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

logarithmic stabilization of the euler bernoulli transmission plate equation with locally distributed kelvin voigt damping abstract in this work we consider a transmission problem for a plate equation where one small part of the domain is made of a viscoelastic material with kelvin voigt constitutive relation we apply the general results due to burq s 10 in the study of asymptotic behavior of solutions and prove that the semigroup associated to the system is logarithmically stable the main ingredient of the proof is the carleman estimates the method consist to use carleman estimates to obtain information on the resolvent for high frequency

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

finite element solution of the helmholtz equation with high wave number part i the h version of the fem abstract the paper addresses the properties of finite element solutions for the helmholtz equation the h version of the finite element method with piecewise linear approximation is applied to a one dimensional model problem new results are shown on stability and error estimation of the discrete model in all propositions assumptions are made on the magnitude of hk only where k is the wavelength and h is the stepwidth of the fe mesh previous analytical results had been shown with the assumption that k 2 h is small for medium and high wavenumber these results do not cover the meshsizes that are applied in practical applications the main estimate reveals that the error in h 1 norm of discrete solutions for the helmholtz equation is polluted when k 2 h is not small the error is then not quasioptimal i e the relation of the fe error to the error of best approximation generally depends on the wavenumber k it is noted that the pollution term in the relative error is of the same order as the phase lead of the numerical solution in the result of this analysis thorough and rigorous understanding of error behavior throughout the range of convergence is gained numerical results are presented that show sharpness of the error estimates and highlight some phenomena of the discrete solution behavior the h p version of the fem is studied in part ii

hp adaptive finite elements in electromagnetics 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 curvilinear elements is presented the proposed method is illustrated and verified by a series of 2d experiments which include elements with curved boundaries and nonhomogeneous media

an cal h 2 matrix based integral equation solver of reduced complexity and controlled accuracy for solving electrodynamic problems using an h 2 matrix as the mathematical framework we compactly represent a dense system matrix by a reduced set of parameters thus enabling a significant reduction in computational complexity the error bound of the h 2 matrix based representation of an electrodynamic problem was derived we show that exponential convergence with respect to the number of interpolation points can be achieved irrespective of the electric size in addition we show that a direct application of h 2 matrix based techniques to electrodynamic problems would result in a complexity greater than o n with n being the matrix size due to the need of increasing the rank when ascending an inverted tree in order to keep a constant order of accuracy a rank function was hence developed to maintain the same order of accuracy in a wide range of electric sizes without compromising computational complexity with this rank function we demonstrate that given a range of electric sizes which lead to a range of n the dense system of o n 2 parameters can be compactly stored in o n units and the dense matrix vector multiplication can be performed in o n operations moreover the same order of accuracy can be kept across this range the method is kernel independent and hence is suitable for any integral equation based formulation in addition it is applicable to arbitrary structures numerical experiments from small electric sizes to 64 wavelengths have demonstrated the performance of the proposed method

a non overlapping domain decomposition method with non matching grids for modeling large finite antenna arrays a non overlapping domain decomposition method ddm is proposed herein to solve maxwell equations in r 3 in this work the maxwell equations are discretized using a vector finite element method with hierarchical h curl vector basis functions there are two major ingredients in the proposed non overlapping ddm a a proper 1st order transmission condition to enforce field continuity across domain boundaries and b a cement technique to allow non matching grids for neighboring domains moreover a detail fourier analysis of the transmission condition for a canonical half space example is presented the analysis provides significant insights into the convergence behavior of the proposed non overlapping ddm for solving electromagnetic radiation problems such as the large finite antenna arrays particularly for the antenna arrays the proposed non overlapping ddm is extremely efficient since the formulation can easily incorporate geometrical repetitions exponentially tapered notch vivaldi antenna arrays with size up to 100x100 elements are solved on a common pc to validate the proposed non overlapping ddm

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

unique continuation for the linearized benjamin bona mahony equation with space dependent potential in this paper we analyze a unique continuation problem for the linearized benjamin bona mahony equation with space dependent potential in a bounded interval with dirichlet boundary conditions the underlying cauchy problem is a characteristic one we prove two unique continuation results by means of spectral analysis and the generalized eigenvector expansion of the solution instead of the usual holmgren type method or carleman type estimates it is found that the unique continuation property depends very strongly on the nature of the potential and in particular on its zero set and not only on its boundedness or integrability properties

modeling of electromagnetic fields in rectangular waveguides by coupled finite infinite elements abstract the paper describes the 3d infinite element for modeling of stationary harmonic electromagnetic fields in waveguides the proposed approximation is a straightforward modification of the analogous approach developed for analysis of scattering problems in unbounded 2d and 3d domains comp meth appl mech engrg 188 2000 625 int j num meth engrg 57 2003 899 exponential shape functions in the longitudinal direction are used similarly as in comp meth appl mech engrg 140 1997 221 however arbitrary order of approximation in the tangential direction may be selected due to compatibility with the hp adaptive edge fe element discretization for maxwell s equations in bounded domains reported in comp meth appl mech engrg 152 1998 103 int j num meth engrg 53 2002 147 comp meth appl mech engrg 169 1999 331

exponential stability of nondissipative linear system in banach space and application to unbounded bilinear systems abstract we consider linear control systems of the form d z t d t a z t b z t where is a real parameter a is the infinitesimal generator of a linear c 0 semigroup of contractions s 0 t on a banach space x and the linear perturbation b is a relatively bounded operator with respect to a we provide necessary and sufficient conditions for exponential stability of the above system our stability results are then applied to establish uniform exponential stabilization of linear and bilinear systems with unbounded control operators applications to hyperbolic like equations are considered

the damped string problem revisited abstract we revisit the damped string equation on a compact interval with a variety of boundary conditions and derive an infinite sequence of trace formulas associated with it employing methods familiar from supersymmetric quantum mechanics we also derive completeness and riesz basis results with parentheses for the associated root functions under less smoothness assumptions on the coefficients than usual using operator theoretic methods rather than detailed eigenvalue and root function asymptotics only

an iteration free domain decomposition method for the fast finite element analysis of electromagnetic problems an iteration free finite element domain decomposition method ddm is proposed for the simulation of 3 d electromagnetic problems the finite element tearing and interconnecting feti with robin type transmission condition is introduced to construct a domain decomposition framework based on hierarchical mathcal h matrix algorithm the numerical green s function of each subdomain can be represented by a data sparse matrix form subsequently the original 3 d problem is reduced to a 2 d problem on the skeleton derived from the finite element discretization of pseudo differential operator the skeleton matrix can also be efficiently approximated with an mathcal h matrix by assembling all the numerical green s functions of subdomains based on mathcal h lu factorization algorithm the computational complexity and memory requirement for the direct solution of the skeleton equation can be reduced to be logarithmic linear the resulting direct feti d feti method completely depends on direct method without any iterative process hence it does not suffer from the issue of convergence rate and avoids redundant computations for multiple right hand side problems numerical examples demonstrate the effectiveness of the proposed method

energy decay rate of wave equations with indefinite damping abstract we consider the one dimensional wave equation with an indefinite sign damping and a zero order potential term using a shooting method we establish the asymptotic expansion of eigenvalues and eigenvectors of the damped wave equation for a large class of coefficients in addition if the damping coefficient is more positive than negative we prove that the energy of system decays uniformly exponentially to zero this sharp result generalizes a previous work of freitas and zuazua 1996

boundary stabilization of a 1 d wave equation with in domain antidamping we consider the problem of boundary stabilization of a 1 d one dimensional wave equation with an internal spatially varying antidamping term this term puts all the eigenvalues of the open loop system in the right half of the complex plane we design a feedback law based on the backstepping method and prove exponential stability of the closed loop system with a desired decay rate for plants with constant parameters the control gains are found in closed form our design also produces a new lyapunov function for the classical wave equation with passive boundary damping

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

exponential stability of an abstract nondissipative linear system in this paper we consider an abstract linear system with perturbation of the form frac dy dt ay varepsilon by on a hilbert space cal h where a is skew adjoint b is bounded and varepsilon is a positive parameter motivated by a work of freitas and zuazua on the one dimensional wave equation with indefinite viscous damping p freitas and e zuazua j differential equations 132 1996 pp 338 352 we obtain a sufficient condition for exponential stability of the above system when b is not a dissipative operator we also obtain a hautus type criterion for exact controllability of system a g where g is a bounded linear operator from another hilbert space to cal h our result about the stability is then applied to establish the exponential stability of several elastic systems with indefinite viscous damping as well as the exponential stabilization of the elastic systems with noncolocated observation and control

toward a universal h p adaptive finite element strategy part 1 constrained approximation and data structure abstract this is the first of a series of papers devoted to the development of an adaptive finite element method to solve various boundary value problems arising in solid and fluid mechanics the paper deals with the general concepts of h p finite element methods constrained approximation and data structure and related issues several numerical examples illustrate the main ideas of the method

approximation properties of the h p version of the finite element method abstract the paper surveys the approximation and convergence properties of the h p version of the finite element method the basic theoretical results together with the main ideas of the proofs numerical examples are given

maxwell eigenvalues and discrete compactness in two dimensions abstract we present an elementary proof of the discrete compactness result for a general class of hp finite elements introduced in 1 2 we discuss h convergence of 2d elements only and in this context the results are not new as the analysis of h curl conforming elements for maxwell s equations can be reduced to the long known results for raviart thomas elements 3 the work is based on the result of kikuchi 4 5 for nedelec s edge triangular elements of the lowest order and presents an alternative to techniques presented in 3 6 in particular the present version does not use an inverse inequality argument and therefore is valid for h adaptive meshes we conclude the presentation with a number of 2d computational experiments including nonconvex domains

toward a universal h p adaptive finite element strategy part 2 a posteriori error estimation abstract in this second paper of the series on h p adaptive finite element methods we present five different techniques for a posteriori error estimation of h p methods for linear elliptic boundary value problems the techniques are referred to as the residual estimation method the duality method the subdomain residual method a method based on interpolation theory and a post processing method the present study examines the theory and behavior of such techniques applied specifically to h p adaptive finite element methods several numerical examples illustrate the efficiency of the methods

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

why finite element discretizations can be factored by triangular hierarchical matrices although the asymptotic complexity of direct methods for the solution of large sparse finite element systems arising from second order elliptic partial differential operators is far from being optimal these methods are often preferred over modern iterative methods this is mainly due to their robustness in this article it is shown that an approximate lu decomposition exists which can be computed in the algebra of hierarchical matrices with almost linear complexity and with the same robustness as the classical lu decomposition low precision approximations may be used for preconditioning iterative solvers as a byproduct we prove that schur complements of stiffness matrices can be approximated with almost linear complexity

a two dimensional self adaptive hp finite element method for the characterization of waveguide discontinuities part i energy norm based automatic hp adaptivity abstract the accurate analysis and characterization of waveguide discontinuities is an important issue in microwave engineering in some cases the discontinuities are an unavoidable result of mechanical or electric transitions which effects have to be minimized in other cases the discontinuities are deliberately introduced into the waveguide to perform a certain electric function this is the first of two papers analyzing different types of rectangular waveguide discontinuities by using a fully automatic hp adaptive finite element method in this paper a fully automatic energy norm based hp adaptive finite element fe strategy applied to a number of relevant waveguide structures is presented the methodology produces exponential convergence rates in terms of the energy norm error of the solution against the problem size number of degrees of freedom extensive numerical results demonstrate the suitability of the hp method for solving different rectangular waveguide discontinuities these results illustrate the flexibility reliability and high accuracy of the method the self adaptive hp fem provides similar sometimes more accurate results than those obtained with semi analytical techniques such as the mode matching method for problems where semi analytical methods can be applied at the same time the hp fem provides the flexibility of modeling more complex waveguide structures and including the effects of dielectrics metallic screws round corners etc which cannot be easily considered when using semi analytical techniques in the second part the work is extended by presenting a fully automatic goal oriented hp adaptive fe in terms of the scattering or s parameters which are widely used in microwave engineering for the characterization of microwave devices

asymptotic stability for intermittently controlled second order evolution equations motivated by several works on ordinary differential equations we are interested in the asymptotic stability of intermittently controlled partial differential equations we give a condition of asymptotic stability for second order evolution equations uniformly damped by an on off feedback this result extends to the case of partial differential equations a previous result of r a smith concerning ordinary differential equations

a preconditioned dual primal finite element tearing and interconnecting method for solving three dimensional time harmonic maxwell s equations a new preconditioned dual primal nonoverlapping domain decomposition method is proposed for the finite element solution of three dimensional large scale electromagnetic problems with the aid of two lagrange multipliers the new method converts the original volumetric problem to a surface problem by using a higher order transmission condition at the subdomain interfaces to significantly improve the convergence of the iterative solution of the global interface equation similar to the previous version a global coarse problem related to the degrees of freedom at the subdomain corner edges is formulated to propagate the residual error to the whole computational domain at each iteration which further increases the rate of convergence in addition a fully algebraic preconditioner based on matrix splitting is constructed to make the proposed domain decomposition method even more robust and scalable perfectly matched layers pmls are considered for the boundary truncation when solving open region problems the influence of the pml truncation on the convergence performance is investigated by examining the convergence of the transmission condition for an interface inside the pml numerical examples including wave propagation and antenna radiation problems truncated with pmls are presented to demonstrate the validity and the capability of this method

hierarchical matrix techniques based on matrix decomposition algorithm for the fast analysis of planar layered structures the matrix decomposition algorithm mda provides an efficient matrix vector product for the iterative solution of the integral equation ie by a blockwise compression of the impedance matrix the mda with a singular value decomposition svd recompression scheme i e so called mda svd method shows strong ability for the analysis of planar layered structures however iterative solution faces the problem of convergence rate an efficient hierarchical h lu decomposition algorithm based on the h matrix techniques is proposed to handle this problem exploiting the data sparse representation of the mda svd compressed impedance matrix h lu decomposition can be efficiently implemented by h matrix arithmetic h matrix techniques provide a flexible way to control the accuracy of the approximate h lu factors h lu decomposition with low accuracy can be used as an efficient preconditioner for the iterative solver due to its low computational cost while h lu decomposition with high accuracy can be used as a direct solver for dealing with multiple right hand side rhs vector problems particularly numerical examples demonstrate that the proposed method is very robust for the analysis of various planar layered structures

achieving arbitrarily large decay in the damped wave equation we exhibit a sequence of viscous dampings for the fixed string that yields arbitrarily fast attenuation of any and all initial disturbances the limit case produces extinction of all solutions in finite time

stability results for the wave equation with indefinite damping abstract the one dimensional wave equation with damping of indefinite sign in a bounded interval with dirichlet boundary conditions is considered it is proved that solutions decay uniformly exponentially to zero provided the damping potential is in thebv class has positive average is small enough and satisfies a finite number of further constraints guaranteeing that the derivative of the real part of the eigenvalues is negative when the damping vanishes this sharp result completes a previous one by the first author showing that an indefinite sign damping always produces unstable solutions if it is large enough and it answers by the afirmative to a conjecture concerning small damping terms the method of proof relies on the developments by s cox and the second author on the high frequency asymptotic expansion of the spectrum for damped wave equations and on the characterization of the decay rate in terms of the spectral abscissa

the rate at which energy decays in a viscously damped hinged euler bernoulli beam we study the best decay rate of the solutions of a damped euler bernoulli beam equation with a homogeneous dirichlet boundary conditions we show that the fastest decay rate is given by the supremum of the real part of the spectrum of the infinitesimal generator of the underlying semigroup if the damping coefficient is in l infty 0 1

a new dual primal domain decomposition approach for finite element simulation of 3 d large scale electromagnetic problems a novel dual primal non overlapping domain decomposition method ddm for the finite element solution of three dimensional 3d large scale electromagnetic problems is proposed this method reduces the computational complexity from solving the original 3d problem to an equivalent interface problem by utilizing the idea of the dual primal finite element tearing and interconnecting feti dpem method the new method which is referred to as the feti dpem2 combines the dual primal idea with two lagrange multipliers and implements robin type transmission condition at the subdomain interfaces to significantly improve the convergence of the interface solution in the high frequency region similar to the original version a global coarse problem related to the degrees of freedom at the subdomain corner edges is designed to propagate the residual error to the whole computational domain at each iteration which further increases the convergence numerical examples are presented to demonstrate the validity and the capability of this method the results show that the proposed method produces fast solutions to large scale problems in any frequency band

stabilization of the wave equations with potential and indefinite damping by means of global carleman type estimate we study the stabilization problem of the wave equations with potential and indefinite damping the energy decay rate of the system is given explicitly also we obtain an upper bound estimate on the negative damping to guarantee the energy of the system decays exponentially

exponential stability of the plate equations with potential of second order and indefinite damping we study the exponential stability of the plate equations with potential of second order and indefinite sign damping term by means of a global carleman type estimate and the usual perturbation method we show that the energy of the system decays exponentially provided that the negative damping is sufficiently small both the energy decay rate and the upper bound estimate on the negative damping are given explicitly

adaptive multiresolution antenna modeling using hierarchical mixed order tangential vector finite elements hierarchical mixed order tangential vector finite elements tvfes for tetrahedra are attractive for accurate and efficient finite element or hybrid finite element boundary integral fe bi simulation of complicated electromagnetic problems they provide versatility in the geometrical modeling of physical structures guarantee solutions free of spurious modes and allow a local increase of resolution by combination of mixed order tvfes of different orders within a computational domain regions with higher order mixed order tvfes can be selected a priori or be found adaptively via methods for a posteriori error estimation or indication this paper demonstrates the merits of various explicit residual methods for a posteriori error indication via adaptive refinement of fe bi solutions of electromagnetic radiation problems using hierarchical mixed order tvfes for tetrahedra

exponential decay of energy of evolution equations with locally distributed damping consider an evolution equation with energy dissipation frac partial partial t y x t ay x t by x t on a bounded x domain omega where by signifies a dissipative perturbation to an otherwise energy conserving system this dissipation may be due to medium impurities viscous effects or artificially imposed dampers and stabilizers it is distributed over only part of the domain omega the question of when the dissipation is effective enough to cause uniform exponential decay of energy is examined because of the locally distributed nature of energy dissipation the problem lacks coercivity and is not directly solvable by energy identities thus to get conditions sufficient for uniform exponential decay a different approach needs to be taken provided here is a set of tight sufficient conditions in terms of the influence of the dissipative operatorbon the separated eigenmodes or clustered eigenmodes ofa the main theorems are general enough to treat the wave and bea

a fast domain decomposition method for the solution of electromagnetic scattering by large objects a nonoverlapping domain decomposition method is proposed for the finite element solution of the scattering problem by electrically large inhomogeneous infinite cylinders of arbitrary cross section to minimize the size of the total computational domain a second order absorbing boundary condition abc is applied upon an outer boundary of arbitrary shape which may be conformal to the surface of the scatterer this domain is then partitioned into concentric subdomains circumscribing the object a second order transmission condition derived from the abc is prescribed upon the interfaces between two adjacent subdomains this particular configuration is responsible for the fast convergence of the domain decomposition iterative algorithm which is parallelizable numerical results obtained with a nonparallelized computer code are presented which emphasize the superiority of this technique in terms of memory storage requirements and computing times over the standard finite element approach as well as over the rigorous hybrid finite element integral equation formulation

bresse system with indefinite damping abstract we consider the bresse system in a bounded domain 0 l r 1 the system has an indefinite damping mechanism i e with a damping function a a x possibly changing sign presented only in the equation for the rotation angle we shall prove that the system is still exponentially stable under the same conditions as in the positive constant damping case and provided a 1 l 0 l a x d x 0 and a a l 2 for small enough in the arguments we shall also give a new proof of exponential stability for the constant case a a

timoshenko systems with indefinite damping abstract we consider the timoshenko system in a bounded domain 0 l r 1 the system has an indefinite damping mechanism i e with a damping function a a x possibly changing sign present only in the equation for the rotation angle we shall prove that the system is still exponentially stable under the same conditions as in the positive constant damping case and provided a 0 l a x d x 0 and a a l 2 for small enough the decay rate will be described explicitly in the arguments we shall also give a new proof of exponential stability for the constant case a a moreover we give a precise description of the decay rate and demonstrate that the system has the spectrum determined growth sdg property i e the type of the induced semigroup coincides with the spectral bound for its generator

the optimal convergence of the h p version of the finite element method with quasi uniform meshes in the framework of the jacobi weighted besov spaces we analyze the convergence of the h p version of finite element solutions on quasi uniform meshes and the lower and upper bounds of errors for elliptic problems on polygons both lower and upper bounds are proved to be optimal in h and p which leads to the optimal convergence of the h p version of the finite element method with quasi uniform meshes for elliptic problems on polygons the results proved for the h p version include the h version with quasi uniform meshes and the p version with quasi uniform degrees as two special cases

eigenvalue asymptotics inverse problems and a trace formula for the linear damped wave equation abstract we determine the general form of the asymptotics for dirichlet eigenvalues of the one dimensional linear damped wave operator as a consequence we obtain that given a spectrum corresponding to a constant damping term this determines the damping term in a unique fashion we also derive a trace formula for this problem

on the spectrum of euler bernoulli beam equation with kelvin voigt damping abstract the spectral property of an euler bernoulli beam equation with clamped boundary conditions and internal kelvin voigt damping is considered the essential spectrum of the system operator is rigorously identified to be an interval on the left real axis under some assumptions on the coefficients it is shown that the essential spectrum contains continuous spectrum only and the point spectrum consists of isolated eigenvalues of finite algebraic multiplicity the asymptotic behavior of eigenvalues is presented

feti dp a dual primal unified feti method part i a faster alternative to the two level feti method the feti method and its two level extension feti 2 are two numerically scalable domain decomposition methods with lagrange multipliers for the iterative solution of second order solid mechanics and fourth order beam plate and shell structural problems respectively the feti 2 method distinguishes itself from the basic or one level feti method by a second set of lagrange multipliers that are introduced at the subdomain cross points to enforce at each iteration the exact continuity of a subset of the displacement field at these specific locations in this paper we present a dual primal formulation of the feti 2 concept that eliminates the need for that second set of lagrange multipliers and unifies all previously developed one level and two level feti algorithms into a single dual primal feti dp method we show that this new feti dp method is numerically scalable for both second order and fourth order problems we also show that it is more robust and more computationally efficient than existing feti solvers particularly when the number of subdomains and or processors is very large copyright 2001 john wiley sons ltd

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

exponential stability of wave equations with potential and indefinite damping abstract first we consider the linear wave equation u t t u x x a x u t b x u 0 on a bounded interval 0 l r the damping function a is allowed to change its sign if a 1 l 0 l a x d x is positive and the spectrum of the operator x x b is negative exponential stability is proved for small a a l 2 explicit estimates of the decay rate are given in terms of a and the largest eigenvalue of x x b second we show the existence of a global small smooth solution of the corresponding nonlinear wave equation u t t u x x a x u t b x u 0 if additionally the negative part of a is small enough compared with

exponential stability for wave equations with non dissipative damping abstract we consider the nonlinear wave equation u t t u x x a x u t 0 in a bounded interval 0 l r 1 the function a is allowed to change sign but has to satisfy a 1 l 0 l a x d x 0 for this non dissipative situation we prove the exponential stability of the corresponding linearized system for i possibly large a l with small a a l 2 and ii a class of pairs a l with possibly negative moment 0 l a x sin 2 x l d x estimates for the decay rate are also given in terms of a moreover we show the global existence of smooth small solutions to the corresponding nonlinear system if additionally the negative part of a is small enough

a vector dual primal finite element tearing and interconnecting method for solving 3 d large scale electromagnetic problems a lagrange multiplier based non overlapping domain decomposition method referred to as the dual primal finite element tearing and interconnecting feti dp is formulated for the finite element simulation of large three dimensional 3 d electromagnetic problems this formulation extends the feti dp for solving the scalar helmholtz equation to the solution of the vector curl curl wave equation using edge based finite elements it enforces the field continuity explicitly along the edges shared by more than two subdomains and implicitly at the interfaces between two subdomains through the use of lagrange multipliers with the aid of a direct sparse solver for each subdomain system the large global problem is reduced to a much smaller interface problem from which a neumann boundary condition is obtained at the interfaces between all the subdomains this neumann boundary condition is then used to calculate the field within each subdomain it is shown that the resulting feti dpem method is scalable with respect to the size of finite elements and the number of subdomains it is also scalable with respect to the size of the subdomains when the subdomains with its surfaces enclosed by perfect magnetic conductors cannot support any resonant modes the feti dpem method is applied to the electromagnetic simulation of array type structures where the geometrical redundancy is fully exploited to speedup the simulation and reduce the memory requirement numerical results for the simulation of finite antenna arrays and photonic bandgap devices are presented to demonstrate the application accuracy efficiency and capability of the feti dpem method

full wave analysis of dielectric waveguides at a given frequency new variational formulation to compute propagation constants is proposed based on it vector finite element method is proved to exclude spurious modes provided finite elements possess discrete compactness property convergence analysis is conducted in the framework of collectively compact operators reported theoretical results apply to a wide class of vector finite elements including two families of nedelec and their generalization the hp edge elements numerical experiments fully support theoretical estimates for convergence rates

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

non conformal domain decomposition method with mixed true second order transmission condition for solving large finite antenna arrays a non overlapping and non conformal domain decomposition method ddm is presented for modeling large finite antenna arrays two major benefits of the proposed ddm a a mixed true second order transmission condition sotc with corner edge penalty terms is developed to facilitate fast convergence in the ddm iterations numerical experiments indicate that the convergence of ddm with the aforementioned sotc is insensitive to the sizes of arrays and b the non conformal property of the proposed ddm permits the use of completely independent discretization for each of the sub domains we demonstrate the performance of the proposed approach through several large scale problems

a fast domain decomposition method for solving three dimensional large scale electromagnetic problems an efficient algorithm based on domain decomposition method ddm and partial basic solution vectors pbsv technique is proposed for solving three dimensional 3 d large scale finite periodic electromagnetic problems such as photonic or electromagnetic bandgap structures frequency selective surfaces the entire computational domain is divided into many smaller nonoverlapping subdomains a robin type condition is introduced at the interfaces between subdomains to enforce the field continuity with the help of a set of dual unknowns each subdomain can be tackled independently because of geometric repetitions all the sudomains can be classified into a few building blocks which can be dealt with by an improved pbsv algorithm thus the original problem becomes a much smaller one which involves the unknowns only at the interfaces the resulting linear system of equations is solved by a block symmetric successive over relaxation ssor preconditioned krylov subspace method once the unknowns at the interfaces have been obtained the final solution on each subdomain can easily be calculated independently some numerical examples are provided and show the method is scalable with the number of subdomains

local controllability to stationary trajectories of a burgers equation with nonlocal viscosity abstract this article studies the local controllability to trajectories of a burgers equation with nonlocal viscosity by linearization we are led to an equation with a non local term whose controllability properties are analyzed by using fourier decomposition and biorthogonal techniques once the existence of controls is proved and the dependence of their norms with respect to the time is established for the linearized model a fixed point method allows us to deduce the result for the nonlinear initial problem

solution of elastic scattering problems in linear acoustics using h p boundary element method abstract the work is a continuation of 1 a simplified 3d model problem reduced from the general class of elastic scattering problems is analyzed focusing attention on such practical details of the 3d implementation as a triangles based h p approximation and corresponding data structure integration of singular integrals and its effect on theoretically optimal rates of convergence a posteriori error estimation and sample adaptive strategies

a fem domain decomposition method for photonic and electromagnetic band gap structures this paper introduces an efficient domain decomposition algorithm for the solution of time harmonic electromagnetic fields arising in three dimensional finite size photonic band gap and electromagnetic band gap structures the method is based on the finite element approximation and a nonoverlapping domain decomposition method a set of cement unknowns on the inter domain interfaces has been explicitly introduced to enforce the appropriate field continuities the introduction of these extra unknowns allows for nonconforming nonmatching triangulations across domain eliminating the need for periodic mesh to ensure and improve the convergence of the outer iteration loop robin transmission condition is used to communicate information across interfaces the resulting system of equations is solved with a fast algorithm that loosely resembles the well known finite element tearing and interconnecting algorithm in this algorithm the method solves in the preprocessing step for the robin primal subdomain problems multiple times by exciting one dual unknown at a time this step generates an iteration matrix that is then used to update the dual unknowns in the outer loop iteration the present method becomes extremely efficient for problems with geometric repetitions such as photonic and electromagnetic band gap structures

a novel efficient algorithm for scattering from a complex bor using mixed finite elements and cylindrical pml an efficient finite element method fem is developed to compute scattering from a complex body of revolution bor the bor is composed of a perfect conductor and impedance surfaces and arbitrary inhomogeneous materials the method uses edge based vector basis functions to expand the transverse field components and node based scalar basis functions to expand the angular component the use of vector basis functions eliminates the problem of spurious solutions suffered by other three component fem formulations the fem mesh is truncated with a perfectly matched layer pml in cylindrical coordinates the use of pml in cylindrical coordinates avoids the wasted computation which results from a spherical mesh boundary with an elongated scatterer the fem equations are solved by ordering the unknowns with a reverse cuthill mckee algorithm and applying a banded matrix solution algorithm the method is capable of handling large realistic radar targets and good agreement with measured results is achieved for benchmark targets

asymptotic stability for bresse systems abstract in this paper consider a vibrating system of bresse type in a one dimensional bounded domain with a nonlinear damping acting in the equation of the shear angle displacement and nonlinear localized damping in other equations we show the asymptotic stability without imposing conditions about the equal speed wave propagation using a method developed by lasiecka and tataru 9

instability results for the damped wave equation in unbounded domains abstract we extend some previous results for the damped wave equation in bounded domains in r d to the unbounded case in particular we show that if the damping term is of the form a with bounded a taking on negative values on a set of positive measure then there will always exist unbounded solutions for sufficiently large positive in order to prove these results we generalize some existing results on the asymptotic behaviour of eigencurves of one parameter families of schrodinger operators to the unbounded case which we believe to be of interest in their own right

optimal shape and position of the actuators for the stabilization of a string abstract the energy in a string subject to constant viscous damping k on a subset of length l 0 decays exponentially in time we consider the problem of optimizing the decay rate for the which are the unions of at most n intervals this rate is given by the spectral abscissa of the linear operator associated to the wave equation we are interested in small values of k therefore we consider the derivative of the spectral abscissa at k 0 we prove that except for the case l 1 2 when the number of intervals is not fixed a priori an optimal domain does not exist we study numerically the case of one or two intervals using a genetic algorithm these numerical results are not intuitive in particular the optimal position of one interval is never at the middle of the string

the origin of spurious solutions in computational electromagnetics it is commonly believed that the divergence equations in the maxwell equations are redundant for transient and timeharmonic problems therefore most of the numerical methods in computational electromagnetics solve only two first order curl equations or the second order curl curl equations this misconception is the true origin of spurious modes and inaccurate solutions in computational electromagnetics by studying the div curl system this paper clarifies that the first order maxwell equations are not overdetermined and the divergence equations must always be included to maintain the ellipticity of the system in the space domain to guarantee the uniqueness of the solution and the accuracy of the numerical methods and to eliminate the infinitely degenerate eigenvalue this paper shows that the common derivation and usage of the second order curl curl equations are incorrect and that the solution of helmholtz equations needs the divergence condition to be enforced on an associated part of the boundary the div curl method and the least squares method introduced in this paper provide rigorous derivation of the equivalent second order maxwell equations and their boundary conditions the node based least squares finite element method lsfem is recommended for solving the first order full maxwell equations directly examples of the numerical solutions by lsfem are given to demonstrate that the lsfem is free of spurious solutions