order unconditionally methods are derived. Spatial convergence achieved using higher-order divergence-conforming...

The transmission eigenvalue problem plays a critical role in the theory of qualitative methods for inhomogeneous media inverse scattering theory. Efficient computational tools eigenvalues are needed to motivate improvements theory, and, more importantly, parts algorithms estimating material properties. In this paper, we propose two finite element compute few lowest Maxwell's which interest applications. Since discrete matrix is large, sparse, particular, non-Hermitian due fact that neither...

We consider a problem in nondestructive testing which small changes the (possibly complex valued) refractive index $n(x)$ of an inhomogeneous medium compact support are to be determined from measured far field data due incident plane waves. The is studied by considering modified operator ${\cal F}$ whose kernel difference pattern scattering object and auxiliary with Stekloff boundary condition imposed on domain $B$, where $B$ either or ball containing its interior. It shown that can used...