on the p and hp extension of nedelec s curl conforming elements abstract we establish interpolation error estimates for the hp extension of nedelec s curl and divergence conforming three dimensional finite elements using these interpolation estimates we investigate the use of higher order edge finite elements for the linear three dimensional magnetostatic problem our estimates show that the standard mixed method for the magnetostatic problem can be approximated to optimal order in both h and p

investigation of nonplanar perfectly matched absorbers for finite element mesh truncation we present a detailed theoretical and numerical investigation of the perfectly matched layer pml concept as applied to the problem of mesh truncation in the finite element method fem we show that it is possible to extend the cartesian pml concepts involving half spaces to cylindrical and spherical geometries appropriate for closed boundaries in two and three dimensions by defining lossy anisotropic layers in the relevant coordinate systems by using the method of separation of variables it is possible to solve the boundary value problems in these geometries the analytical solutions demonstrate that under certain conditions outgoing waves are absorbed with negligible reflection and the transmitted wave is attenuated within the pml to reduce the white space in radiation or scattering problems conformal pmls are constructed via parametric mappings it is also verified that the pml concept which was originally introduced for problems governed by maxwell s equations can be extended to cases governed by the scalar helmholtz equation finally numerical results are presented to demonstrate the use of the pml in fem mesh truncation

two equivalent sets application to singular systems abstract in this paper we consider the problem of state feedback control design for continuous singular systems by applying equivalent sets technique a new formulation of dissipativity condition is proposed based on this condition the desired state feedback controller is designed such that the closed loop system is admissible and dissipative for singular markovian systems necessary and sufficient conditions are proposed for the system to be admissible and for the state feedback control design for time delay singular markovian systems a new bounded real lemma is proposed and the corresponding h control problem is studied numerical examples are given to illustrate the effectiveness of the theoretic results developed

on necessary and sufficient conditions for h _ infty output feedback control of markov jump linear systems this note addresses the output feedback hinfin control problem for continuous time markov jump linear systems it is shown that the feasibility of a certain set of linear matrix inequalities is both sufficient and necessary for the existence of a solution under standard assumptions we also give a riccati type sufficient and necessary condition for an hinfin suboptimal controller to exist

analysis of a finite element method for maxwell s equations 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 finite element methods are used to discretize the equations in space in addition it is shown that if some curl conforming elements due to nedelec are used error estimates may also be proved in the l 2 norm

h control for singular markovian jump systems with incomplete knowledge of transition probabilities this paper proposes a h state feedback control for singular markovian jump systems with incomplete knowledge of transition probabilities different from the previous results where the transition rates are completely known or the bounds of the unknown transition rates are given a more general situation where the transition rates are partly unknown and the bounds of the unknown transition rates are also unknown is considered moreover in contrast to the singular markovian jump systems studied recently the proposed method does not require any tuning parameters that arise when handling non convex terms related to the mode dependent lyapunov matrices and the corresponding self mode transition rates also this paper uses all possible slack variables related to the transition rates into the relaxation process which contributes to reduce the conservatism finally two numerical examples are provided to demonstrate the performance of h mode dependent control

an analysis of ne de lec s method for the spatial discretization of maxwell s equations abstract in 1980 nedelec developed a family of curl and divergence conforming finite elements in r 3 he proposed the use of these elements to discretize the time dependent maxwell equations noting that the elements have the advantage that the discrete magnetic displacement can be made exactly divergence free in this paper we shall analyze a slight generalization of nedelec s scheme and prove essentially optimal order convergence estimates in a variety of situations we also demonstrate that the nedelec method can be superconvergent at certain special points and we relate the method to yee s finite difference scheme a by product of our analysis will be a convergence proof for yee s method

parallel processing for the simulation of problems involving scattering of electromagnetic waves abstract the three dimensional simulation of the scattering of electromagnetic waves by obstacles of arbitrary geometrical shape is considered maxwell s curl equations are solved in the time domain on an unstructured mesh of linear tetrahedral elements the discrete equations are formed by a galerkin procedure with a lax wendroff consistent numerical flux function and explicit time stepping parallelisation of the procedure is achieved by mesh decomposition and the use of a single program multiple data model the approach is first validated and is then applied to problems involving the scattering of plane electromagnetic waves by a complete aircraft

elements finis mixtes incompressibles pour l equation de stokes dans ℝ3 we introduce some new families of finite element approximation for the stationary stokes and navier stokes equations in a bounded domain in 3 these elements can used tetahedrons or cubes the approximation satisfie exactly the incompressibility condition

a algorithm for convex minimization for convex minimization we introduce an algorithm based on space decomposition the method uses a bundle subroutine to generate a sequence of approximate proximal points when a primal dual track leading to a solution and zero subgradient pair exists these points approximate the primal track points and give the algorithm s or corrector steps the subroutine also approximates dual track points that are gradients needed for the method s newton predictor steps with the inclusion of a simple line search the resulting algorithm is proved to be globally convergent the convergence is superlinear if the primal dual track points and the objective s hessian are approximated well enough

necessary and sufficient conditions for analysis and synthesis of markov jump linear systems with incomplete transition descriptions this technical note is concerned with exploring a new approach for the analysis and synthesis for markov jump linear systems with incomplete transition descriptions in the study not all the elements of the transition rate matrices trms in continuous time domain or transition probability matrices tpms in discrete time domain are assumed to be known by fully considering the properties of the trms and tpms and the convexity of the uncertain domains necessary and sufficient criteria of stability and stabilization are obtained in both continuous and discrete time numerical examples are used to illustrate the results

modeling of electromagnetic absorption scattering problems using hp adaptive finite elements a model problem for the steady state form of maxwell s equations is considered the problem is formulated in a weak form using a lagrange multiplier laying down a foundation for a general class of novel hp adaptive fe approximations a convergence proof for affine elements is presented the proposed method is illustrated and verified with a series of 2d experiments including elements with curved boundaries and nonhomogeneous media

a time domain unstructured grid approach to the simulation of electromagnetic scattering in piecewise homogeneous media abstract the simulation of the scattering of plane electromagnetic waves by obstacles constructed from piecewise homogeneous material media is considered the governing equations are maxwell s equations which are expressed in a conservation form the solution is obtained on a grid consisting of an unstructured assembly of linear triangular elements in 2d by modifying a technique developed originally for the solution of the compressible euler equations the computed solution is used to determine the radar scattering width of the obstacle

primal dual gradient structured functions second order results links to epi derivatives and partly smooth functions we give second order expansions for quite general nonsmooth functions from the cal v cal u space decomposition point of view the results depend on primal dual gradient structure which we relate to general concepts of second order epi derivatives and partly smooth functions expressions for the associated second order objects are given in terms of cal u subspace hessians

eigenvalue approximation by a mixed method for resonant inhomogeneous cavities with metallic boundaries for an inhomogeneous cavity bounded by a perfect conductor we prove that the approximation of the eigenvalues for the maxwell problem leads to a second order rate of convergence when using mixed finite elements if the cavity has a disconnected boundary the problem has null eigenvalues we verify the existence of null eigenvalues for the approximate problem they do not mix with the others that still converge at the same rate

a stitching method for the generation of unstructured meshes for use with co volume solution techniques abstract the successful implementation of co volume time domain solution techniques requires the use of high quality smooth dual meshes the generation of delaunay voronoi diagrams with these properties for two dimensional domains of complicated geometrical shape is considered in the adopted approach near boundary regions are discretised according to prescribed criteria and the remainder of the computational domain is discretised using an ideal mesh the two meshes are stitched together to provide a consistent mesh for the complete domain after smoothing the resulting mesh is found to be of a quality which exceeds that of meshes produced by standard automatic unstructured mesh generation methods examples involving electromagnetic wave scattering are included to demonstrate the computational performance that can be achieved with a co volume time domain solution algorithm on these meshes

hp finite element discretisation of the electrical impedance tomography problem abstract this paper is concerned with the accurate recovery of the permittivity and conductivity from the solution of the electrical impedance tomography eit inverse problem given the knowledge of either the neumann to dirichlet or the dirichlet to neumann map the linearised eit inverse problem for the fourier regime is discretised by hp finite elements which allows the accurate calculation of the sensitivity matrix entries the variational algorithm of knowles 1998 31 is extended to allow the recovery of both material parameters by solution of the eit problem in the laplace regime the associated forward problem is again discretised by hp finite elements a series of numerical results are included to demonstrate the effectiveness of the proposed techniques

stabilization of singular markovian jump systems with generally uncertain transition rates this note is devoted to investigating the stability and stabilization problems for continuous time singular markovian jump systems smjss with generally uncertain transition rates gutrs in this gutr singular model each transition rate can be completely unknown or only its estimate value is known in terms of a set of coupled linear matrix inequalities lmis a sufficient condition is established to ensure the systems to be regular impulse free and stochastically stable moreover the corresponding sufficient condition on the existence of a mode dependent state feedback controller is derived to guarantee the closed loop systems stochastically admissible by applying the lmi technique finally a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method

h filtering for singular markovian jump systems with partly unknown transition rates abstract this paper suggests h filtering for singular markovian jump systems smjss with partly unknown transition rates while the existing researches in the literature have derived only the sufficient conditions this paper successfully demonstrates the necessary and sufficient condition for the existence of h filtering for smjss with partly unknown transition rates first a new bounded real lemma for smjs is derived in terms next the matrix inequalities which come from the bounded real lemma for the filtering error system with partly unknown transition rates are reformulated into the strict lmis two numerical examples are presented to show the effectiveness of the proposed result

hierarchic hp edge element families for maxwell s equations on hybrid quadrilateral triangular meshes we construct and study a set of hierarchic basis functions for the galerkin discretisation of the space h curl 169 suitable for hybrid meshes containing both quadrilateral and triangular elements with arbitrary non uniform order polynomial approximation we investigate the conditioning and dispersive behaviour of the elements in addition numerical examples are shown which demonstrate the accuracy of the space for computing solutions of the time harmonic maxwell s equations that have singularities

a two dimensional infinite element for maxwell s equations abstract the paper describes an implementation of the infinite element for two dimensional steady state maxwell s equations proposed by l demkowicz and m pal comput meth appl mech engrg in press the element is compatible with the hp fe element discretizations for maxwell s equations in bounded domains reported in l demkowicz and l vardapetyan comput meth appl mech engrg 152 1 2 1996 103 124 and w rachowicz and l demkowicz comput meth appl mech engrg in press

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

new developments in state estimation for nonlinear systems based on an interpolation formula accurate state estimators for nonlinear systems can be derived the estimators do not require derivative information which makes them simple to implement

brief paper stability and stabilization of continuous time singular hybrid systems in this paper the problems of stability and state feedback stabilization for a class of continuous time singular hybrid systems are investigated a new sufficient and necessary condition for a continuous time singular hybrid system to be regular impulse free and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities lmis moreover a new sufficient and necessary condition is presented for the existence of the state feedback controller in terms of a set of coupled strict matrix inequalities finally a numerical example is given to illustrate the effectiveness of the obtained theoretical results

dynamic output feedback control for singular markovian jump system lmi approach for the dynamic output feedback stabilization of continuous time singular markovian jump systems this paper introduces the necessary and sufficient condition whereas the previous research works suggested the sufficient conditions a special choice of the block entries of lyapunov matrices leads to derive the necessary and sufficient condition in terms of linear matrix inequalities a numerical example shows the validity of the derived results

on mathcalvu theory for functions with primal dual gradient structure we consider a general class of convex functions having what we call primal dual gradient structure it includes finitely determined max functions and maximum eigenvalue functions as well as other infinitely defined max functions for a function in this class we discuss a space decomposition that allows us to identify a subspace on which the function appears to be smooth moreover using the special structure of such a function we compute smooth trajectories along which certain second order expansions can be obtained we also give an explicit expression for the hessian of a related lagrangian

a superlinear space decomposition algorithm for constrained nonsmooth convex program a class of constrained nonsmooth convex optimization problems that is piecewise c 2 convex objectives with smooth convex inequality constraints are transformed into unconstrained nonsmooth convex programs with the help of exact penalty function the objective functions of these unconstrained programs are particular cases of functions with primal dual gradient structure which has connection with vu space decomposition then a vu space decomposition method for solving this unconstrained program is presented this method is proved to converge with local superlinear rate under certain assumptions an illustrative example is given to show how this method works

arbitrary order edge elements for electromagnetic scattering simulations using hybrid meshes and a pml the use of arbitrary order edge elements for the simulation of two dimensional electromagnetic scattering problems on hybrid meshes of triangles and quadrilaterals is described single frequency incident waves generated by a source in the far field are considered and the solution is determined in the frequency domain for numerical simulation the solution domain is truncated at a finite distance from the perfectly conducting scatterer and the non reflecting boundary condition at the truncated boundary is imposed by the use of a perfectly matched layer pml several examples are included to demonstrate the performance of the proposed procedure copyright 2002 john wiley sons ltd

nurbs enhanced finite element method nefem the development of nurbs enhanced finite element method nefem is revisited this technique allows a seamless integration of the cad boundary representation of the domain and the finite element method fem the importance of the geometrical model in finite element simulations is addressed and the benefits and potential of nefem are discussed and compared with respect to other curved finite element techniques

frequency and time domain electromagnetic scattering simulations employing higher order edge elements finite elements are often used for electromagnetic scattering simulations where the main goal is the accurate predicting of the radar cross section or scattering width output edge element discretizations are popular as they are known to eliminate the problems of spurious modes and allow the easy implementation of boundary conditions and material interfaces this work employs a technique which uses higher order edge elements for scattering problems set in both the frequency and time domains in three and two dimensions respectively such approximations are attractive as they are known to give a higher level of accuracy for a given number of degrees of freedom when compared to lower order approximations appropriate solution techniques are proposed for the system of linear equations which arises in each case numerical examples demonstrate the effectiveness of the proposed procedures

mapped spheroidal wave envelope elements for unbounded wave problems this paper describes a family of axisymmetric spheroidal wave envelope elements for modelling exterior wave problems they are of variable radial order and can be used to represent steady and transient wave fields the formulation is presented for the axisymmetric case using elements which are based on oblate and prolate spheroidal geometries these offer the prospect of reduced dimensionality in comparison to conventional spherically formulated elements when used to represent wave fields in the vicinity of slender or flat objects conjugated weighting functions are used to give frequency independent acoustic mass stiffness and damping matrices this facilitates a simple extension of the method to transient problems the effectiveness and accuracy of the method is demonstrated by a comparison of computed and analytic solutions for sound fields generated by a rigid sphere in steady harmonic oscillation by a rigid sphere excited from rest and by a circular plate vibrating in a plane baffle

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner