a general method for recovering equilibrating element tractions abstract a new geometrical presentation of a general method for recovering equilibrating element tractions is developed for 2d finite element models of problems in structural mechanics the data for the method consists of the prescribed loading and the stress fields resulting from a conventional linear elastic finite element analysis the geometrical presentation utilises the physical concepts of nodal forces and maxwell force diagrams based on nodal equilibrium only small problems have to be solved for each node this presentation complements the original algebraic approach of ladeveze and extends the method to cover the use of hierarchical p elements in regular meshes and general higher order elements in 1 irregular meshes as encountered in h p mesh refinement the same presentation is considered for the recovery of residual tractions as required in the solution of the local residual problem comparison is made with related methods for obtaining residual tractions in particular those proposed by bank and weiser and ainsworth et al detailed examples are included to illustrate the presentation this paper considers only the fundamental aspects of recovering equilibrating tractions the knowledge gained may be used in various applications such as error analysis limit analysis and structural design

an hp adaptive finite element method for scattering problems in computational electromagnetics an hp adaptive finite element fe approach is presented for a reliable efficient and accurate solution of 3d electromagnetic scattering problems the radiation condition in the far field is satisfied automatically by approximation with infinite elements ie near optimal discretizations that can effectively resolve local rapid variations in the scattered field are sought adaptively by mesh refinements blended with graded polynomial enrichments the p enrichments need not be spatially isotropic the discretization error can be controlled by a self adaptive process which is driven by implicit or explicit a posteriori error estimates the error may be estimated in the energy norm or in a quantity of interest a radar cross section rcs related linear functional is used in the latter case adaptively constructed solutions are compared to pure uniform p approximations numerical highly accurate and fairly converged solutions for a number of generic problems are given and compared to previously published results copyright 2004 john wiley sons ltd

l p improving estimates for some classes of radon transforms in this paper we give l p l q estimates and the l p regularizing estimate of radon transforms associated to real analytic functions and we also give estimates of the decay rate of the if operator norm of corresponding oscillatory integral operators for l p l q estimates and estimates of the decay rate of the l p operator norm we obtain sharp results except for extreme points however for l p regularity we allow some restrictions on the phase function

automated multi level substructuring amls for electromagnetics abstract we present an algebraic setting of an automated multi level substructuring amls method for electromagnetic maxwell eigenproblem solution to our knowledge it is novel and it involves a non trivial generalisation of the corresponding method for elastodynamics and acoustics in comparison to the amls method for elliptic problems the electromagnetic stiffness matrix is singular it has a large kernel of gradients of h 1 conforming shape functions this difficulty was overcome by confining the method to solenoidal fields only the goal of amls is to achieve a high level of dimensional reduction inexpensively using multi level modal substructuring enabling reliable solution of huge response problems without compromising the accuracy of the quantity of interest as proof of concept we present simple numerical experiments on rectangular domains verifying a correct implementation of a truly multi level version of the generalised algorithm for real life applications the algorithm need to be equipped with automated nested mesh dissection and an algorithm for automatic subdomain eigenspace truncation finally the algorithm needs to be tuned and parallelised

pattern generating travelling waves in a discrete multicellular system with lateral inhibition abstract on a one dimensional string of cells the juxtacrine signalling model for delta notch lateral inhibition by collier et al j r collier n a m monk p k maini j h lewis pattern formation by lateral inhibition with feedback a mathematical model of delta notch intercellular interaction j theoret biol 183 1996 429 446 exhibits a predominant alternating pattern of cells expressing either delta or notch as well as many aperiodic patterns despite this multistationarity in the idealised situation of no noise travelling waves invading the unstable homogeneous state only generate the predominant alternating pattern in their wake all over the lattice however this robustness is totally lost in the presence of stochastic noise because the invaded initial state is unstable using linear approximations around the initial homogeneous state and around the final patterned state we are able to derive analytically all essential properties of the wave the shape of the wave front the unique alternating pattern generated by the wave and the asymptotic speed of the wave front we show that the asymptotic wave speed equals the theoretical minimum wave speed the latter agrees extremely well with the value estimated from numerical simulations thus in this system travelling waves are pulled by the leading edge of the front

front propagation into unstable states universal algebraic convergence towards uniformly translating pulled fronts fronts that start from a local perturbation and propagate into a linearly unstable state come in two classes pulled fronts and pushed fronts the term pulled front expresses that these fronts are pulled along by the spreading of linear perturbations about the unstable state accordingly their asymptotic speedv equals the spreading speed of perturbations whose dynamics is governed by the equations linearized about the unstable state the central result of this paper is the analysis of the convergence of asymptotically uniformly traveling pulled fronts towardsv we show that when such fronts evolve from sufficiently steep initial conditions which initially decay faster than e x forx 1 t hey have auniversal relaxation behavioras timet 1 the velocity of a pulled front always relaxes algebraically like v t d v 3 2t c 3 p d d 2 t 3 2 c o 1 t 2 the parametersv and d are determined through a saddle point analysis from the equation of motion linearized about the unstable invaded state this front velocity is independent of the precise value of the front amplitude which one tracks to measure the front position the interior of the front is essentially slaved to the leading edge and develops universally as x t d8v t x rt dt 0 v t 0 c o 1 t 2 where8v x vt is a uniformly translating front solution with velocity v v our result which can be viewed as a general center manifold result for pulled front propagation is derived in detail for the well known nonlinear diffusion equation of type t d 2 x c 3 where the invaded unstable state is d 0 even for this simple case the subdominant t 3 2 term extends an earlier result of bramson our analysis is then generalized to more general sets of partial differential equations with higher spatial or temporal derivatives to pdes with memory kernels and also to difference equations such as those that occur in numerical finite difference codes our universal result for pulled fronts thus implies independence i of the level curve which is used to track the front position ii of the precise nonlinearities iii of the precise form of the linear operators in the dynamical equation and iv of the precise initial conditions as long as they are sufficiently steep the only remainders of the explicit form of the dynamical equation are the nonlinear solutions 8v and the three saddle point parameters v and d as our simulations confirm all our analytical predictions in every detail it can be concluded that we have a complete analytical understanding of the propagation mechanism and relaxation behavior of pulled fronts if they are uniformly translating for t 1 an immediate consequence of the slow algebraic relaxation is that the standard moving boundary approximation breaks down for weakly curved pulled fronts in two or three dimensions in addition to our main result for pulled fronts we also discuss the propagation and convergence of fronts emerging from

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

universal algebraic relaxation of velocity and phase in pulled fronts generating periodic or chaotic states we investigate the asymptotic relaxation of so called pulled fronts propagating into an unstable state and generalize the universal algebraic velocity relaxation of uniformly translating fronts to fronts that generate periodic or even chaotic states a surprising feature is that such fronts also exhibit a universal algebraic phase relaxation for fronts that generate a periodic state like those in the swift hohenberg equation or in a rayleigh benard experiment this implies an algebraically slow relaxation of the pattern wavelength just behind the front which should be experimentally testable

pattern forming pulled fronts bounds and universal convergence we analyze the dynamics of pattern forming fronts which propagate into an unstable state and whose dynamics is of the pulled type so that their asymptotic speed is equal to the linear spreading speed v we discuss a method that allows to derive bounds on the front velocity and which hence can be used to prove for among others the swift hohenberg equation the extended fisher kolmogorov equation and the cubic complex ginzburg landau equation that the dynamically relevant fronts are of the pulled type in addition we generalize the derivation of the universal power law convergence of the dynamics of uniformly translating pulled fronts to both coherent and incoherent pattern forming fronts the analysis is based on a matching analysis of the dynamics in the leading edge of the front to the behavior imposed by the nonlinear region behind it numerical simulations of fronts in the swift hohenberg equation are in full accord with our analytical predictions

a posteriori finite element bounds for linear functional outputs of elliptic partial differential equations we present a domain decomposition finite element technique for efficiently generating lower and upper bounds to outputs which are linear functionals of the solutions to symmetric or nonsymmetric second order coercive linear partial differential equations in two space dimensions the method is based upon the construction of an augmented lagrangian in which the objective is a quadratic energy reformulation of the desired output and the constraints are the finite element equilibrium equations and intersubdomain continuity requirements the bounds on the output for a suitably fine truth mesh discretization are then derived by appealing to a dual max min relaxation evaluated for optimally chosen adjoint and hybrid flux candidate lagrange multipliers generated by a k element coarser working mesh approximation independent of the form of the original partial differential equation the computation on the truth mesh is reduced to k decoupled subdomain local symmetric neumann problems the technique is illustrated for the convection diffusion and linear elasticity equations

an amplitude finite element formulation for electromagnetic radiation and scattering electromagnetic radiation and scattering in an exterior domain within the context of a finite element method has traditionally involved imposing a suitable absorbing boundary condition on the truncation boundary of the numerical domain to inhibit reflection from it in this work based on the wilcox asymptotic expansion of the electric far field we propose an amplitude formulation within the framework of the nodal finite element method whereby the highly oscillatory radial part of the field is separated out a priori so that the standard lagrange interpolation functions that are used have to capture a relatively gently varying function since these elements can be used in the immediate vicinity of the radiator or scatterer with few exceptions which we enumerate it is more effective compared to methods that impose absorbing boundary conditions at the truncation boundary especially for high frequency problems the proposed method is based on the standard galerkin finite element formulation and uses standard lagrange interpolation functions standard gaussian quadrature and the same degrees of freedom as a conventional formulation we show the effectiveness of the proposed formulation on a wide variety of radiation and scattering problems involving both conducting and dielectric bodies and involving both convex and non convex domains with sharp corners

a three dimensional self adaptive hp finite element method for the characterization of waveguide discontinuities abstract we propose the use of a highly accurate three dimensional 3d fully automatic hp adaptive finite element method fem for the characterization of rectangular waveguide discontinuities these discontinuities are either the unavoidable result of mechanical electrical transitions or deliberately introduced in order to perform certain electrical functions in modern communication systems the proposed numerical method combines the geometrical flexibility of finite elements with an accuracy that is often superior to that provided by semi analytical methods it supports anisotropic refinements on irregular meshes with hanging nodes and isoparametric elements it makes use of hexahedral elements compatible with high order h curl discretizations the 3d hp adaptive fem is applied for the first time to solve a wide range of 3d waveguide discontinuity problems of microwave communication systems in which exponential convergence of the error is observed

a finite volume method for the approximation of maxwell s equations in two space dimensions on arbitrary meshes a new finite volume method is presented for discretizing the two dimensional maxwell equations this method may be seen as an extension of the covolume type methods to arbitrary possibly non conforming or even non convex n sided polygonal meshes thanks to an appropriate choice of degrees of freedom an equivalent formulation of the scheme is given in terms of discrete differential operators obeying discrete duality principles the main properties of the scheme are its energy conservation its stability under a cfl like condition and the fact that it preserves gauss law and divergence free magnetic fields second order convergence is demonstrated numerically on non conforming and distorted meshes

radon transforms and finite type conditions the purpose of this paper is to study averaging operators of radon transform type we shall formulate suitable finite type conditions and prove lp sobolev and lplq estimates the results will be essentially sharp for operators associated with families of curves in the plane let xc and t be smooth manifolds dimx3 nl dim2 nr and let m be a submanifold in xc x t with conormal bundle n m we denote by t the codimension of m we shall always assume that the projections lry m x and 7rt m 42 are surjective with rank dirx nl rank dr9 nr this in particular implies that n m c t x o x t o where 0 refers to the zero sections in t x and t 2 respectively this is the usual assumption for the canonical relation associated with lagrangian distributions arising as kernels of fourier integral operators the assumptions on dirx d7rt imply that for fixed x e x y e 2 the sets amx y e t x y e mi m x ye2x x y em i

an infinite element for maxwell s equations a new infinite element ie approximation for steady state maxwell s equations is proposed the ie is compatible with a new class of hp finite element fe discretizations presented in 13 32 following 12 a convergence analysis for the proposed coupled fe ie approximations is presented

endpoint l p l q estimates for degenerate radon transforms in mathbb r 2 associated with real analytic functions abstract we consider degenerate radon transforms of the form rf t x int mathbb r f t s x y y psi x y dy where psi is supported in a small neighborhood of the origin under the condition that s is real analytic we prove complete l p l q estimates for r

phase accuracy comparisons and improved far field estimates for 3 d edge elements on tetrahedral meshes abstract edge element methods have proved very effective for 3 d electromagnetic computations and are widely used on unstructured meshes however the accuracy of standard edge elements can be criticised because of their low order this paper analyses discrete dispersion relations together with numerical propagation accuracy to determine the effect of tetrahedral shape on the phase accuracy of standard 3 d edge element approximations in comparison to other methods scattering computations for the sphere obtained with edge elements are compared with results obtained with vertex elements and a new formulation of the far field integral approximations for use with edge elements is shown to give improved cross sections over conventional formulations

an hp adaptive finite element method for electromagnetics part 3 a three dimensional infinite element for maxwell s equations this paper is a continuation of reference 26 cecot demkowicz and rachowicz computer methods in applied mechanics and engineering 2000 188 625 643 and describes an implementation of the infinite element for three dimensional time harmonic maxwell s equations proposed in reference 15 demkowicz and pal computer methods in applied mechanics and engineering 1998 164 77 94 the element is compatible with the hp finite element discretizations for maxwell s equations in bounded domains reported in references 16 18 computer methods in applied mechanics and engineering 1998 152 103 124 1999 169 331 344 2000 187 307 337 copyright 2003 john wiley sons ltd

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

adaptive finite element techniques for the maxwell equations using implicit a posteriori error estimates we consider an implicit a posteriori error estimation technique for the adaptive solution of the maxwell equations with nedelec edge finite element methods on three dimensional domains on each element of the tessellation an equation for the error is formulated and solved with a properly chosen local finite element basis the discrete bilinear form of the local problems is shown to satisfy an inf sup condition which ensures the well posedness of the error equations an adaptive solution algorithm is developed based on the obtained error estimates the performance of the method is tested on various problems including non convex domains with non smooth boundaries the numerical results show that the estimated error computed by the implicit a posteriori error estimation technique correlates well with the actual error on the meshes generated adaptively with the help of the error estimator the achieved accuracy is higher than on globally refined meshes with comparable number degrees of freedom moreover the rate of the error convergence on the locally adapted meshes is faster than that on the globally refined meshes

infinite boundary elements for electromagnetics consider a two dimensional plane wave transverse magnetic mode scattering from a perfectly electric conducting ground plane let the ground plane be of infinite extent and comprise two regions a near field and a far field in the far field let the ground plane be flat and let us choose the co ordinates x y such that it lies on the axis y 0 over the interior region let the profile of the ground plane change such that it can lie partially above and also partially below the axis y 0 finally let us assume that the source of the excitation lies above the ground plane to model this general class of problems a method of moments electric field integral equation formulation is proposed which uses infinite boundary elements to model the far field and boundary elements to model the near field in the far field the field variable is approximated by the highest order terms in the far field asymptotic expansion the integrals over the infinite boundary elements are infinite in extent and contain oscillatory terms and hence require special integration rules the formulation is tested for the specific problem of a semi circular cylindrical protrusion of radius a lying above an infinite flat ground plane such that ka 1 where k is the wave number this problem is chosen because it has an analytic solution in the form of a bessel function expansion hence the accuracy of the formulation can be tested in particular the radar cross section results for various angles of incidence of the plane wave source are calculated and compared with analytic results copyright 2007 john wiley sons ltd

the p and h p versions of the finite element method basic principles and properties in the classical form of the finite element method called the hversion piecewise polynomials of fixed degree p are used and the mesh size h is decreased for accuracy in this paper we discuss the fundamental theoretical ideas behind the relatively recent p version and h p version in the p version a fixed mesh is used and p is allowed to increase the h p version combines both approaches the authors describe and explain the basic properties and characteristics of these newer versions especially in areas where their behavior is significantly different from that of the h version simplified proofs of key concepts are included and computational illustrations of several results are provided a benchmark comparison between the various versions in included