a stream virtual element formulation of the stokes problem on polygonal meshes in this paper we propose and analyze a novel stream formulation of the virtual element method vem for the solution of the stokes problem the new formulation hinges upon the introduction of a suitable stream function space characterizing the divergence free subspace of discrete velocities and it is equivalent to the velocity pressure inf sup stable mimetic scheme presented in l beirao da veiga et al j comput phys 228 2009 pp 7215 7232 up to a suitable reformulation into the vem framework both schemes are thus stable and linearly convergent but the new method results to be more desirable as it employs much less degrees of freedom and it is based on a positive definite algebraic problem several numerical experiments assess the convergence properties of the new method and show its computational advantages with respect to the mimetic one

gap metrics for time varying linear systems in a continuous time setting a recently proposed time varying generalisation of vinnicombe s v gap is shown to have the properties of a metric on a class of causal linear continuous time systems that admit normalised strong graph representations an alternative time varying gap metric is then defined in more general terms and a corresponding robust stability result is derived for linear feedback interconnections finally it is shown that the time varying gap and v gap metrics induce the same topology this being the coarsest topology under which feedback stability and closed loop sensitivity are both robust properties c 2014 elsevier b v all rights reserved

optimal diagonal scaling for infinity norm optimization abstract a solution is presented for the previously unsolved diagonally scaled multivariable infinity norm optimization problem of minimizing d s a s s x s d 1 s over the set of stable minimum phase diagonal d s and stable x s this problem is of central importance in the synthesis of feedback control laws for robust stability and insensitivity in the presence of structured plant uncertainty the result facilitates the design of feedback controllers which optimize the excess stability margin 3 or equivalently the structured singular value 4 of diagonally perturbed feedback systems

existence of right and left representations of the graph for linear periodically time varying systems the graph representation of a system the set of all input output pairs has gained considerable attention in the control literature in view of its usefulness for the analysis of feedback systems in this paper it is shown that the graph of any stabilizable linear periodically time varying lptv continuous time system can be expressed as the range and kernel of bounded causal lptv systems that are respectively left and right invertible by bounded causal lptv systems these so called strong right and strong left representations are closely related to the perhaps more common notion of coprime factor representations as an example of their usefulness a neat characterization of closed loop stability is obtained in terms of strong right and strong left representations of the plant and controller graphs this in turn leads to a youla style parametrization of stabilizing controllers all of the results obtained accommodate possibly infinite dimensional input and output spaces and apply as a special case to sampled data control systems furthermore they are particularly useful for robustness analysis in terms of the gap metric

why do stabilizing controllers stabilize an alternative notion of a stabilizing controller is presented being defined in terms of the trajectories of plant and controller it is well suited for situations in which the controller s action is an interconnecting one in the second part of the paper a parametrization is given of the kernel representations of all controllers that give rise to an a priori specified closed loop behavior as a special case the parametrization yields all stabilizing controllers unlike the youla parametrization it also includes the so called singular stabilizing controllers

an alternative solution to the h optimal control problems abstract in this paper we present an alternative solution to the problem min x h n n a bxc where a b rmand c are rational matrices in h n n the solution circumvents the need to extract the matrix inner factors of b and c providing a multivariable extension of sarason s h interpolation theory 1 to the case of matrix valued b s and c s the result has application to the diagonally scaled optimization problem int d a bxc d 1 where the infimum is over d x h n n d diagonal

design optimization of conformal antennas by integrating stochastic algorithms with the hybrid finite element method previous work in antenna optimization has primarily focused on applications of optimization algorithms in conjunction with problem specific or semi analytic tools however previous developments in fast algorithms now offer the possibility of designs and moreover allow for full flexibility in material specification across three dimensions as an example this paper combines genetic algorithms ga and simulated annealing sa with fast hybrid finite element boundary integral simulations to develop full three dimensional 3 d antenna designs using shape topology as well as material optimization to illustrate these optimization methods as well as compare between ga and sa three different antenna designs are considered first a folded slot antenna is optimized for broad band performance followed by an irregular shaped dual band antenna design as a third design which combines shape and material optimization a bandgap substrate is designed to substantially increase the bandwidth of a patch residing on the optimized substrate

a counterexample on continuous coprime factors in georgiou and smith 1992 the following question was raised consider a linear shift invariant system on l sub 2 0 spl infin let the graph of the system have fourier transform mn h sup 2 i e the system has a transfer function p n m where m n are elements of c sub a f spl isin h sup spl infin f is continuous on the compactified right half plane is it possible to normalize m and n i e to ensure m sup 2 n sup 2 1 in c sub a the author shows by example that this is not always possible

controller discretization a gap metric framework for analysis and synthesis although techniques for directly synthesising sampled data sd compensators are available in the literature feedback controller design is perhaps best understood in a purely continuous time setting as such a feedback controller is often designed in the continuous time domain and then discretized for digital implementation it is important for the discretization step involved to yield an sd approximation which captures the essential features of the original controller from the perspective of closed loop behavior in this note a gap metric framework is developed for studying the controller discretization problem for linear time invariant lti plants and controllers importantly knowledge of a gap metric distance between an lti controller and an sd approximation permits explicit characterization of the possible difference in closed loop performance with any lti plant for which the lti controller is known to work well accounting for intersample behavior the central result of the new framework gives rise to an algorithm for computing a gap metric measure of the distance between an lti controller and a given discretization and a technique for synthesising a sd approximation which is optimal with respect to this metric

full wave analysis of dielectric frequency selective surfaces using a vectorial modal method a novel vectorial modal method is presented for studying guidance and scattering of frequency selective structures based on lossy all dielectric multilayered waveguide gratings for both te and tm polarizations the wave equation for the transverse magnetic field is written in terms of a linear differential operator satisfying an eigenvalue equation the definition of an auxiliary problem whose eigenvectors satisfy an orthogonality relationship allows for a matrix representation of the eigenvalue equation our proposed technique has been applied to the study of lossy all dielectric periodic guiding media with periodicity in one dimension this method yields the propagation constants and field distributions in such media the reflection and transmission coefficients of a single layer under a plane wave excitation can be obtained by imposing the boundary conditions study of the scattering parameters of the whole multilayered structure is accomplished by the cascade connection of components as characterized by their scattering parameters results obtained with this method for the propagation characteristics of a one dimensional periodic dielectric medium are compared with those presented by other authors and results for the scattering of several dielectric frequency selective surfaces dfss are compared with both theoretical and experimental results presented in the literature finding a very good agreement a symmetrical band stop filter with a single waveguide grating is also demonstrated theoretically

stability analysis for time varying systems via quadratic constraints abstract in this paper we introduce the concept of quadratic constraint qc to deal with various stability problems for infinite dimensional linear discrete time varying ltv systems first we derive a necessary and sufficient condition for the close loop stability based on quadratic constraints qcs an equivalent condition of this stability criterion presents the relationship between the stabilization of each finite dimensional truncation system and that of the whole system moreover applying this stability criterion and the complete finiteness of the nest algebra we show that the plant is stabilizable if and only if it has a single strong representation finally we use qcs to give a necessary and sufficient condition for the robust stabilization of connected uncertainty set defined by gap metric

a unifying framework for robust synchronization of heterogeneous networks via integral quadratic constraints a general framework for analysing robust synchronization in large scale heterogenous networks is proposed based on the theory of integral quadratic constraints iqcs dynamic agents are represented as linear time invariant single input single output systems the agents exchange information according to a sparse dynamical interconnection operator in order to achieve synchronization where their outputs are steered to the same possibly time varying signal the main technical hindrance to applying iqcs in this context lies with the presence of the marginally stable dynamics which define the trajectory to which the agents outputs synchronize it is shown that by working with conditions defined on modified signal spaces of interest and exploiting the graph structure underlying the connections between the dynamic systems iqc methods can be applied directly to synchronization analysis without recourse to loop transformations which may obscure the inherent structural properties of the multi agent networked systems decentralized and scalable conditions for synchronization are proposed within this setting the iqc framework is demonstrated to unify and generalize some of the existing results in the literature including certain nyquist type consensus certificates for time delay systems moreover it allows the role of feedback in robustness against uncertainty to be better manifested within the context of synchronization

robust stability of feedback systems a geometric approach using the gap metric a geometric framework for robust stabilization of infinite dimensional time varying linear systems is presented the uncertainty of a system is described by perturbations of its graph and is measured in the gap metric necessary and sufficient conditions for robust stability are generalized from the time invariant case an example is given to highlight an important difference between the obstructions which limit the size of a stabilizable gap ball in the time varying and time invariant cases several results on the gap metric and the gap topology are established that are central in a geometric treatment of the robust stabilizability problem in the gap in particular the concept of a graphable subspace is introduced in the paper subspaces that fail to be graphable are characterized by an index condition on a certain semi fredholm operator

virtual element methods for plate bending problems abstract we discuss the application of virtual elements to linear plate bending problems in the kirchhoff love formulation as we shall see in the virtual element environment the treatment of the c 1 continuity condition is much easier than for traditional finite elements the main difference consists in the fact that traditional finite elements for every element k and for every given set of degrees of freedom require the use of a space of polynomials or piecewise polynomials for composite elements for which the given set of degrees of freedom is unisolvent for virtual elements instead we only need unisolvence for a space of smooth functions that contains a subset made of polynomials whose degree determines the accuracy as we shall see the non polynomial part of our local spaces does not need to be known in detail and therefore the construction of the local stiffness matrix is simple and can be done for much more general geometries

on the computation of the gap metric for ltv systems abstract in this paper we consider the robust stabilization problem for linear discrete time varying ltv systems using the gap metric in particular we show that the time varying tv directed gap reduces to an operator with a tv hankel plus toeplitz structure computation of the norm of such an operator can be carried out using an iterative scheme involving a tv hankel operator defined on a space of hilbert schmidt causal operators the infimization in the tv directed gap formula is shown to be in fact a minimum by using duality theory the latter holds as well in the time invariant case

on the virtual element method for three dimensional linear elasticity problems on arbitrary polyhedral meshes abstract we explore the recently proposed virtual element method vem for the numerical solution of boundary value problems on arbitrary polyhedral meshes more specifically we focus on the linear elasticity equations in three dimensions and elaborate upon the key concepts underlying the first order vem while the point of departure is a conforming galerkin framework the distinguishing feature of vem is that it does not require an explicit computation of the trial and test spaces thereby circumventing a barrier to standard finite element discretizations on arbitrary grids at the heart of the method is a particular kinematic decomposition of element deformation states which in turn leads to a corresponding decomposition of strain energy by capturing the energy of linear deformations exactly one can guarantee satisfaction of the patch test and optimal convergence of numerical solutions the decomposition itself is enabled by local projection maps that appropriately extract the rigid body motion and constant strain components of the deformation as we show computing these projection maps and subsequently the local stiffness matrices in practice reduces to the computation of purely geometric quantities in addition to discussing aspects of implementation of the method we present several numerical studies in order to verify convergence of the vem and evaluate its performance for various types of meshes

a stress displacement virtual element method for plane elasticity problems abstract the numerical approximation of 2d elasticity problems is considered in the framework of the small strain theory and in connection with the mixed hellinger reissner variational formulation a low order virtual element method vem with a priori symmetric stresses is proposed several numerical tests are provided along with a rigorous stability and convergence analysis

the nonconforming virtual element method for elasticity problems abstract we present the nonconforming virtual element method for linear elasticity problems in the pure displacement formulation this method is uniformly convergent for the nearly incompressible case the optimal convergence in the h 1 norm is proved under some regularity assumptions we mention that for the lowest order case on triangular meshes the nonconforming virtual element method coincides with the nonconforming finite element method presented by brenner and sung 1992 19 up to an approximation of the right hand side besides we also present the nonconforming virtual element method for the pure traction problem which is proved to be uniformly convergent with respect to the lame constant finally we demonstrate the optimal convergence and stability of the nonconforming virtual element method by some numerical results

pareto optimal microwave filter design using multiobjective differential evolution microwave filters play an important role in modern wireless communications a novel method for the design of multilayer dielectric and open loop ring resonator olrr filters under constraints is presented the proposed design method is based on generalized differential evolution gde3 which is a multiobjective extension of differential evolution de gde3 algorithm can be applied for global optimization to any engineering problem with an arbitrary number of objective and constraint functions gde3 is compared against other evolutionary multiobjective algorithms like nondominated sorting genetic algorithm ii nsga ii multiobjective particle swarm optimization mopso and multiobjective particle swarm optimization with fitness sharing mopso fs for a number of microwave filter design cases in the multilayer dielectric filter design case a predefined database of low loss dielectric materials is used the results indicate the advantages of this approach and the applicability of this design method

efficient calculation of the free space periodic green s function electromagnetic scattering from periodic structures can be formulated in terms of an integral equation that has as its kernel a periodic green s function the periodic green s function can be derived as a response to an array of line point sources spatial domain or as a response to series of current sheets spectral domain these responses are a fourier transform pair and are slowly convergent summations the convergence problems in each domain arise from unavoidable singularities in the reciprocal domain a method is discussed to overcome the slow convergence by using the poisson summation formula and summing in a combination of spectral and spatial domains a parameter study is performed to determine an optimum way to weigh the combination of domains simple examples of scattering from a one dimensional array of strips and two dimensional array of plates are used to illustrate the concepts

a numerical method for computing the structured singular value abstract this article suggests a new approach to computing doyle s structured singular value ssv of a matrix the ssv is a notion important in robust control and several iteration schemes exist for approximation a solution 1 2 4 8 10 11 our idea is to pick a special case of the general problem which we believe to be natural and give an algorithm for studying it based on off the shelf packages once we are committed to this special case we discuss a very general plant uncertainty problem it embraces real as well as complex plant perturbations of many kinds the idea is simple and we believe very natural to the problem

the nonconforming virtual element method for the stokes equations we present the nonconforming virtual element method vem for the numerical approximation of velocity and pressure in the steady stokes problem the pressure is approximated using discontinuous piecewise polynomials while each component of the velocity is approximated using the nonconforming virtual element space on each mesh element the local virtual space contains the space of polynomials of up to a given degree plus suitable nonpolynomial functions the virtual element functions are implicitly defined as the solution of local poisson problems with polynomial neumann boundary conditions as typical in vem approaches the explicit evaluation of the non polynomial functions is not required this approach makes it possible to construct nonconforming virtual spaces for any polynomial degree regardless of the parity for two and three dimensional problems and for meshes with very general polygonal and polyhedral elements we show that the nonconforming vem is inf sup stable and establish optimal a pri

virtual elements for the navier stokes problem on polygonal meshes a family of virtual element methods for the two dimensional navier stokes equations is proposed and analyzed the schemes provide a discrete velocity field which is pointwise divergence free a ri

connection of multiplicative relative perturbation in coprime factors and gap metric uncertainty in this paper it is shown that a linear uncertain system described by a certain l multiplicative or relative perturbation in its coprime factors that are not necessarily normalized is the same as the one described by a gap or l gap metric ball hence all the stability robustness results for gap or l gap metric uncertainty carry over to this type of coprime factor perturbation uncertain systems described by h multi plicative or relative perturbations in coprime factors are also studied in this paper necessary and su cient conditions for robust stability of a feedback system with coprime factors of both the plant and the controller subject to simultaneous h multiplicative or relative perturbations are obtained

characterization and efficient computation of the structured singular value the concept of structured singular value was recently introduced by doyle 1 as a tool for the analysis and synthesis of feedback systems with structured uncertainties it is a key to the design of control systems under joint robustness and performance specifications and it very nicely complements the h infty approach to control system design in this paper it is shown that the structured singular value can be obtained as the solution of several smooth optimization problems properties of these optimization problems are exhibited leading to a fast algorithm that always yields the structured singular value for block structures of size no larger than 3 and often does for block structures of larger size

a robust control framework for linear time invariant spatially distributed systems a robust control framework for linear time invariant lti spatially distributed systems is outlined in this paper we adopt an input output approach which takes account of the spatially distributed nature of the input and output signals for such systems the approach is a generalization of h infty xspace control in the sense that the 2 norm in both time and space is used to quantify the size of signals it is shown that a frequency domain representation in the form of a graph symbol exists for every lti spatially distributed system under very mild assumptions the graph symbol gives rise to left and right coprime representations if the system is also stabilizable we investigate fundamental issues of feedback control such as feedback stability and robust stability to plant and or controller uncertainty quantified in the gap metric this includes a generalization of the sefton ober gap formula to the infinite dimensional operator case a design example in which an electrostatically destabilized membrane is feedback stabilized concludes the paper

a maximum modulus theorem for linear fractional transformations abstract a main result in the structured singular value theory is a maximum modulus like theorem for a special case of linear fractional transformations we extend that result to general linear fractional transformations

frequency domain uncertainty and the graph topology a new metric on linear time invariant systems is defined this metric is no greater than the gap metric and is in fact the smallest metric for which a certain robust stabilization result holds unlike other known metrics which induce the graph topology it has a clear frequency response interpretation this allows questions regarding robustness in the face of parametric uncertainty to be considered in terms of this metric

mixed virtual element methods for elastodynamics with weak symmetry abstract we propose and analyze a mixed virtual element method for linear elastodynamics in velocity stress formulation with weak symmetry in this formulation the symmetry of the stress is relaxed by the rotation of the displacement and the system of second order differential equation in time is reduced to first order differential equations in time by introducing velocity the proposed method uses h div conforming virtual element space of order k k 1 for the stress and discontinuous piecewise polynomial spaces of degree k for the velocity and rotation for time discretization we use the crank nicolson scheme both semidiscrete and fully discrete error estimates are robust for nearly incompressible materials numerical experiments confirm our theoretical predictions

analysis and synthesis on a generalized stability region the generalization of the spl nu gap metric to a finitely connected stability region is derived the results hold for the class of all linear time invariant systems which admit a continuous coprime factorization including the nonrational case a limited extension of the h sub spl infin loopshaping synthesis procedure is obtained via conformal mapping an example is given where enlargement of the stability region can be used to transform the problem into one which is solvable via uniform stability margin optimization

analysis of some finite elements for the stokes problem we study some finite elements which are used in the approximation of the stokes problem so as to obtain error estimates of optimal order resume nous etudions deux elements finis utilises pour l approximation du probleme de stokes et obtenons des estimations d erreur d ordre optimal

h text div h div and h mathbf curl h curl conforming virtual element methods in the present paper we construct virtual element spaces that are h mathrm div h div conforming and h mathbf curl h curl conforming on general polygonal and polyhedral elements these spaces can be interpreted as a generalization of well known finite elements we moreover present the basic tools needed to make use of these spaces in the approximation of partial differential equations finally we discuss the construction of exact sequences of vem spaces

a two operator approach to robust stabilization of linear systems on robust non fragile feedback stabilization is studied for causal linear time invariant lti input output systems defined in an l 2 signal space setup or equivalently in an l 2 j setup in the frequency domain two operator descriptions for the plant and the controller are used with bounded operators defined on the full space l 2 basic properties of causal lti operators on weighted l 2 spaces l 2 w which are relevant to stabilization theory are also established for different choices of the weighting function w weighted l 2 spaces allow the inclusion of persistent signals such as steps and thus provide the potential of important generalizations of the robust stabilization theory on l 2 in particular it is shown that there is a large class of weights w for which the l 2 w setup leads to h optimization this implies that robust h design can be applied to a large class of weighted l 2 spaces on problems of closability of unstable causal lti convolution operators are discussed t

graphs closability and causality of linear time invariant discrete time systems in this paper a linear time invariant discrete time system is considered by regarding it as an unbounded operator on 2 n 2 z cn or cz the graphs of closed systems are characterized and properties such as causality and closability of systems are studied it is shown that the closure of a causal closable system on 2 n cn and cz is again causal whereas this is in general not the case for systems on 2 z necessary and sufficient conditions which guarantee that this property hold for systems on 2 z are given many of the results extend without change to the continuous time case

large scale optimization of eigenvalues optimization problems involving eigenvalues arise in many applications let x be a vector of real parameters and let a x be a continuously differentiable symmetric matrix function of x we consi

mimetic finite difference method for the stokes problem on polygonal meshes various approaches to extend finite element methods to non traditional elements general polygons pyramids polyhedra etc have been developed over the last decade the construction of basis functions for such elements is a challenging task and may require extensive geometrical analysis the mimetic finite difference mfd method works on general polygonal meshes and has many similarities with low order finite element methods both schemes try to preserve the fundamental properties of the underlying physical and mathematical models the essential difference between the two schemes is that the mfd method uses only the surface representation of discrete unknowns to build the stiffness and mass matrices since no extension of basis functions inside the mesh elements is required practical implementation of the mfd method is simple for polygonal meshes that may include degenerate and non convex elements in this article we present a new mfd method for the stokes problem on arbitrary polygonal meshes and analyze its stability the method is developed for the general case of tensor coefficients which allows us to apply it to a linear elasticity problem as well numerical experiments show for the velocity variable second order convergence in a discrete l 2 norm and first order convergence in a discrete h 1 norm for the pressure variable first order convergence is shown in the l 2 norm

an interior point method for minimizing the maximum eigenvalue of a linear combination of matrices we consider the problem of finding lambda opt mathop inf limits x in r m lambda max a 0 sum limits i 1 m x i a i 1 and an optimal solution xopt if it exists here the a i are given symmetric matrices in ir n n for 0 i m and max a is the largest eigenvalue of a matrix a problem 1 can be rewritten as a convex differentiable problem with a positive definite constraint positive definiteness can easily be verified numerically via cholesky decomposition moreover the cone of positive definite matrices a is characterized by the domain of the smooth convex barrier function log det a

robust input output stabilization on z for persistent signals robustness of feedback stabilization is studied for causal linear time invariant input output systems defined on the full time axis z the signal space setting used includes also certain unbounded signals this study has been possible due to the use of two operator plant models ay bu this avoids the intrinsic difficulties of unbounded causal input output plant mappings y gu on z the full time axis robust stabilization results obtained here are analogous to those on the semi infinite time axis n in the finite dimensional case however there are certain important differences between the full time axis results and the semi infinite time axis results for infinite dimensional systems even when two operator plant models are used

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

high order virtual element method on polyhedral meshes abstract we develop a numerical assessment of the virtual element method for the discretization of a diffusion reaction model problem for higher polynomial order k and three space dimensions although the main focus of the present study is to illustrate some h convergence tests for different orders k we also hint on other interesting aspects such as structured polyhedral voronoi meshing robustness in the presence of irregular grids sensibility to the stabilization parameter and convergence with respect to the order k

exploring high order three dimensional virtual elements bases and stabilizations abstract we present numerical tests of the virtual element method vem tailored for the discretization of a three dimensional poisson problem with high order polynomial degree up to p 10 besides we discuss possible reasons for which the method could return suboptimal wrong error convergence curves among these motivations we highlight ill conditioning of the stiffness matrix and not particularly clever choices of the stabilizations we propose variants of the definition of face bulk degrees of freedom as well as of stabilizations which lead to methods that are much more robust in terms of numerical performances

a posteriori error estimates for the virtual element method an posteriori error analysis for the virtual element method vem applied to general elliptic problems is presented the resulting error estimator is of residual type and applies on very general polygonal polyhedral meshes the estimator is fully computable as it relies only on quantities available from the vem solution namely its degrees of freedom and element wise polynomial projection upper and lower bounds of the error estimator with respect to the vem approximation error are proven the error estimator is used to drive adaptive mesh refinement in a number of test problems mesh adaptation is particularly simple to implement since elements with consecutive co planar edges faces are allowed and therefore locally adapted meshes do not require any local mesh post processing

on robustness in the gap metric and coprime factor uncertainty for ltv systems abstract in this paper we study the problem of robust stabilization for discrete linear time varying ltv systems subject to time varying normalized coprime factor uncertainty operator theoretic results which generalize similar results known to hold for linear time invariant infinite dimensional systems are developed in particular we compute an upper bound for the maximal achievable stability margin under tv normalized coprime factor uncertainty in terms of the norm of an operator with a time varying hankel structure we point to a necessary and sufficient condition which guarantees compactness of the tv hankel operator and in which case singular values and vectors can be used to compute the time varying stability margin and tv controller

synthesis of novel all dielectric grating filters using genetic algorithms the feasibility of novel all dielectric waveguide grating filters is demonstrated using a genetic algorithm ga to solve for material dielectric constants and geometric boundaries separating homogeneous regions of the periodic cell in particular the gas show that simple geometries not previously reported utilizing a small number of layers and or gratings can be found to yield bandpass or stop band filters with user defined linewidth the evaluation of the fitness of a candidate design entails the solution of an integral equation for the electric field in the cell using the method of moments mom our implementation is made efficient by using only very few design frequency points and accurately approximating a given filter transfer function by a quotient of polynomials as a function of frequency additionally the problem impedance matrices are conveniently represented as the product of a material independent matrix and a vector of dielectric constants thus allowing us to fill the matrices only once our code has been parallelized for the cray t3d to take advantage of the intrinsic parallelization efficiencies offered by the gas solutions are illustrated for a very narrow band single grating transmission filter and a relatively broad band double grating reflection filter additionally a solution for a five homogeneous layers fabry perot filter is also presented

robustness analysis of nonlinear feedback systems an input output approach this paper presents an approach to robustness analysis for nonlinear feedback systems we pursue a notion of model uncertainty based on the closeness of input output trajectories which is not tied to a particular uncertainty representation such as additive parametric structured etc the basic viewpoint is to regard systems as operators on signal spaces we present two versions of a global theory where stability is captured by induced norms or by gain functions we also develop local approaches over bounded signal sets and give a treatment for systems with potential for finite time escape we compute the relevant stability margin for several examples and demonstrate robustness of stability for some specific perturbations e g small time delays we also present examples of nonlinear control systems which have zero robustness margin and are destabilized by arbitrarily small gap perturbations the paper considers the case where uncertainty is present in the controller as well as the plant and the generalization of the approach to the case where uncertainty occurs in several subsystems in an arbitrary interconnection

equivalent projectors for virtual element methods in the original virtual element space with degree of accuracy k projector operators in the h 1 seminorm onto polynomials of degree k can be easily computed on the other hand projections in the l 2 norm are available only on polynomials of degree k 2 directly from the degrees of freedom here we present a variant of the virtual element method that allows the exact computations of the l 2 projections on all polynomials of degree k the interest of this construction is illustrated with some simple examples including the construction of three dimensional virtual elements the treatment of lower order terms the treatment of the right hand side and the l 2 error estimates

a low order locking free virtual element for linear elasticity problems abstract we propose and analyze a low order virtual element for linear elasticity problems it can be seen as an evolution of the bernardi raugel element to general polygonal meshes like the bernardi raugel element the local degrees of freedoms for the new virtual element are the values of two components of v at vertexes and the values of the lowest moment of normal component of v on each edge the proposed method is well posed and optimal error estimates are obtained in the l 2 and h 1 norms moreover the generic constants in these estimates are shown to be uniform with respect to the lame coefficient numerical tests are provided to illustrate the good performance of the method and confirm our theoretical predictions

linear feedback systems and the graph topology it is established for general linear systems that the gap metric induces the coarsest topology with respect to which both closed loop stability and closed loop performance are robust properties in earlier works similar topological results were obtained by exploiting the existence of particular coprime factor system representations not known to exist in general by contrast the development here does not rely on any specific system representations systems are simply characterized as subspaces of norm bounded input output pairs and the analysis hinges on the underlying geometric structure of the feedback stabilization problem unlike other work developed within such a framework fundamental issues concerning the causality of feedback interconnections are discussed explicitly the key result of this paper concerns the difference between linear feedback interconnections with identical controllers in terms of a performance robustness related closed loop mapping upper and lower bounds on the induced norm of this difference are derived allowing for possibly infinite dimensional input output spaces and time varying behavior the bounds are both proportional to the gap metric distance between the plants which clearly demonstrates the gap to be an appropriate measure of the difference between open loop systems from the perspective of closed loop behavior to conclude an example is presented to show that bounds of the form derived here for linear systems do not hold in a general nonlinear setting

some basic formulations of the virtual element method vem for finite deformations abstract we present a general virtual element method vem framework for finite elasticity which emphasizes two issues element level volume change volume average of the determinant of the deformation gradient and stabilization to address the former issue we provide exact evaluation of the average volume change in both 2d and 3d on properly constructed local displacement spaces for the later issue we provide a new stabilization scheme that is based on the trace of the material tangent modulus tensor which captures highly heterogeneous and localized deformations two vem formulations are presented a two field mixed and an equivalent displacement based which is free of volumetric locking convergence and accuracy of the vem formulations are verified by means of numerical examples and engineering applications are demonstrated

virtual element method for two dimensional linear elasticity problem in mixed weakly symmetric formulation abstract we propose and analyze a virtual element method for two dimensional linear elasticity problem in mixed weakly symmetric formulation that is to say stresses are not require to be symmetric but only to satisfy a weaker condition based on lagrange multipliers the proposed method is well posed and the error bounds are shown to be uniform with the incompressibility parameter numerical tests confirm the convergence rate that is expected from the theory

gap metric robustness analysis of linear periodically time varying feedback systems quantitative robust stability results are established in this paper for feedback systems that evolve in continuous time and exhibit linear periodically time varying lptv behavior the results presented are analogous to results known to hold for linear time invariant lti systems although they do not follow directly from these system uncertainty is measured using the gap metric which quantifies the distance between systems in terms of the aperture between their graphs the subspaces corresponding to all input output pairs for each system the main robustness result characterizes the largest gap ball of lptv plants stabilized by a nominal lptv feedback controller known to stabilize a nominal lptv plant at the center of this ball a key step in the proof of this result makes use of a formula derived for the directed gap between lptv systems this formula is essentially a generalization of georgiou s for lti systems importantly all of the results presented apply to a class of sampled data control systems as a special case

on graphs conic relations and input output stability of nonlinear feedback systems this paper presents necessary and sufficient conditions for the stability of general interconnected dynamical systems the results are expressed in terms of the graphs of the interconnection s subsystems conditions for robustness of stability for an interconnection with additive disturbances are also provided finally the paper gives sufficient conditions for stability using conic sector conditions that generalize earlier conditions and that incorporate a recent nonlinear small gain idea

virtual elements for linear elasticity problems we discuss the application of virtual elements to linear elasticity problems for both the compressible and the nearly incompressible case virtual elements are very close to mimetic finite differences see for linear elasticity l beirao da veiga m2an math model numer anal 44 2010 pp 231 250 and in particular to higher order mimetic finite differences as such they share the good features of being able to represent in an exact way certain physical properties conservation incompressibility etc and of being applicable in very general geometries the advantage of virtual elements is the ductility that easily allows high order accuracy and high order continuity