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

on the weak monotonicity of gini means and other mixture functions weak monotonicity was recently proposed as a relaxation of the monotonicity condition for averaging aggregation and weakly monotone functions were shown to have desirable properties when averaging data corrupted with outliers or noise we extended the study of weakly monotone averages by analyzing their transforms and we established weak monotonicity of several classes of averaging functions in particular gini means and mixture operators mixture operators with gaussian weighting functions were shown to be weakly monotone for a broad range of their parameters this study assists in identifying averaging functions suitable for data analysis and image processing tasks in the presence of outliers

characterizing compactness of geometrical clusters using fuzzy measures certain tasks in image processing require the preservation of fine image details while applying a broad operation to the image such as image reduction filtering or smoothing in such cases the objects of interest are typically represented by small spatially cohesive clusters of pixels which are to be preserved or removed depending on the requirements when images are corrupted by the noise or contain intensity variations generated by imaging sensors identification of these clusters within the intensity space is problematic as they are corrupted by outliers this paper presents a novel approach to accounting for spatial organization of the pixels and to measuring the compactness of pixel clusters based on the construction of fuzzy measures with specific properties monotonicity with respect to the cluster size invariance with respect to translation reflection and rotation and discrimination between pixel sets of fixed cardinality with different spatial arrangements we present construction methods based on sugeno type fuzzy measures minimum spanning trees and fuzzy measure decomposition we demonstrate their application to generating fuzzy measures on real and artificial images

an iterative solver for p version finite elements in three dimensions abstract a new iterative method for systems arising from p version finite elements is presented and computational experience reported for conforming solid serendipity elements of order up to p 8 and real world structures with 5000 elements and over 1 million degrees of freedom the method uses a domain decomposition technique with each element taken to be a subdomain and a coarse space consisting of p 1 elements to overcome the i o bottleneck only access to a fast matrix vector multiplication instead of stiffness data is needed during iterations in terms of wall clock time the method outperforms on ibm rs 6000 an earlier method running on cray xmp

efficient finite element solvers for the maxwell equations in the frequency domain the present paper shows that certain instabilities encountered with nedelec type finite element implementations of the vector wave equation can be eliminated by a family of lagrange multiplier methods the considered approaches can be interpreted as coupled vector and scalar potential methods including an ungauged formulation we advocate the latter form for use with iterative solvers we discuss an inexpensive high frequency variant of the method and show how hierarchical finite element bases can be utilized to derive efficient partially gauged formulations of higher order based on the multigrid idea a schwartz type solver is constructed which can overcome a major insufficiency of conventional preconditioners

efficient preconditioning for the p version finite element method in two dimensions parallel preconditioners are formulated and analyzed for systems of equations arising from the p version finite element method applied to second order self adjoint elliptic boundary value problems in two dimensions by using new theoretical results for polynomial spaces it is proved that the condition number of the preconditioned system grows as log 2 p where p is the degree of the polynomial space numerical results are presented showing that the condition number indeed grows very slowly with p

improved conditioning of finite element matrices using new high order interpolatory bases the condition number of finite element matrices constructed from interpolatory bases will grow as the polynomial degree of the basis functions is increased the worst case scenario for this growth rate is exponential and in this paper we demonstrate through computational example that the traditional set of uniformly distributed interpolation points yields this behavior we propose a set of nonuniform interpolation points which yield a much improved polynomial growth rate of condition number these points can be used to construct several types of popular hexahedral basis functions including the 0 form standard lagrangian 1 form curl conforming and 2 form divergence conforming varieties we demonstrate through computational example the benefits of using these new interpolatory bases in finite element solutions to maxwell s equations in both the frequency and time domain

on the rate of convergence of the preconditioned conjugate gradient method we derive new estimates for the rate of convergence of the conjugate gradient method by utilizing isolated eigenvalues of parts of the spectrum we present a new generalized version of an incomplete factorization method and compare the derived estimates of the number of iterations with the number actually found for some elliptic difference equations and for a similar problem with a model empirical distribution function

solution of the finite element vector helmholtz equation by means of eigenvalue displacement in this paper after an examination of the spectrum of the system matrix of the discrete vector helmholtz equation a novel technique that makes edge finite element matrices more suitable for lanczos based solvers is introduced this technique works by displacing the eigenvalues related to static modes to a more favorable part of the spectrum the displacement is achieved by means of a matrix that is added to the system matrix

construction of nearly orthogonal nedelec bases for rapid convergence with multilevel preconditioned solvers this paper presents a systematic approach to constructing high order tangential vector basis functions for the multilevel finite element solution of electromagnetic wave problems the new bases allow easy computation of a preconditioner to eliminate or at least weaken the indefiniteness of the system matrix and thus reduce the condition number of the system matrix when these bases are used in multilevel solutions where the multilevels correspond to the order of the basis functions the resulting p multilevel ilu preconditioned conjugate gradient method mpcg provides an optimal rate of convergence we first derive an admissible set of vectors of order p and decompose this set into two subspaces rotational and irrotational gradient we then reduce the number of vectors by making them orthogonal to all previously constructed lower order bases the remaining vectors are made mutually orthogonal in both the vector space and in the range space of the curl operator the resulting vector basis functions provide maximum orthogonality while maintaining tangential continuity of the field the zeroth order space is further decomposed using a scalar vector formulation to eliminate convergence problems at extremely low frequencies numerical experiments show that number of iterations needed for the solution by mpcg is basically constant regardless of the order of the basis or of the matrix size computational speed is improved by several orders of magnitude due to the fast matrix solution of mpcg and to the high accuracy of the higher order bases

de rham diagram for hp finite element spaces abstract we prove that the hp finite elements for h curl spaces introduced in 1 fit into a general de rham diagram involving hp approximations the corresponding interpolation operators generalize the notion of hp interpolation introduced in 2 and are different from the classical operators of nedelec and raviart thomas

convergence of an antidiffusion lagrange euler scheme for quasilinear equations this paper presents an explicit scheme which may be broken into several steps the first one is a transport phase for a time step with a projection on a lagrangian mesh then a new projection is performed on a fixed eulerian mesh lastly a corrected antidiffusion step of the shasta type occurs a stability condition appears to make the scheme easily computable this condition allows larger timesteps than the well known courant friedrichs lewy condition a more complex version of the scheme is proposed which works without any stability condition convergence towards the entropy solution is proved a few numerical experiments are reported showing the quality of the approximation of shocks or giving some information about the precision

aggregation functions based on penalties this article studies a large class of averaging aggregation functions based on minimizing a distance from the vector of inputs or equivalently minimizing a penalty imposed for deviations of individual inputs from the aggregated value we provide a systematization of various types of penalty based aggregation functions and show how many special cases arise as the result we show how new aggregation functions can be constructed either analytically or numerically and provide many examples we establish connection with the maximum likelihood principle and present tools for averaging experimental noisy data with distinct noise distributions

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

a new family of exponential based high order dgtd methods for modeling 3 d transient multiscale electromagnetic problems a new family of exponential based time integration methods are proposed for the time domain maxwell s equations discretized by a high order discontinuous galerkin dg scheme formulated on locally refined unstructured meshes these methods which are developed from the lawson method remove the stiffness on the time explicit integration of the semidiscrete operator associated with the fine part of the mesh and allow for the use of high order time explicit scheme for the coarse part operator they combine excellent stability properties with the ability to obtain very accurate solutions even for very large time step sizes here the explicit time integration of the lawson transformed semidiscrete system relies on a low storage runge kutta lsrk scheme leading to a combined lawson lsrk scheme in addition efficient techniques are presented to further improve the efficiency of this exponential based time integration for the efficient calculation of matrix exponential we employ the krylov subspace method numerical experiments are presented to assess the stability verify the accuracy and numerical convergence of the lawson lsrk scheme they also demonstrate that the dg time domain methods based on the proposed time integration scheme can be much faster than those based on classical fully explicit time stepping schemes with the same accuracy and moderate memory usage increase on locally refined unstructured meshes and are thus very promising for modeling 3 d multiscale electromagnetic problems

construction of image reduction operators using averaging aggregation functions in this work we present an image reduction algorithm based on averaging aggregation functions we axiomatically define the concepts of image reduction operator and local reduction operator we study the construction of the latter by means of averaging functions and we propose an image reduction algorithm image reduction operator we analyze the properties of several averaging functions and their effect on the image reduction algorithm finally we present experimental results where we apply our algorithm in two different applications analyzing the best operators for each concrete application

weak monotonicity of lehmer and gini means we analyze directional monotonicity of several mixture functions in the direction 1 1 1 called weak monotonicity our particular focus is on power weighting functions and the special cases of lehmer and gini means we establish limits on the number of arguments of these means for which they are weakly monotone these bounds significantly improve the earlier results and hence increase the range of applicability of gini and lehmer means we also discuss the case of affine weighting functions and find the smallest constant which ensures weak monotonicity of such mixture functions

higher order interpolatory vector bases for computational electromagnetics low order vector basis functions compatible with the nedelec 1980 representations are widely used for electromagnetic field problems higher order functions are receiving wider application but their development is hampered by the complex procedures used to generate them and lack of a consistent notation for both elements and bases in this paper fully interpolatory higher order vector basis functions of the nedelec type are defined in a unified and consistent manner for the most common element shapes it is shown that these functions can be obtained as the product of zeroth order nedelec representations and interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties of the vector functions are discussed and expressions for the vector functions of arbitrary polynomial order are presented sample numerical results confirm the faster convergence of the higher order functions

multi p preconditioners a class of algebraic multi p methods for solving the p version of the finite element equations is first presented and discussed it is then shown how these multi p methods can be used as preconditioners for the conjugate gradient cg method in particular it is shown that given any preconditioner mp to cg a multi p preconditioner bp based on mp can be constructed which leads to a smaller condition number and hence faster convergence numerical experiments on representative problems indicate that the condition numbers after multi p preconditionings are in fact independent of p the numerical results also show greater efficiency for the preconditioned conjugate gradient pcg method with the multi p preconditioners in terms of number of iterations and cpu time when compared with two sophisticated linear equation solvers 1 a direct frontal solver specially designed for the p version of the finite element analysis 2 a highly tuned pcg code in itpack2c http www netlib org itpack 1994 preliminary comparisons of the number of iterations are also made with rockits solvers international inc boulder co 1994 a new commercial code used for the p version

the problem of selecting the shape functions for a p type finite element abstract the paper addresses the question of the optimal selection of the shape functions for p type finite elements and discusses the effectivity of the conjugate gradient and multilevel iteration method for solving the corresponding linear system the selection of the shape functions is of major importance for the performance of the solver based on iterative methods neither the theory nor practice of the optimal selection of the shape functions is available yet we have seen that the condensation approach which has obvious advantages from the point of parallel computations is a very effective tool for keeping the condition number under the control and is especially advantageous for the conjugate gradient method

stabilizing the hierarchical basis by approximate wavelets ii implementation and numerical results this paper is the second part of a work on stabilizing the classical hierarchical basis hb by using wavelet like basis functions implementation techniques are of major concern for the multilevel preconditioners proposed by the authors in the first part of the work which deals with algorithms and their mathematical theory numerical results are presented to confirm the theory established there a comparison of the performance of a number of multilevel methods is conducted for elliptic problems of three space variables

higher order triangular basis functions and solution performance of the cg method new sets of hierarchical higher order basis functions in fem for triangle elements are constructed using a systematic orthogonalization approach that yield better conditioning and investigated with different preconditioners jacobi icc ilu and sainv presented theoretical and numerical results indicate that certain preconditioners are insensitive to the condition number of the basis functions advantageous properties of basis functions in relation to preconditioners are viewed from the perspective of similarity and congruence transforms of the basis functions this provides an alternative view for a systematic construction of the basis functions that couples with a specific preconditioner to optimize the solution performance

numerical stability for some equations of gas dynamics abstact the isentropic gas dynamics equations in eulerian coordinates are expressed by means of the density p and the momentum q pu instead of the velocity u in order to get domains bounded and invariant in the p q plane for a wide class of pressure lawsp p and in the monodimensional case a numerical scheme of the transport projection type is proposed which builds an approximate solution valued in such a domain since the characteristic speeds are bounded in this set the stability condition is easily fulfilled and then estimates in the lw norm are derived at any time step similar results are extended to the model involving friction and topographical terms and for a simplified model of supersonic flows the nonapplication of this study to the gas dynamics in lagrangian coordinates is shown

nonlinear beam plasma interaction using finite difference methods abstract we study the numerical solution of a hyperbolic system arising from the following physical problem the interaction of a beam of particles and a plasma both being described by a fluid model which are coupled by the poisson equation the equations are solved by lagrangian eulerian anti diffusive techniques combined with an antidifused version of the lax friedrichs scheme in a one dimensional semi infinite system this allows the use of courant numbers well above one an imposed boundary condition for the beam injection allows beam front and neutralisation effects to be described suitably the main physical applicaton as one is concerned with beam radiation is the observation of the saturation of the wave emission by trapping the beam in the wave it excites