a note on multiple solutions of some semilinear elliptic problems abstract we discuss the existence of multiple solutions of nonlinear elliptic equations by a combination of variational topological methods and the generalized conley index theory we obtain several positive solutions and sign changing solutions our main point is to show the usefulness of the morse inequalities for morse decompositions in the generalized conley index theory

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

invariant sets of descending flow in critical point theory with applications to nonlinear differential equations abstract properties of invariant sets of descending flow defined by a pseudogradient vector field of a functional in a banach space are studied in this way several critical points can be found by constructing different invariant sets on which the functional is bounded below under suitable conditions the existence of at least four critical points of a functional is proved each critical point being in a certain invariant set the theoretical results are applied to nonlinear elliptic boundary value problems and nonlinear systems of ordinary differential equations in variant cases at least four solutions are obtained for these equations

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

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

applications of local linking to critical point theory we prove the existence of nontrivial critical points of functionals with a local linking at 0 applications to elliptic boundary value problems and to hamiltonian systems are given c 1995 academic press inc

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

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 variational approach to subquadratic perturbations of elliptic systems abstract we consider subquadratic perturbations of semilinear elliptic systems which are in variational form a unified approach to both the cooperative and noncooperative problems is presented and a condition of nonquadraticity at infinity is introduced to treat the resonant cases through minimax techniques

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

solutions for resonant elliptic systems with nonodd or odd nonlinearities we consider by minimax techniques a class of cooperative elliptic systems at resonance if the nonlinear term is nonodd we establish some new existence theorems about nontrivial solutions if the nonlinearity is odd we obtain existence of infinitely many solutions a topic about which very little is known

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

adaptive tuning of the fuzzy controller for robots an adaptive tuning algorithm of the fuzzy controller is developed for a class of serial link robot arms the algorithm can on line tune parameters of premise and consequence parts of fuzzy rules of the fuzzy basis function fbf controller the main part of the fuzzy controller is a fuzzy basis function network to approximate unknown rigid serial link robot dynamics under some mild assumptions a stability analysis guarantees that both tracking errors and parameter estimate errors are bounded moreover a robust technique is adopted to deal with uncertainties including approximation errors and external disturbances simulations of the proposed controller on the puma 560 robot arm demonstrate the effectiveness

compactness results for schrodinger equations with asymptotically linear terms abstract we study the nonlinear problem u v x f x u x r n lim x u x 0 where the schrodinger operator v is semibounded and the nonlinearity f is linearly bounded we establish compactness of palais smale sequences and cerami sequences for the associated energy functional under general spectral theoretic assumptions applying these results we obtain existence of three nontrivial solutions if the energy functional has a mountain pass geometry

critical point theory for indefinite functionals with symmetries letxbe a hilbert space and c1 x r be strongly indefinite assume in addition that a compact lie groupgacts orthogonally onxand that is invariant in order to find critical points of we develop the limit relative category of fournieret al in the equivariant context we use this to prove two generalizations of the symmetric mountain pass theorem and a linking theorem in the case of the mountain pass theorem the mountain range is allowed to lie in a subspace of infinite codimension also other conditions of the classical symmetric mountain pass theorem forg z 2 due to ambrosetti and rabinowitz can be weakened considerably for example we are able to deal with infinite dimensional fixed point spaces the proofs consist of a direct reduction to a relative borsuk ulam type theorem this provides a new proof even for the classical mountain pass theorem the abstract critical point theorems are applied to an elliptic system with dirichlet boundary conditions we only need a weak version of the usual superquadraticity condition the linking theorem can be applied to asymptotically linear hamiltonian systems which are symmetric with respect to a generalized symplectic group action

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