analysis of multilevel methods for eddy current problems in papers by arnold falk and winther and by hiptmair novel multigrid methods for discrete h curl elliptic boundary value problems have been proposed such problems frequently occur in computational electromagnetism particularly in the context of eddy current simulation this paper focuses on the analysis of those nodal multilevel decompositions of the spaces of edge finite elements that form the foundation of the multigrid methods it provides a significant extension of the existing theory to the case of locally vanishing coefficients and nonconvex domains in particular asymptotically uniform convergence of the multigrid method with respect to the number of refinement levels can be established under assumptions that are satisfied in realistic settings for eddy current problems the principal idea is to use approximate helmholtz decompositions of the function space h curl into an h1 regular subspace and gradients the main results of standard multilevel theory for h1 elliptic problems can then be applied to both subspaces this yields preliminary decompositions still outside the edge element spaces judicious alterations can cure this

edge elements on anisotropic meshes and approximation of the maxwell equations this paper deals with some edge element methods on a class of anisotropic meshes based on tetrahedra and prismatic pentahedral elements anisotropic local interpolation error estimates are derived for all these types of elements and for functions from classical and weighted sobolev spaces as a particular application the numerical approximation of the maxwell equations in domains with edges is investigated using nedelec s edge elements where anisotropic finite element meshes are appropriate some anisotropic regularity results of the solutions of maxwell equations on such domains are proved some numerical tests are described and inverse estimates are established both showing that our theoretical orders of convergence are optimal

c 0 elements for generalized indefinite maxwell equations in this paper we develop the c 0 finite element method for a generalized curlcurl grad div indefinite maxwell problem in a lipschitz domain such as nonconvex polygon for which the solution of the problem may be nonsmooth and only have the h r regularity for some r 1 the ingredients of our method are that two mass lumping l 2 projectors are applied to curl and div operators in the problem and that c 0 linear element or isoparametric bilinear element enriched with one element bubble on every triangle element or with two element bubbles on every quadrilateral element respectively is employed for each component of the nonsmooth solution due to the fact that the element bubbles can be statically eliminated at element levels our method is essentially three nodes or four nodes c 0 lagrange element method with two fortin type interpolations established a very technical duality argument is elaborated to estimate the error for the indefinite problem for the nonsmooth solution having the h r regularity where r may vary in the interval 0 1 we obtain the error bound mathcal o h r in an energy norm some numerical experiments are performed to confirm the theoretical error bounds

arma models their kronecker indices and their mcmillan degree this paper highlights some difficulties with the use of arma models with leading unit coefficient matrix in system identification it is shown that the mcmillan degree of such models is not in any easy way related to the row degrees of the polynomial factors of the arma model a rank test is given for the mcmillan degree of such models and it is shown that this degree will generically be a multiple of the dimension of the observation vector

hybrid electric magnetic methods in eddy current problems we discuss a method of approximation of eddy current equations in bounded space that relies on the use of the electric field as primary variable in the conductive parts and of the magnetic field in the air theoretical issues about this hybrid approach are addressed is the problem well posed and one shows that edge elements offer a straightforward way to discretize such formulations the now popular a v method is then shown to come as a variant of this formulation in such a way that it allows the use of standard nodal elements however attention is called on the fact that the numerical convergence of the latter method may be in question

arma canonical forms obtained from constructibility invariants in recent approaches multivariable arma models have been derived from observable canonical mfds but it was realized that these models have a number of serious limitations and disadvantages this paper presents a new approach based on the idea of observing the state from past outputs which leads to the construction of monic arma models defined by the constructibility invariants the derivation and structural properties of these constructibility forms are investigated

a least squares finite element method for the magnetostatic problem in a multiply connected lipschitz domain a new least squares finite element method is developed for the curl div magnetostatic problem in lipschitz and multiply connected domains filled with anisotropic nonhomogeneous materials in order to deal with possibly low regularity of the solution local l 2 projectors are introduced to standard least squares formulation and applied to both curl and div operators coercivity is established by adding suitable mesh dependent bilinear terms as a result any continuous finite elements lower order elements are enriched with suitable bubbles can be employed a desirable error bound is obtained bf u bf u h 0 le c bf u tilde bf u 0 where bf u h and tilde bf u are the finite element approximation and the finite element interpolant of the exact solution bf u respectively numerical tests confirm the theoretical results

a high order accurate parallel solver for maxwell s equations on overlapping grids a scheme for the solution of the time dependent maxwell s equations on composite overlapping grids is described the method uses high order accurate approximations in space and time for maxwell s equations written as a second order vector wave equation high order accurate symmetric difference approximations to the generalized laplace operator are constructed for curvilinear component grids the modified equation approach is used to develop high order accurate approximations that use only three time levels and have the same time stepping restriction as the second order scheme discrete boundary conditions for perfect electrical conductors and for material interfaces are developed and analyzed the implementation is optimized for component grids that are cartesian resulting in a fast and efficient method the solver runs on parallel machines with each component grid distributed across one or more processors numerical results in two and three dimensions are presented for the fourth order accurate version of the method these results demonstrate the accuracy and efficiency of the approach

an adaptive finite element method for the h ψ formulation of time dependent eddy current problems in this paper we develop an adaptive finite element method based on reliable and efficient a posteriori error estimates for the h formulation of eddy current problems with multiply connected conductors multiply connected domains are considered by making cuts the competitive performance of the method is demonstrated by an engineering benchmark problem team workshop problem 7 and a singular problem with analytic solution

a fast algorithm for errors in variables filtering this note concerns the optimal estimation of the input and output sequences of linear time invariant errors in variables eiv processes an efficient recursive filtering algorithm is proposed it is an innovation based approach that relies on the triangular decomposition of block toeplitz matrices unlike the other algorithms described in the literature the proposed one is characterized by a computational complexity which increases only linearly with the order of the process both the siso and mimo cases are analyzed an extension of the described algorithm to eiv models with colored input and output noises is considered as well

brief minimal representations of mimo time varying systems and realization of cyclostationary models this paper describes a family of minimally parameterized state space models for completely n step observable multi input multi output time varying systems and their algebraical links with equivalent input output models these results are then used to develop an algorithm for the realization of generic input output sequences generated by a periodic system a complete numerical example is also developed to illustrate all steps of the algorithm described in the paper

strong consistency of ml estimators using partial fraction and elementary subsystem representation of multivariable systems the strong consistency of ml estimators for partial fraction matrix pfm and elementary subsystem ess representations of vector arma processes will be discussed for the case when the structure is overestimated the main results of the paper are the off line strong consistency theorems of ml estimators for pfm representation when the number of poles is overestimated and for the ess representations when the number of ess s associated with the poles is overestimated

vector autoregressive moving average identification for macroeconomic modeling a new methodology this paper develops a new methodology for identifying the structure of varma time series models the analysis proceeds by examining the echelon form and presents a fully automatic strongly consistent data driven approach to model specification a novel feature of the inferential procedures developed here is that they work in terms of a canonical representation based on the kronecker invariants in which the variables are expressed in the form of scalar dynamic structural equations derived from the varma system this feature facilitates the construction of procedures which from the perspective of macroeconomic modeling can be efficacious in that they do not rely on var approximations techniques that are applicable to both asymptotically stationary and unit root partially nonstationary cointegrated time series models are presented the inferential potential of the techniques is illustrated via simulation experiments that use data generating mechanisms based on real world examples drawn from the time series literature aspects of the kronecker invariants that impinge on practical application and that have not hitherto been discussed in the literature are explored

a finite element method for a curlcurl graddiv eigenvalue interface problem in this paper we propose and study a finite element method for a curlcurl graddiv eigenvalue interface problem its solution may be of piecewise non h 1 we would like to approximate such a solution in an h 1 conforming finite element space with the discretizations of both curl and div operators of the underlying eigenvalue problem in two finite element spaces the proposed method is essentially a standard h 1 conforming element method up to element bubbles which can be statically eliminated at element levels we first analyze the proposed method for the related source interface problem by establishing the stability and the error bounds we then analyze the underlying eigenvalue interface problem and we obtain the error bounds mathcal o h 2r 0 for eigenvalues which correspond to eigenfunctions in prod j 1 j h r omega j 3 hookrightarrow h r 0 omega 3 space where the piecewise regularity r and the global regularity r 0 may belong to the most interesting interval 0 1

a discontinuous galerkin method on refined meshes for the two dimensional time harmonic maxwell equations in composite materials in this paper a discontinuous galerkin method for the two dimensional time harmonic maxwell equations in composite materials is presented the divergence constraint is taken into account by a regularized variational formulation and the tangential and normal jumps of the discrete solution at the element interfaces are penalized due to an appropriate mesh refinement near exterior and interior corners the singular behaviour of the electromagnetic field is taken into account optimal error estimates in a discrete energy norm and in the l 2 norm are proved in the case where the exact solution is singular

singularities of electromagnetic fields in polyhedral domains in this paper we investigate the singular solutions of time harmonic maxwell equations in a domain which has edges and polyhedral corners it is now well known that in the presence of non convex edges the solution fields have no square integrable gradients in general and that the main singularities are the gradients of singular functions of the laplace operator 4 5 we show how this type of result can be derived from the classical mellin analysis and how this analysis leads to sharper results concerning the singular parts which belong to h 1 for the singular functions we exhibit simple and explicit formulas based on generalized dirichlet and neumann singularities for the laplace operator these formulas are more explicit than the results announced in our note 10

on different finite element methods for approximating the gradient of the solution to the helmholtz equation abstract we consider the numerical solution of the helmholtz equation by different finite element methods in particular we are interested in finding an efficient method for approximating the gradient of the solution we first approximate the gradient by the standard ritz galerkin method as a second method a two stage method due to aziz and werschulz 1980 is presented it is shown that this method gives the same accuracy in the computed gradient and in the computed solution also in the nonconforming case finally a direct method with asymptotic error estimates is given it turns out that the presented direct method is of lowest computational complexity test examples are presented to illustrate the accuracy of the methods

discontinuous least squares finite element method for the div curl problem in this paper we consider the div curl problem posed on nonconvex polyhedral domains we propose a least squares method based on discontinuous elements with normal and tangential continuity across interior faces as well as boundary conditions weakly enforced through a properly designed least squares functional discontinuous elements make it possible to take advantage of regularity of given data divergence and curl of the solution and obtain convergence also on nonconvex domains in general this is not possible in the least squares method with standard continuous elements we show that our method is stable derive a priori error estimates and present numerical examples illustrating the method

interface solutions of partial differential equations with point singularity abstract partial differential equations pdes such as those that describe linear elastic fracture mechanics admit analytic solutions with low regularity at crack tips existing numerical methods for such pdes suffer from the constraint of this low regularity and fail to deliver an optimal high order rate of convergence we approach this problem by i choosing an artificial interface to enclose the center of low regularity and ii representing the solution in the interior of artificial interface as unknown linear combination of known low regularity modes of the solution this results in an interface formulation of the original pde and the linear combination is represented in the interface conditions by enforcing the smooth component of the numerical solution in the interior domain to be approximately zero a least squares problem is obtained for the unknown coefficients the solution of this least squares problem will provide the approximate interface conditions for the numerical solution of the pde in the exterior domain the potential of our interface formulation is favorably demonstrated by numerical experiments on one and two dimensional poisson equations with low regularity solutions high order numerical solutions of unknown coefficients and pdes are obtained this proves the potential of the proposed interface formulation as the theoretical basis for solving linear elastic fracture mechanics problems we address the relations between our interface formulation and domain decomposition methods as well as a regularization strategy for the poisson boltzmann equation with singular charge density

augmented formulations for solving maxwell equations we consider augmented variational formulations for solving the static or time harmonic maxwell equations for that a term is added to the usual h curl conforming formulations it consists of a weighted l2 scalar product between the divergence of the em and the divergence of test fields in this respect the methods we present are h curl div conforming we also build mixed augmented variational formulations with either one or two lagrange multipliers to dualize the equation on the divergence and when applicable the relation on the tangential or normal trace of the field it is proven that one can derive formulations which are equivalent to the original static or time harmonic maxwell equations in the latter case spurious modes are automatically excluded numerical analysis and experiments will be presented in the forthcoming paper augmented formulations for solving maxwell equations numerical analysis and experiments in preparation

mixed discontinuous galerkin approximation of the maxwell operator we introduce and analyze a discontinuous galerkin discretization of the maxwell operator in mixed form here all the unknowns of the underlying system of partial differential equations are approximated by discontinuous finite element spaces of the same order for piecewise constant coefficients the method is shown to be stable and optimally convergent with respect to the mesh size numerical experiments highlighting the performance of the proposed method for problems with both smooth and singular analytical solutions are presented

discrete models for linear multivariable systems the primary purpose of this paper is to codify a number of independent but interrelated results in linear multivariable discrete time systems in particular a relationship between forward shift and backward shift representations is established conditions for causality in either representation are presented as are algorithms for obtaining state space representations of a large class of causal discrete time systems the effect on the transfer matrix of non zero initial conditions is explicitly shown the finite and infinite poles and zeros of square invertible systems are defined and related to the lack of row or column properness of particular representations the role of the interactor and inverse interactor in zero determination is also discussed

a generalised instrumental variable estimator for multivariable errors in variables identification problems a new and very general estimation method the generalised instrumental variable estimator give has been introduced to deal with the errors in variables identification the give contains several well known estimation methods as special cases that can be obtained by various user choices in give these methods include the bias eliminating least squares method a number of different versions of the frisch scheme and the extended compensated least squares method this article shows how previous analysis for single input single output systems can be extended in a non trivial way to also cope with multi input multi output systems various computational aspects of give are presented and it is shown how the parameter estimates can be computed in an efficient way the asymptotic distribution of the parameter estimates is also derived and analysed

analysis of a continuous finite element method for h mathrm curl mathrm div elliptic interface problem in this paper we develop a continuous finite element method for the curlcurl grad div vector second order elliptic problem in a three dimensional polyhedral domain occupied by discontinuous nonhomogeneous anisotropic materials in spite of the fact that the curlcurl grad div interface problem is closely related to the elliptic interface problem of vector laplace operator type the continuous finite element discretization of the standard variational problem of the former generally fails to give a correct solution even in the case of homogeneous media whenever the physical domain has reentrant corners and edges to discretize the curlcurl grad div interface problem by the continuous finite element method we apply an element local l 2 projector to the curl operator and a pseudo local l 2 projector to the div operator where the continuous lagrange linear element enriched by suitable element and face bubbles may be employed it is shown that the finite element problem retains the same coercivity property as the continuous problem an error estimate mathcal o h r in an energy norm is obtained between the analytical solution and the continuous finite element solution where the analytical solution is in prod l 1 l h r omega l 3 for some r in 1 2 1 due to the domain boundary reentrant corners and edges e g nonconvex polyhedron and due to the interfaces between the different material domains in omega bigcup l 1 l omega l

a singular field method for maxwell s equations numerical aspects for 2d magnetostatics the present paper deals with the solution of maxwell type problems by means of nodal h1 conforming finite elements in a nonconvex piecewise regular domain surrounded by a perfect conductor such a discretization cannot in general approximate the singular behavior of the electromagnetic field near reentrant corners or edges the singular field method consists of adding to the finite element discretization space some particular fields which take into account the singular behavior the latter are deduced from the singular functions associated with the scalar laplace operator the theoretical justification of this approach as well as the analysis of the convergence of the approximation are presented for a very simple model problem arising from magnetostatics in a translation invariant setting but the study can be easily extended to numerous maxwell type problems the numerical implementation of both variants is studied for a domain containing a single reentrant corner

an adaptive perfectly matched layer technique for 3 d time harmonic electromagnetic scattering problems an adaptive perfectly matched layer pml technique for solving the time harmonic electromagnetic scattering problems is developed the pml parameters such as the thickness of the layer and the fictitious medium property are determined through sharp a posteriori error estimates combined with the adaptive finite element method the adaptive pml technique provides a complete numerical strategy to solve the scattering problem in the framework of fem which produces automatically a coarse mesh size away from the fixed domain and thus makes the total computational costs insensitive to the thickness of the pml absorbing layer numerical experiments are included to illustrate the competitive behavior of the proposed adaptive method

regular decomposition and a framework of order reduced methods for fourth order problems this paper is devoted to the construction of order reduced method of fourth order problems a constructive framework is presented such that a problem on the high regularity space can be deduced to an equivalent system on three low regularity spaces which are connected by a regular decomposition corresponding to a decomposition of the regularity of the high order space the generated numerical schemes based on the deduced problems can be of lower complicacy and the framework is fit for various fourth order problems three fourth order problems are then discussed under the framework including one in two dimension and two in three dimension they are each corresponding to a regular decomposition and thus are discretised based on the discretised analogues of the regular decomposition optimal error estimates are given

autoregressive models of singular spectral matrices this paper deals with autoregressive ar models of singular spectra whose corresponding transfer function matrices can be expressed in a stable ar matrix fraction description d 1 q b with b a tall constant matrix of full column rank and with the determinantal zeros of d q all stable i e in q 1 q c to obtain a parsimonious ar model a canonical form is derived and a number of advantageous properties are demonstrated first the maximum lag of the canonical ar model is shown to be minimal in the equivalence class of ar models of the same transfer function matrix second the canonical form model is shown to display a nesting property under natural conditions finally an upper bound is provided for the total number of real parameters in the obtained canonical ar model which demonstrates that the total number of real parameters grows linearly with the number of rows in w q

computation of maxwell singular solution by nodal continuous elements abstract in this paper we propose and analyze a nodal continuous and h 1 conforming finite element method for the numerical computation of maxwell s equations with singular solution in a fractional order sobolev space h r where r may take any value in the most interesting interval 0 1 the key feature of the method is that mass lumping linear finite element l 2 projections act on the curl and divergence partial differential operators so that the singular solution can be sought in a setting of l 2 space we shall use the nodal continuous linear finite elements enriched with one element bubble in each element to approximate the singular and non h 1 solution discontinuous and nonhomogeneous media are allowed in the method some error estimates are given and a number of numerical experiments for source problems as well as eigenvalue problems are presented to illustrate the superior performance of the proposed method

a singular field method for the solution of maxwell s equations in polyhedral domains it is well known that in the case of a regular domain the solution of the time harmonic maxwell s equations allows a discretization by means of nodal finite elements this is achieved by solving a regularized problem similar to the vector helmholtz equation the present paper deals with the same problem in the case of a nonconvex polyhedron it is shown that a nodal finite element method does not approximate in general the solution to maxwell s equations but actually the solution to a neighboring variational problem involving a different function space indeed the solution to maxwell s equations presents singularities near the edges and corners of the domain that cannot be approximated by lagrange finite elements a new method is proposed involving the decomposition of the solution field into a regular part that can be treated numerically by nodal finite elements and a singular part that has to be taken into account explicitly this singular field method is presented in various situations such as electri

a delta regularization finite element method for a double curl problem with divergence free constraint to deal with the divergence free constraint in a double curl problem rm curl mu 1 rm curl u f and rm div varepsilon u 0 in omega where mu and varepsilon represent the physical properties of the materials occupying omega we develop a delta regularization method rm curl mu 1 rm curl u delta delta varepsilon u delta f to completely ignore the divergence free constraint rm div varepsilon u 0 we show that u delta converges to u in h rm curl omega norm as delta rightarrow 0 the edge finite element method is then analyzed for solving u delta with the finite element solution u delta h a quasioptimal error bound in the h rm curl omega norm is obtained between u and u delta h including a uniform with respect to delta stability of u delta h in the h rm curl omega norm all the theoretical analysis is done in a general setting where mu and varepsilon may be discontinuous an

on the stability of general cubic quartic functional equations in menger probabilistic normed spaces in this paper the stability of the general cubic quartic functional equation f x ky f x ky k2 f x y f x y 2 1 k2 f x k4 k2 4 f 2y 8f y f 2x 16f x where f x f x f x in the setting of menger probabilistic normed spaces is proved

general results on the mcmillan degree and the kronecker indices of arma and mfd models this paper shows that the mcmillan degree of general arma and mfd models is equal to the pole zero excess of the matrix consisting of the polynomial factors furthermore the left kronecker indices are equal to the row degrees of this matrix if and only if it is row reduced and irreducible for left coprime arma and mfd models the mcmillan degree and the left kronecker indices are related to the determinantal degree and the row degrees of a suitable submatrix of the polynomial factors under certain necessary and sufficient conditions this information can even be inferred from the denominator matrices in the arma and mfd models finally a rank test is presented for actually computing the mcmillan degree of left coprime arma and mfd models

system order and structure indices of linear systems in polynomial form linear time invariant finite dimensional discrete time systems are very often specified in a polynomial form representation in either a forward or backward shift operator sometimes called mfd and arma form in this paper it is shown that there exists a unifying theory for the determination of mcmillan degree and kronecker observability indices of systems represented by polynomial matrices in the two shift operators considering the mfd and arma forms as special cases treating dynamical systems in terms of their behaviour i e the set of admissible signal trajectories the notions of mcmillan degree and observability indices can be generalized to non controllable as well as to non causal systems

optimally conditioned instrumental variable approach for frequency domain system identification accurate frequency domain system identification demands for reliable computational algorithms the aim of this paper is to develop a new algorithm for parametric system identification with favorable convergence properties and optimal numerical conditioning recent results in frequency domain instrumental variable identification are exploited which lead to enhanced convergence properties compared to classical identification algorithms in addition bi orthonormal polynomials with respect to a data dependent bi linear form are introduced for system identification hereby optimal numerical conditioning of the relevant system of equations is achieved this is shown to be particularly important for the class of instrumental variable algorithms for which numerical conditioning is typically quadratic compared to alternative frequency domain identification algorithms superiority of the proposed algorithm is demonstrated by means of both simulation and experimental results

mathematical analysis of conducting and superconducting transmission lines this paper is concerned with a mathematical study of guided propagation in the microstrip transmission lines used in microelectronics in the first part the case of a zero thickness perfectly conducting strip is considered using a regularized formulation of maxwell s equations it is shown that finding guided modes amounts to the spectral analysis of a noncompact family of self adjoint operators the existence of guided modes is then proved thanks to the min max principle in the second part we deal with the case of a zero thickness superconducting strip an asymptotic model derived from london s equation is studied and the existence of guided modes is deduced from the case of the perfectly conducting strip copyright 2000 society for industrial and applied mathematics

structural properties and structure estimation of vector difference equations this paper discusses the structure estimation problem in the identification of vector difference equations vde the structural properties of vdes derived from canonical state space and matrix fraction descriptions of multivariable linear systems are studied based on the rules established for the structure of canonical vde representation a residual error type structure seeking procedure is developed the effectiveness of the proposed method is illustrated by simulation examples

a hinged plate equation and iterated dirichlet laplace operator on domains with concave corners abstract fourth order hinged plate type problems are usually solved via a system of two second order equations for smooth domains such an approach can be justified however when the domain has a concave corner the bi laplace problem with navier boundary conditions may have two different types of solutions namely u 1 with u 1 u 1 h 1 and u 2 h 2 h 1 we will compare these two solutions a striking difference is that in general only the first solution obtained by decoupling into a system preserves positivity that is a positive source implies that the solution is positive the other type of solution is more relevant in the context of the hinged plate we will also address the higher dimensional case our main analytical tools will be the weighted sobolev spaces that originate from kondratiev in two dimensions we will show an alternative that uses conformal transformation next to rigorous proofs the results are illustrated by some numerical experiments for planar domains

a nonconforming finite element method for a two dimensional curl curl and grad div problem a numerical method for a two dimensional curl curl and grad div problem is studied in this paper it is based on a discretization using weakly continuous p 1 vector fields and includes two consistency terms involving the jumps of the vector fields across element boundaries optimal convergence rates up to an arbitrary positive epsilon in both the energy norm and the l 2 norm are established on graded meshes the theoretical results are confirmed by numerical experiments

on the zero dynamics of linear input output models zeros are of extreme importance in linear systems theory especially unstable zeros which degrade achievable performance furthermore the presence of a zero in a state space model implies the exi

properties of the parametrization of monic arma systems abstract some properties of the parametrization of multi input multi output monic arma systems with prescribed column degrees are considered in particular we give a minimal cover for the set of transfer functions corresponding to all arma systems in terms of this parametrization we investigate the relation between the kronecker indices and the prescribed column degrees and we investigate the boundary of a certain parameter space and of the corresponding set of transfer functions

iterative solutions for electromagnetic fields at perfectly reflective and transmissive interfaces using clifford algebra and the multidimensional cauchy integral a technique is presented for calculating the solution of maxwell s equations using a cfie based on the cauchy integral and formulated in the guise of clifford algebra this formulation has a geometric interpretation leading to an iterative method of solution which is easily proven as convergent and correct for both perfectly reflective and perfectly transmissive interfaces simple test cases involving a cubic boundary and plane wave and dipole sources are used to investigate the numerical performance of the method

an adaptive multilevel method for time harmonic maxwell equations with singularities we develop an adaptive edge finite element method based on reliable and efficient residual based a posteriori error estimates for low frequency time harmonic maxwell equations with singularities the resulting discrete problem is solved by the multigrid preconditioned minres minimum residual iteration algorithm we demonstrate the efficiency and robustness of the proposed method by extensive numerical experiments for cavity problems with singular solutions which include in particular scattering over screens

numerical solution to the time dependent maxwell equations in two dimensional singular domains in this paper we present a method to solve numerically the time dependent maxwell equations in nonsmooth and nonconvex domains indeed the solution is not of regularity h1 in space in general moreover the space of h1 regular fields is not dense in the space of solutions thus an h1 conforming finite element method can fail even with mesh refinement the situation is different than in the case of the laplace problem or of the lame system for which mesh refinement or the addition of conforming singular functions work to cope with this difficulty the singular complement method is introduced this method consists of adding some well chosen test functions these functions are derived from the singular solutions of the laplace problem also the scm preserves the interesting features of the original method easiness of implementation low memory requirements small cost in terms of the cpu time to ascertain its validity some concrete problems are solved numerically