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

investigation of nonplanar perfectly matched absorbers for finite element mesh truncation we present a detailed theoretical and numerical investigation of the perfectly matched layer pml concept as applied to the problem of mesh truncation in the finite element method fem we show that it is possible to extend the cartesian pml concepts involving half spaces to cylindrical and spherical geometries appropriate for closed boundaries in two and three dimensions by defining lossy anisotropic layers in the relevant coordinate systems by using the method of separation of variables it is possible to solve the boundary value problems in these geometries the analytical solutions demonstrate that under certain conditions outgoing waves are absorbed with negligible reflection and the transmitted wave is attenuated within the pml to reduce the white space in radiation or scattering problems conformal pmls are constructed via parametric mappings it is also verified that the pml concept which was originally introduced for problems governed by maxwell s equations can be extended to cases governed by the scalar helmholtz equation finally numerical results are presented to demonstrate the use of the pml in fem mesh truncation

markov and semi markov switching of source appearances for nonstationary independent component analysis independent component analysis ica is currently the most popularly used approach to blind source separation bss the problem of recovering unknown source signals when their mixtures are observed but the actual mixing process is unknown many ica algorithms assume that a fixed set of source signals consistently exists in mixtures throughout the time series to be examined however real world signals often have such difficult nonstationarity that each source signal abruptly appears or disappears thus the set of active sources dynamically changes with time in this paper we propose switching ica swica which focuses on such situations the proposed approach is based on the noisy ica formulated as a generative model we employ a special type of hidden markov model hmm to represent such prior knowledge that the source may abruptly appear or disappear with time the special hmm setting then provides an effect of variable selection in a dynamic way we use the variational bayes vb method to derive an effective approximation of bayesian inference for this model in simulation experiments using artificial and realistic source signals the proposed method exhibited performance superior to existing methods especially in the presence of noise the compared methods include the natural gradient ica with a nonholonomic constraint and the existing ica method incorporating an hmm source model which aims to deal with general nonstationarities that may exist in source signals in addition the proposed method could successfully recover the source signals even when the total number of true sources was overestimated or was larger than that of mixtures we also propose a modification of the basic markov model into a semi markov model and show that the semi markov one is more effective for robust estimation of the source appearance

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

parallel processing for the simulation of problems involving scattering of electromagnetic waves abstract the three dimensional simulation of the scattering of electromagnetic waves by obstacles of arbitrary geometrical shape is considered maxwell s curl equations are solved in the time domain on an unstructured mesh of linear tetrahedral elements the discrete equations are formed by a galerkin procedure with a lax wendroff consistent numerical flux function and explicit time stepping parallelisation of the procedure is achieved by mesh decomposition and the use of a single program multiple data model the approach is first validated and is then applied to problems involving the scattering of plane electromagnetic waves by a complete aircraft

overlearning in marginal distribution based ica analysis and solutions the present paper is written as a word of caution with users of independent component analysis ica in mind to overlearning phenomena that are often observed we consider two types of overlearning typical to high order statistics based ica these algorithms can be seen to maximise the negentropy of the source estimates the first kind of overlearning results in the generation of spike like signals if there are not enough samples in the data or there is a considerable amount of noise present it is argued that if the data has power spectrum characterised by 1 f curve we face a more severe problem which cannot be solved inside the strict ica model this overlearning is better characterised by bumps instead of spikes both overlearning types are demonstrated in the case of artificial signals as well as magnetoencephalograms meg several methods are suggested to circumvent both types either by making the estimation of the ica model more robust or by including further modelling of the data

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

a constrained em algorithm for independent component analysis we introduce a novel way of performing independent component analysis using a constrained version of the expectation maximization em algorithm the source distributions are modeled as d one dimensional mixtures of gaussians the observed data are modeled as linear mixtures of the sources with additive isotropic noise this generative model is fit to the data using constrained em the simpler soft switching approach is introduced which uses only one parameter to decide on the sub or supergaussian nature of the sources we explain how our approach relates to independent factor analysis

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner

blind separation of instantaneous mixtures of nonstationary sources most source separation algorithms are based on a model of stationary sources however it is a simple matter to take advantage of possible nonstationarities of the sources to achieve separation this paper develops novel approaches in this direction based on the principles of maximum likelihood and minimum mutual information these principles are exploited by efficient algorithms in both the off line case via a new joint diagonalization procedure and in the on line case via a newton like procedure some experiments showing the good performance of our algorithms and evidencing an interesting feature of our methods are presented their ability to achieve a kind of super efficiency the paper concludes with a discussion contrasting separating methods for non gaussian and nonstationary models and emphasizing that as a matter of fact what makes the algorithms work is strictly speaking not the nonstationarity itself but rather the property that each realization of the source signals has a time varying envelope

nonholonomic orthogonal learning algorithms for blind source separation independent component analysis or blind source separation extracts independent signals from their linear mixtures without assuming prior knowledge of their mixing coefficients it is known that the independent signals in the observed mixtures can be successfully extracted except for their order and scales in order to resolve the indeterminacy of scales most learning algorithms impose some constraints on the magnitudes of the recovered signals however when the source signals are nonstationary and their average magnitudes change rapidly the constraints force a rapid change in the magnitude of the separating matrix this is the case with most applications e g speech sounds electroencephalogram signals it is known that this causes numerical instability in some cases in order to resolve this difficulty this article introduces new nonholonomic constraints in the learning algorithm this is motivated by the geometrical consideration that the directions of change in the separating matrix should be orthogonal to the equivalence class of separating matrices due to the scaling indeterminacy these constraints are proved to be nonholonomic so that the proposed algorithm is able to adapt to rapid or intermittent changes in the magnitudes of the source signals the proposed algorithm works well even when the number of the sources is overestimated whereas the existent algorithms do not assuming the sensor noise is negligibly small because they amplify the null components not included in the sources computer simulations confirm this desirable property

a time domain unstructured grid approach to the simulation of electromagnetic scattering in piecewise homogeneous media abstract the simulation of the scattering of plane electromagnetic waves by obstacles constructed from piecewise homogeneous material media is considered the governing equations are maxwell s equations which are expressed in a conservation form the solution is obtained on a grid consisting of an unstructured assembly of linear triangular elements in 2d by modifying a technique developed originally for the solution of the compressible euler equations the computed solution is used to determine the radar scattering width of the obstacle

mean field approaches to independent component analysis we develop mean field approaches for probabilistic independent component analysis ica the sources are estimated from the mean of their posterior distribution and the mixing matrix and noise level is estimated by maximum a posteriori map the latter requires the computation of a good approximation to the correlations between sources for this purpose we investigate three increasingly advanced mean field methods the variational also known as naive mean field approach linear response corrections and an adaptive version of the thouless anderson and palmer 1977 tap mean field approach which is due to opper and winther 2001 the resulting algorithms are tested on a number of problems on synthetic data the advanced mean field approaches are able to recover the correct mixing matrix in cases where the variational mean field theory fails for handwritten digits sparse encoding is achieved using nonnegative source and mixing priors for speech the mean field method is able to separate in the underdetermined overcomplete case of two sensors and three sources one major advantage of the proposed method is its generality and algorithmic simplicity finally we point out several possible extensions of the approaches developed here

a stitching method for the generation of unstructured meshes for use with co volume solution techniques abstract the successful implementation of co volume time domain solution techniques requires the use of high quality smooth dual meshes the generation of delaunay voronoi diagrams with these properties for two dimensional domains of complicated geometrical shape is considered in the adopted approach near boundary regions are discretised according to prescribed criteria and the remainder of the computational domain is discretised using an ideal mesh the two meshes are stitched together to provide a consistent mesh for the complete domain after smoothing the resulting mesh is found to be of a quality which exceeds that of meshes produced by standard automatic unstructured mesh generation methods examples involving electromagnetic wave scattering are included to demonstrate the computational performance that can be achieved with a co volume time domain solution algorithm on these meshes

hp finite element discretisation of the electrical impedance tomography problem abstract this paper is concerned with the accurate recovery of the permittivity and conductivity from the solution of the electrical impedance tomography eit inverse problem given the knowledge of either the neumann to dirichlet or the dirichlet to neumann map the linearised eit inverse problem for the fourier regime is discretised by hp finite elements which allows the accurate calculation of the sensitivity matrix entries the variational algorithm of knowles 1998 31 is extended to allow the recovery of both material parameters by solution of the eit problem in the laplace regime the associated forward problem is again discretised by hp finite elements a series of numerical results are included to demonstrate the effectiveness of the proposed techniques

hierarchic hp edge element families for maxwell s equations on hybrid quadrilateral triangular meshes we construct and study a set of hierarchic basis functions for the galerkin discretisation of the space h curl 169 suitable for hybrid meshes containing both quadrilateral and triangular elements with arbitrary non uniform order polynomial approximation we investigate the conditioning and dispersive behaviour of the elements in addition numerical examples are shown which demonstrate the accuracy of the space for computing solutions of the time harmonic maxwell s equations that have singularities

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

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

arbitrary order edge elements for electromagnetic scattering simulations using hybrid meshes and a pml the use of arbitrary order edge elements for the simulation of two dimensional electromagnetic scattering problems on hybrid meshes of triangles and quadrilaterals is described single frequency incident waves generated by a source in the far field are considered and the solution is determined in the frequency domain for numerical simulation the solution domain is truncated at a finite distance from the perfectly conducting scatterer and the non reflecting boundary condition at the truncated boundary is imposed by the use of a perfectly matched layer pml several examples are included to demonstrate the performance of the proposed procedure copyright 2002 john wiley sons ltd

variable selection via gibbs sampling abstract a crucial problem in building a multiple regression model is the selection of predictors to include the main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets this procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices in this framework the promising subsets of predictors can be identified as those with higher posterior probability the computational burden is then alleviated by using the gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices those subsets with higher probability the promising ones can then be identified by their more frequent appearance in the gibbs sample

nurbs enhanced finite element method nefem the development of nurbs enhanced finite element method nefem is revisited this technique allows a seamless integration of the cad boundary representation of the domain and the finite element method fem the importance of the geometrical model in finite element simulations is addressed and the benefits and potential of nefem are discussed and compared with respect to other curved finite element techniques

frequency and time domain electromagnetic scattering simulations employing higher order edge elements finite elements are often used for electromagnetic scattering simulations where the main goal is the accurate predicting of the radar cross section or scattering width output edge element discretizations are popular as they are known to eliminate the problems of spurious modes and allow the easy implementation of boundary conditions and material interfaces this work employs a technique which uses higher order edge elements for scattering problems set in both the frequency and time domains in three and two dimensions respectively such approximations are attractive as they are known to give a higher level of accuracy for a given number of degrees of freedom when compared to lower order approximations appropriate solution techniques are proposed for the system of linear equations which arises in each case numerical examples demonstrate the effectiveness of the proposed procedures

mapped spheroidal wave envelope elements for unbounded wave problems this paper describes a family of axisymmetric spheroidal wave envelope elements for modelling exterior wave problems they are of variable radial order and can be used to represent steady and transient wave fields the formulation is presented for the axisymmetric case using elements which are based on oblate and prolate spheroidal geometries these offer the prospect of reduced dimensionality in comparison to conventional spherically formulated elements when used to represent wave fields in the vicinity of slender or flat objects conjugated weighting functions are used to give frequency independent acoustic mass stiffness and damping matrices this facilitates a simple extension of the method to transient problems the effectiveness and accuracy of the method is demonstrated by a comparison of computed and analytic solutions for sound fields generated by a rigid sphere in steady harmonic oscillation by a rigid sphere excited from rest and by a circular plate vibrating in a plane baffle

first passage and first exit times of a bessel like stochastic process we study a stochastic process x t which is a particular case of the rayleigh process and whose square is the bessel process with various applications in physics chemistry biology economics finance and other fields the stochastic differential equation is dx t nd x t dt 2d dw t where w t is the wiener process the drift term can arise from a logarithmic potential or from taking x t as the norm of a multidimensional random walk due to the singularity of the drift term for x t 0 different natures of boundary at the origin arise depending on the real parameter n entrance exit and regular for each of them we calculate analytically and numerically the probability density functions of first passage times or first exit times nontrivial behavior is observed in the case of a regular boundary