on the negative squares of indefinite sturm liouville operators abstract the number of negative squares of all self adjoint extensions of a simple symmetric operator of defect one with finitely many negative squares in a krein space is characterized in terms of the behaviour of an abstract titchmarsh weyl function near 0 and these results are applied to a large class of symmetric and self adjoint indefinite sturm liouville operators with indefinite weight functions

toward hp adaptive solution of 3d electromagnetic scattering from cavities an effective hp adaptive finite element fe approach is presented for a reliable and accurate solution of 3d electromagnetic scattering problems the far field is approximated with the infinite element method this allows one to reduce the external domain discretised with finite elements to a minimum preserving the possibility of arbitrary reduction of the error as the method does not introduce modelling error the work is focused on scattering from cavity backed apertures recessed in a ground plane near optimal discretisations that can effectively resolve local rapid variations in the scattered field can be obtained adaptively by local mesh refinements so called h type refinements blended with graded polynomial enrichments p enrichments the discretisation error can be controlled by a self adaptive process which is driven by a posteriori error estimates in terms of the energy norm or in a quantity of interest the radar cross section rcs is an example of the latter h and p adaptively constructed solutions are compared to pure uniform p approximations numerical highly accurate and fairly converged solutions for generic cavities are given and compared to previously published results

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

potential function estimates for quasi einstein metrics abstract in this paper we derive the growth pinching estimates for potential functions of quasi einstein metrics on complete noncompact connected manifolds based on the estimates for the scalar curvature and the using of the weighted measure comparison theorem our results show that the estimates for potential functions rely on the sign of constants and

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

on the spectral theory of singular indefinite sturm liouville operators we consider a singular sturm liouville differential expression with an indefinite weight function and we show that the corresponding self adjoint differential operator in a krein space locally has the same spectral properties as a definitizable operator

hierarchal vector boundary elements and p adaption for 3 d electromagnetic scattering this paper describes the development of new vector boundary elements for solving electromagnetic em scattering problems the new elements are suitable for the magnetic field integral equation mfie electrical field integral equation efie or the combination field integral equation cfie the basis functions are assigned to the edges of an element rather than to its nodes the new element guarantees the continuity of the normal component of the surface current across element edges furthermore the basis functions are hierarchical from linear to higher order which enables one to use the new elements in a p adaption scheme

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

hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements new vector finite elements are proposed for electromagnetics the new elements are triangular or tetrahedral edge elements tangential vector elements of arbitrary polynomial order they are hierarchal so that different orders can be used together in the same mesh and p adaption is possible they provide separate representation of the gradient and rotational parts of the vector field explicit formulas are presented for generating the basis functions to arbitrary order the basis functions can be used directly or after a further stage of partial orthogonalization to improve the matrix conditioning matrix assembly for the frequency domain curl curl equation is conveniently carried out by means of universal matrices application of the new elements to the solution of a parallel plate waveguide problem demonstrates the expected convergence rate of the phase of the reflection coefficient for tetrahedral elements to order 4 in particular the full order elements have only the same asymptotic convergence rate as elements with a reduced gradient space such as the whitney element however further tests reveal that the optimum balance of the gradient and rotational components is problem dependent

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

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

spectral points of type π and π of self adjoint operators in krein spaces via approximative eigensequences we introduce the notion of spectral points of type and for self adjoint operators in krein spaces they are stable under compact perturbations for real spectral points of type and which are not in the interior of the spectrum we prove that the growth of the resolvent in some neighbourhood of them is of finite order there exists a local spectral function with singularities it turns out that all spectral subspaces corresponding to sufficiently small neighbourhoods of points of type or type are pontryagin spaces

comparison geometry for the bakry emery ricci tensor for riemannian manifolds with a measure m g edvolg we prove mean curvature and volume comparison results when the bakry emery ricci tensor is bounded from below and f is bounded or rf is bounded from below generalizing the classical ones i e when f is constant this leads to extensions of many theorems for ricci curvature bounded below to the bakry emery ricci tensor in particular we give extensions of all of the major comparison theorems when f is bounded simple examples show the bound on f is necessary for these results

diameter estimate for compact quasi einstein metrics in this paper we prove a gradient estimate for the potential function of a nontrivial compact quasi einstein metric with constant 0 based on this gradient estimate we derive the lower bound estimate for the diameter

basic problems of a posteriori error estimation abstract this paper addresses basic questions regarding the reliability of a posteriori error estimation it analyzes in detail an a posteriori estimator for linear elements on triangular meshes it gives the bounds of the effectivity index depending on the geometry of the triangles and smoothness of the approximated solution the theoretical results are in concordance with the results of our numerical experiments the second part analyzes a one parametric family of estimators in the one dimensional setting and their optimal selection for adaptively constructed meshes

accumulation of complex eigenvalues of indefinite sturm liouville operators spectral properties of singular sturm liouville operators of the form with the indefinite weight x sgn x on are studied for a class of potentials with lim x v x 0 the accumulation of complex and real eigenvalues of a to zero is investigated and explicit eigenvalue problems are solved numerically

multilevel methods for p adaptive finite element analysis of electromagnetic scattering in p adaptive finite element analysis the large sparse matrix that arises can be block structured according to the hierarchical level of the unknowns a multilevel preconditioner for the matrix is a v cycle that starts by applying gauss seidel to the highest level then the next level down and so on on the other side of the v gauss seidel is applied in the reverse order at the bottom of the v is the lowest order system which typically is solved exactly with a direct solver however for a complex geometry even the lowest order system may be too large for direct factorization here an alternative is proposed to continue the v cycle downwards first into a set of auxiliary node based spaces then through a series of progressively smaller matrices generated by an algebraic multigrid method the smallest matrix is solved by factorization the method is applied to p adaptive analysis of a five resonator iris filter a split ring resonator loaded waveguide a buckyball metallic frame surrounding a conducting sphere and a noncommensurate frequency selective surface tetrahedral elements up to fourth order are used the largest matrix has over 12 million rows and 0 6 billion nonzero entries

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

a krein space approach to symmetric ordinary differential operators with an indefinite weight function on considere les proprietes spectrales du probleme differentiel l f 1 n p 0 f n n 1 n 1 p 1 f n 1 n 1 p n f rf sur un intervalle fini ou infini a b avec des coefficients reels localement sommables 1 p 0 p 1 p n r sous l hypothese que p 0 0 et que la fonction poids r change de signe sur a b

bounds on the non real spectrum of differential operators with indefinite weights ordinary and partial differential operators with an indefinite weight function can be viewed as bounded perturbations of non negative operators in krein spaces under the assumption that 0 and infty are not singular critical points of the unperturbed operator it is shown that a bounded additive perturbation leads to an operator whose non real spectrum is contained in a compact set and with definite type real spectrum outside this set the main results are quantitative estimates for this set which are applied to sturm liouville and second order elliptic partial differential operators with indefinite weights on unbounded domains

monotonicity formulas via the bakry emery curvature abstract we prove several monotone formulas for smooth metric measure spaces with nonnegative m bakry emery curvature first we define a f r and v f r for the weighted green function and establish the monotone formulas these formulas are parallel to the weighted volume comparison theorem on smooth metric measure spaces with nonnegative m bakry emery curvature second we define the weighted nash entropy fisher information and perelman s entropy then we get the monotone formulas along the weighted heat equation via the m bakry emery curvature

definitizable operators and quasihyperbolic operator polynomials abstract the main concern of this paper is bounded operators a on a hilbert space with inner product which are selfadjoint in an indefinite scalar product say x y gx y and have entirely real spectrum in addition all points of spectrum are required to have determinate type a notion refining earlier ideas of krein langer et al which implies a strong stability property under perturbations the central result states that the spectrum is of this type if and only if the operator in question is uniformly definitizable i e gp a for some polynomial p as a first application characterizations of compact uniformly definitizable operators on pontrjagin spaces are obtained then the basic ideas are extended to selfadjoint monic operator polynomials via their linearizations in particular a new class of quasihyperbolic polynomials qhp with real and determinate spectrum is introduced it is shown that qhp have nontrivial monic factors the special cases of strongly hyperbolic and quadratic polynomials are also discussed in particular a factorization theorem is proved for a class of gyroscopically stabilized quadratic polynomials which originate in recent investigations of problems in mechanics

an explicit a posteriori error indicator for electromagnetic finite element boundary integral analysis within the finite element method fem there is always an error associated with the solution quantifying this error is a very important aspect of fe analysis since it can increase confidence in a solution and can be used to drive adaptive refinements of the discretization optimizing the quality of the solution relative to the number of degrees of freedom and in turn reducing computational cost this paper presents an a posteriori error indicator for time harmonic electromagnetic analysis in three dimensions when using a galerkin fe approach with curl conforming elements and including a nonlocal boundary integral boundary condition as well as a dominant mode port boundary condition the error indicator is residual based of an explicit nature and constitutes a bound on an error energy measure the error indicator is evaluated by presenting results relating to common microwave engineering applications which shows that it can be used successfully to estimate the relative error distribution and that it can successfully serve within an adaptive algorithm

a procedure for a posteriori error estimation for h p finite element methods abstract a new approach to a posteriori error estimation is outlined which is applicable to general h p finite element approximations of general classes of boundary value problems the approach makes use of duality arguments and is based on the element residual method erm important aspects of the method are that it provides a systematic approach toward deriving element boundary conditions for the erm it leads to an upper bound for the global error in an appropriate energy norm and it is valid for non uniform and irregular h p meshes in the present exposition a brief outline of the theoretical foundations of the method is given together with the results of its application to several representative problems these results show that the approach is applicable to general linearly elliptic systems including unsymmetrical operators and that the method is valid for broad classes of linear and non linear problems

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

adaptive finite element methods in computational mechanics we present a general approach to adaptivity for finite element methods and give applications to linear elasticity non linear elasto plasticity and nonlinear conservation laws including numerical results

on lfp spectrum and τ quasi einstein metric abstract in this paper we study l f p spectrum estimates for some smooth potential function f on complete noncompact riemannian manifolds via the bakry emery curvature as its applications we give the upper bound estimate of the l f 2 spectrum for the complete noncompact quasi einstein metric we give an example to show the sharpness of our estimate we also get a lower bound estimate when 0 1 and 0

accurate and efficient simulation of antennas using hierarchical mixed order tangential vector finite elements for tetrahedra hierarchical mixed order tangential vector finite elements tvfes for tetrahedral elements are attractive for accurate and efficient finite element method simulation of complicated electromagnetic problems they provide versatility in the geometric modeling of physical structures guarantee solutions free of spurious modes and allow local increase of resolution by selective expansion of the unknown electromagnetic field i e by combination of mixed order tvfes of different orders within a computational domain for a realistic antenna radiation problem this paper demonstrates that field expansion using lowest and higher order hierarchical mixed order tvfes selectively is vastly superior in terms of accuracy memory as well as central processing unit cpu time to field expansion using a lowest order mixed order tvfe only

adaptive finite element boundary integral analysis for electromagnetic fields in 3 d this paper presents a complete adaptive finite element boundary integral fe bi analysis scheme for the time harmonic electromagnetic analysis of three dimensional inhomogeneous scatterers radiators in free space the adaptive scheme is based on an fe bi formulation which yields electric and magnetic field solutions simultaneously it employs a posteriori error estimates which exploit the availability of both field solutions and estimates error distributions and global solution quality for the electric and magnetic fields separately it automatically determines which elements should be refined in order to equi distribute the estimated error based on the type of refinement requested h p or hp this automatic determination is based on extrapolating the elemental error estimates the algorithm terminates when specified tolerance levels are reached by the electric and or magnetic field global solution quality estimates the only required user specifications within the algorithm are the termination tolerances and the types of refinements to effect results are presented which show that within the scope of the presented error measures significant reductions in computational cost may be achieved the proposed scheme could be used with other types of error estimates and it could be adapted to other fe or fe bi formulations