convergence and superconvergence of staggered discontinuous galerkin methods for the three dimensional maxwell s equations on cartesian grids in this paper a new type of staggered discontinuous galerkin methods for the three dimensional maxwell s equations is developed and analyzed the spatial discretization is based on staggered cartesian grids so that many good properties are obtained first of all our method has the advantages that the numerical solution preserves the electromagnetic energy and automatically fulfills a discrete version of the gauss law moreover the mass matrices are diagonal thus time marching is explicit and is very efficient our method is high order accurate and the optimal order of convergence is rigorously proved it is also very easy to implement due to its cartesian structure and can be regarded as a generalization of the classical yee s scheme as well as the quadrilateral edge finite elements furthermore a superconvergence result that is the convergence rate is one order higher at interpolation nodes is proved numerical results are shown to confirm our theoretical statements and applications to problems in unbounded domains with the use of pml are presented a comparison of our staggered method and non staggered method is carried out and shows that our method has better accuracy and efficiency

cloaking via change of variables for the helmholtz equation the transformation optics approach to cloaking uses a singular change of coordinates which blows up a point to the region being cloaked this paper examines a natural regularization obtained by 1 blowing up a ball of radius rather than a point and 2 including a well chosen lossy layer at the inner edge of the cloak we assess the performance of the resulting near cloak as the regularization parameter tends to 0 in the context of dirichlet and neumann boundary measurements for the time harmonic helmholtz equation since the goal is to achieve cloaking regardless of the content of the cloaked region we focus on estimates that are uniform with respect to the physical properties of this region in three space dimensions our regularized construction performs relatively well the deviation from perfect cloaking is of order in two space dimensions it does much worse the deviation is of order 1 log in addition to proving these estimates we give numerical examples demonstrating their sharpness some authors have argued that perfect cloaking can be achieved without losses by using the singular change of variable based construction in our regularized setting the analogous statement is false without the lossy layer there are certain resonant inclusions depending in general on that have a huge effect on the boundary measurements 2010 wiley periodicals inc

a priori and posteriori error analysis for time dependent maxwell s equations abstract we consider time dependent maxwell s equations discretized by variable time steps in time domain and edge elements in spatial domain first the stability and optimal a priori error estimate are proved for both semi and fully discrete schemes then a posteriori error analysis is carried out for both schemes

mathematical analysis and finite element time domain simulation of arbitrary star shaped electromagnetic cloaks in this paper we establish the explicit expression for two dimensional 2d electromagnetic cloaks of arbitrary star shapes without explicit contour expressions of the objects furthermore 2d arbi

on approximate electromagnetic cloaking by transformation media we give a comprehensive study on regularized approximate electromagnetic cloaking in the spherical geometry via the transformation optics approach the following aspects are investigated i near invisibility cloaking of passive media as well as active radiating sources ii the existence of cloak busting inclusions without lossy medium lining iii overcoming the cloaking busts by employing a lossy layer outside the cloaked region and iv the frequency dependence of the cloaking performances we address these issues and connect the obtained asymptotic results to singular ideal cloaking numerical verifications and demonstrations are provided to show the sharpness of our analytical study

developing a time domain finite element method for modeling of electromagnetic cylindrical cloaks in this paper we propose a time domain finite element method for modeling of electromagnetic cloaks the permittivity and permeability of the cloak model are described by the drude dispersion model the model to be solved is quite challenging in that we have to solve a coupled problem with different partial differential equations given in different regions our method is based on a mixed finite element method using edge elements with different types of meshes in different regions numerical results demonstrate that our algorithm is quite effective for simulating cloaks in time domain to our knowledge this is the first cloak simulation carried out by the time domain finite element method

approximate cloaking for the helmholtz equation via transformation optics and consequences for perfect cloaking in this paper we study approximate cloaking of active devices for the helmholtz equation in the whole space of dimension 2 or 3 using the scheme introduced by kohn shen vogelius and weinstein more precisely we assess the degree of invisibility determine the limit of the field inside the cloaked and cloaking regions and show that the scheme is unstable with respect to the material parameters as a consequence we obtain some feasible properties of perfect cloaking 2011 wiley periodicals inc

painleve analysis yoshida s theorems and direct methods in the search for integrable hamiltonians treating as an example two dimensional similarity invariant hamiltonians with polynomial velocity dependent potentials the authors show how painleve analysis yoshida s theorems and direct methods can be combined in the search for integrable hamiltonians new integrable systems are found one of which has a polynomial second invariant of fifth order in the momenta most of the necessary calculations have been performed by applying various reduce packages developed for that purpose

an adaptive edge element method with perfectly matched absorbing layers for wave scattering by biperiodic structures an edge element adaptive strategy with error control is developed for wave scattering by biperiodic structures the unbounded computational domain is truncated to a bounded one by a perfectly matched layer pml technique the pml parameters such as the thickness of the layer and the medium properties are determined through sharp a posteriori error estimates numerical experiments are presented to illustrate the competitive behavior of the proposed adaptive method

well posedness study for a time domain spherical cloaking model in this paper we study a time domain spherical cloaking model recently introduced by zhao and hao 2009 this model is quite complicated and is composed of four coupled differential equations here we first prove the existence and uniqueness of a solution for this model then we obtain a stability result which analysis is quite involved due to the coupling between the four variables to our best knowledge this is the first well posedness study carried out for the time domain cloaking model with metamaterials

enhancement of near cloaking part ii the helmholtz equation the aim of this paper is to extend the method of ammari et al commun math phys 2012 to scattering problems we construct very effective near cloaking structures for the scattering problem at a fixed frequency these new structures are before using the transformation optics layered structures and are designed so that their first scattering coefficients vanish inside the cloaking region any target has near zero scattering cross section for a band of frequencies we analytically show that our new construction significantly enhances the cloaking effect for the helmholtz equation

on the construction of monopoles we show that any self dual su 2 monopole may be constructed either by ward s twistor method or nahm s use of the adhm construction the common factor in both approaches is an algebraic curve whose jacobian is used to linearize the non linear ordinary differential equations which arise in nahm s method we derive the non singularity condition for the monopole in terms of this curve and apply the result to prove the regularity of axially symmetric solutions

bootstrapping state space models gaussian maximum likelihood estimation and the kalman filter abstract the bootstrap is proposed as a method for assessing the precision of gaussian maximum likelihood estimates of the parameters of linear state space models our results also apply to autoregressive moving average models since they are a special case of state space models it is shown that for a time invariant stable system the bootstrap applied to the innovations yields asymptotically consistent standard errors to investigate the performance of the bootstrap for finite sample lengths simulation results are presented for a two state model with 50 and 100 observations two cases are investigated one with real characteristic roots and one with complex characteristic roots the bootstrap is then applied to two real data sets one used in a test for efficient capital markets and one used to develop an autoregressive integrated moving average model for quarterly earnings data we find the bootstrap to be of definite value over the conventional asymptotics

first integrals and yoshida analysis of nahm s equations first integrals of nahm s equations for monopole solutions in yang mills theories are explicitly given for various special cases taking into account the scale invariance all kowalewski exponents are determined both the polynomial first integrals and the kowalewski exponents are obtained with the help of a reduce program package this leads to a completely consistent picture in the sense of the analysis recently proposed by yoshida 1983

estimating missing observations in economic time series abstract two related problems are considered the first concerns the maximum likelihood estimation of the parameters in an arima model when some of the observations are missing or subject to temporal aggregation the second concerns the estimation of the missing observations both problems can be solved by setting up the model in state space form and applying the kalman filter

convergence and optimality of adaptive edge finite element methods for time harmonic maxwell equations we consider a standard adaptive edge finite element method aefem based on arbitrary order nedelec edge elements for three dimensional indefinite time harmonic maxwell equations we prove that the aefem gives a contraction for the sum of the energy error and the scaled error estimator between two consecutive adaptive loops provided the initial mesh is fine enough using the geometric decay we show that the aefem yields the best possible decay rate of the error plus oscillation in terms of the number of degrees of freedom the main technical contribution of the paper is in the establishment of a quasi orthogonality and a localized a posteriori error estimator

finite element methods with matching and nonmatching meshes for maxwell equations with discontinuous coefficients we investigate the finite element methods for solving time dependent maxwell equations with discontinuous coefficients in general three dimensional lipschitz polyhedral domains both matching and nonmatching finite element meshes on the interfaces are considered and optimal error estimates for both cases are obtained the analysis of the latter case is based on an abstract framework for nested saddle point problems along with a characterization of the trace space for h curl d a new extension theorem for h curl d functions in any lipschitz domain d and a novel compactness argument for deriving discrete inf sup conditions

a locally divergence free nonconforming finite element method for the time harmonic maxwell equations a new numerical method for computing the divergence free part of the solution of the time harmonic maxwell equations is studied in this paper it is based on a discretization that uses the locally divergence free crouzeix raviart nonconforming p 1 vector fields and includes a consistency term involving the jumps of the vector fields across element boundaries optimal convergence rates up to an arbitrary positive e in both the energy norm and the l 2 norm are established on graded meshes the theoretical results are confirmed by numerical experiments

nahm s equations and the classification of monopoles solutions of nahm s system of ordinary differential equations are produced by variational methods this leads to an explicit parametrisation of the solutions to the bogomolny equation over 3