a domain decomposition method for the exterior helmholtz problem a new domain decomposition method is presented for the exterior helmholtz problem the nonlocal dirichlet to neumann dtn map is used as a nonreflecting condition on the outer computational boundary the computational domain is divided into nonoverlapping subdomains with sommerfeld type conditions on the adjacent subdomain boundaries to ensure uniqueness an iterative scheme is developed where independent subdomain boundary value problems are obtained by applying the dtn operator to values from the previous iteration the independent problems are then discretized with finite elements and can be solved concurrently numerical results are presented for a two dimensional model problem and both the solution accuracy and convergence rate are investigated

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

generalized belief propagation for the noiseless capacity and information rates of run length limited constraints the performance of the generalized belief propagation algorithm to compute the noiseless capacity and mutual information rates of finite size two dimensional and three dimensional run length limited constraints is investigated in both cases the problem is reduced to estimating the partition function of graphical models with cycles the partition function is then estimated using the region based free energy approximation technique for each constraint a method is proposed to choose the basic regions and to construct the region graph which provides the graphical framework to run the generalized belief propagation algorithm simulation results for the noiseless capacity of different constraints as a function of the size of the channel are reported in the cases that tight lower and upper bounds on the shannon capacity exist convergence to the shannon capacity is discussed for noisy constrained channels simulation results are reported for mutual information rates as a function of signal to noise ratio

short note distinguishing correct from incorrect pml proposals and a corrected unsplit pml for anisotropic dispersive media we show that some previous proposals for perfectly matched layer pml absorbers in anisotropic media or for waveguides at oblique incidence are not in fact true pmls in previous work we similarly showed a failure of several pml proposals for periodic media photonic crystals we therefore argue that a more careful validation scheme is required for pml proposals in contrast to past authors who have typically checked only that reflections are small for a fixed resolution and suggest a simple validation scheme that can be readily applied to any pml proposal regardless of derivation or implementation we demonstrate this test for a corrected unsplit field pml valid for anisotropic dispersive media implemented in both planewave expansion and finite difference time domain fdtd methods

time domain finite difference and finite element methods for maxwell equations in complex media extensions of finite difference time domain fdtd and finite element time domain fetd algorithms are reviewed for solving transient maxwell equations in complex media also provided are a few representative examples to illustrate the modeling capabilities of fdtd and fetd for complex media the term complex media refers here to media with dispersive bi anisotropic inhomogeneous and or nonlinear properties present in the constitutive tensors

laplace transformations of hydrodynamic type systems in riemann invariants periodic sequences the conserved densities of hydrodynamic type systems in riemann invariants satisfy a system of linear second order partial differential equations for linear systems of this type darboux introduced laplace transformations generalizing the classical transformations in the scalar case it is demonstrated that laplace transformations can be pulled back to the transformations of the corresponding hydrodynamic type systems we discuss periodic laplace sequences of hydrodynamic type systems with emphasis on the simplest nontrivial case of period 2 for systems in riemann invariants a complete discription of closed quadruples is proposed they turn out to be related to a special quadratic reduction of the 2 1 dimensional 3 wave system which can be reduced to a triple of pairwise commuting monge ampere equations in terms of the lame and rotation coefficients laplace transformations have a natural interpretation as the symmetries of the dirac operator associated with the 2 1 dimensional n wave system the 2 component laplace transformations can also be interpreted as the symmetries of the 2 1 dimensional integrable equations of davey stewartson type laplace transformations of hydrodynamic type systems originate from a canonical geometric correspondence between systems of conservation laws and line congruences in projective space

some remarks on the stability of time domain electromagnetic simulations aspects of the stability of time domain update schemes for electromagnetic problems are examined based on the consideration of system amplification matrices arising from the discretization of maxwell s equations in the sequence space we discuss time domain stability for a given discretization scale and under three different assumptions of decreasing generality general updates general leapfrog updates and reciprocal leapfrog updates

a comparison of approximate boundary conditions and infinite element methods for exterior helmholtz problems we compare the accuracy of a variety of approximate boundary conditions abcs and two versions of an infinite element method iem for approximating solutions of exterior helmholtz problems the infinite elements are of variable order in the radial direction and differ only in whether the test functions in the weak formulation are conjugated or not we find that the accuracy of the abcs decreases with increasing frequency and that at higher frequencies their accuracy is several orders of magnitude lower than that obtained with the iems we show that the convergence rate of the conjugated element is slower than the rate for the unconjugated element and that the latter element fails to converge in the far field

a pml using a convolutional curl operator and a numerical reflection coefficient for general linear media a general time domain representation of the chew and weedon 1994 stretched coordinate perfectly matched layer pml absorbing boundary condition is described this new approach mathematically operates on the spatial field derivatives and allows the pml update equations to be trivially derived from any set of general linear medium update equations a method for calculating the frequency dependent reflection coefficient for this form of the pml is derived for general linear media two and three dimensional numerical test results which validate the calculation of the reflection coefficient are presented the range of numerical tests include the pml matching of free space a magnetoplasma and a free space waveguide improving the reflection coefficient is examined

kikuchi approximation method for joint decoding of ldpc codes and partial response channels in this letter we apply the kikuchi approximation method to the problem of joint decoding of a low density parity check code and a partial response channel the kikuchi method is in general more powerful than the conventional loopy belief propagation bp algorithm and can produce better approximations to an underlying inference problem we will first review the kikuchi approximation method and the generalized bp algorithm which is an iterative message passing algorithm based on this method we will then report simulation results which show that the kikuchi method outperforms the best conventional iterative method

convergence of the infinite element methods for the helmholtz equation in separable domains to the best knowledge of the authors this work presents the first convergence analysis for the infinite element method iem for the helmholtz equation in exterior domains the approximation applies to separable geometries only combining an arbitrary finite element fe discretization on the boundary of the domain with a spectral like approximation in the radial direction with shape functions resulting from the separation of variables the principal idea of the presented analysis is based on the spectral decomposition of the problem

improved conditioning of infinite elements for exterior acoustics an optimized version of the so called mapped wave envelope elements also known as astley leis elements is introduced these elements extend to infinity in one dimension and therefore provide an approach to the simulation of exterior acoustical problems in both frequency and time domains their formulation is improved significantly through the proper choice of polynomial bases in the direction of radiation in particular certain jacobi polynomials are identified which behave well with respect to conditioning of the system matrices as a consequence the size of the finite element discretization may reduce considerably without any loss of accuracy in addition the new polynomial bases lead to superior performance of the infinite elements in conjunction with iterative solvers

a general approach to extend berenger s absorbing boundary condition to anisotropic and dispersive media previous studies have focused on the extension of the berenger s 1994 absorbing boundary condition abc the perfectly matched layer pml to anisotropic and dispersive media we describe how the pml can be extended for anisotropic and or dispersive media or even bianisotropic media with little analytical effort in a simple and general conceptual setting by using an analytical continuation of the coordinate space of the maxwell s equations to a complex variables domain using this approach there is no conceptual distinction between the derivation of pml for more complex media and the derivation for isotropic dispersionless media

on the pollution effect in fe solutions of the 3d helmholtz equation we study convergence of the fem for a 3d problem of rigid scattering using separation of variables analytical results are presented for stability and error estimation for an h version galerkin fem with mesh refinement in radial direction we prove an upper bound that contains a pollution term similar to previous results in 1d and 2d this estimate is evaluated computationally using a 3d fem iem infinite elements implementation the tabulated and plotted errors show the theoretically predicted pollution effect in the fe error

nearly h1 optimal finite element methods abstract we examine the problem of finding the h 1 projection onto a finite element space of an unknown field satisfying a specified boundary value problem solving the projection problem typically requires knowing the exact solution we circumvent this issue and obtain a petrov galerkin formulation which achieves h 1 optimality requiring weighting functions to be defined locally on the element level permits only approximate h 1 optimality in multi dimensional configurations we investigate the relation between our formulation and other stabilized fem formulations we show in particular that our formulation leads to a derivation of the supg method in special cases the present formulation reduces to that of residual free bubbles finally we present guidelines for obtaining the petrov weight functions and include a numerical example for the helmholtz equation

perturbation theory for anisotropic dielectric interfaces and application to subpixel smoothing of discretized numerical methods we derive a correct first order perturbation theory in electromagnetism for cases where an interface between two anisotropic dielectric materials is slightly shifted most previous perturbative methods give incorrect results for this case even to lowest order because of the complicated discontinuous boundary conditions on the electric field at such an interface our final expression is simply a surface integral over the material interface of the continuous field components from the unperturbed structure the derivation is based on a localized coordinate transformation technique which avoids both the problem of field discontinuities and the challenge of constructing an explicit coordinate transformation by taking the limit in which the coordinate perturbation is infinitesimally localized around the boundary not only is our result potentially useful in evaluating boundary perturbations e g from fabrication imperfections in highly anisotropic media such as many metamaterials but it also has a direct application in numerical electromagnetism in particular we show how it leads to a subpixel smoothing scheme to ameliorate staircasing effects in discretized simulations of anisotropic media in such a way as to greatly reduce the numerical errors compared to other proposed smoothing schemes

boundary conditions for the numerical solution of elliptic equations in exterior regions elliptic equations in exterior regions frequently require a boundary condition at infinity to ensure the weill posedness of the problem examples of practical applications include the helmholtz equation and laplace s equation computational procedures based on a direct discretization of the elliptic problem require the replacement of the condition at infinity by a boundary condition on a finite artificial surface direct imposition of the condition at infinity along the finite boundary results in large errors a sequence of boundary conditions is developed which provides increasingly accurate approximations to the problem in the infinite domain estimates of the error due to the finite boundary are obtained for several cases computations are presented which demonstrate the increased accuracy that can be obtained by the use of the higher order boundary conditions the examples are based on a finite element formulation but finite difference methods can also be used

a stable fdtd algorithm for non diagonal anisotropic dielectrics a stable fdtd algorithm is developed for simulating maxwell s equations in anisotropic dielectric materials with principal axes not aligned with the grid the algorithm is stable because the finite difference operator that converts d to e is symmetric and positive semidefinite for contrast a previously developed asymmetric algorithm is shown to suffer from late time instabilities the presented algorithm has second order error for continuous dielectric materials and the error can be reduced to third order by richardson extrapolation applied to dielectrics with sharp interfaces the algorithm has first order error even when averaging the dielectric within partially filled grid cells however averaging the dielectric permits richardson extrapolation to obtain second order error

pointwise theorems for amenable groups in this paper we prove the pointwise ergodic theorem for general locally compact amenable groups along folner sequences that obey some restrictions these restrictions are mild enough so that such sequences exist for all amenable groups we also prove a generalization of the shannon mcmillan breiman theorem to all discrete amenable groups

mimo detection for high order qam based on a gaussian tree approximation this paper proposes a new detection algorithm for mimo communication systems employing high order qam constellations the factor graph that corresponds to this problem is very loopy in fact it is a complete graph hence a straightforward application of the belief propagation bp algorithm yields very poor results our algorithm is based on an optimal tree approximation of the gaussian density of the unconstrained linear system the finite set constraint is then applied to obtain a cycle free discrete distribution simulation results show that even though the approximation is not directly applied to the exact discrete distribution applying the bp algorithm to the cycle free factor graph outperforms current methods in terms of both performance and complexity the improved performance of the proposed algorithm is demonstrated on the problem of mimo detection

fast direct solution of the helmholtz equation with a perfectly matched layer or an absorbing boundary condition we consider the efficient numerical solution of the helmholtz equation in a rectangular domain with a perfectly matched layer pml or an absorbing boundary condition abc standard bilinear trilinear finite element discretization on an orthogonal mesh leads to a separable system of linear equations for which we describe a cyclic reduction type fast direct solver we present numerical studies to estimate the reflection of waves caused by an absorbing boundary and a pml and we optimize certain parameters of the layer to minimize the reflection copyright 2003 john wiley sons ltd

simulation based computation of information rates for channels with memory the information rate of finite state source channel models can be accurately estimated by sampling both a long channel input sequence and the corresponding channel output sequence followed by a forward sum product recursion on the joint source channel trellis this method is extended to compute upper and lower bounds on the information rate of very general channels with memory by means of finite state approximations further upper and lower bounds can be computed by reduced state methods

a parameter free perfectly matched layer formulation for the finite element based solution of the helmholtz equation this paper presents a parameter free perfectly matched layer pml method for the finite element based solution of the helmholtz equation we employ one of bermudez et al s unbounded absorbing functions for the complex coordinate mapping underlying the pml with this choice the only free parameter that controls the accuracy of the numerical solution for a fixed numerical cost characterised by the number of elements in the bulk and the pml regions is the thickness of the perfectly matched layer pml we show that for the case of planar waves the absorbing function performs best for pmls whose thickness is much smaller than the wavelength we then perform extensive numerical experiments to explore its performance for non planar waves considering domain shapes with smooth and polygonal boundaries different solution types smooth and singular and a wide range of wavenumbers k to identify an optimal range for the normalised pml thickness k pml such that within this range the error introduced by the presence of the pml is consistently small and insensitive to change this implies that if the pml thickness is chosen from within this range no further pml optimisation is required i e the method is parameter free we characterise the dependence of the error on the discretisation parameters and establish the conditions under which the convergence of the solution under mesh refinement is controlled exclusively by the discretisation of the bulk mesh bermudez et al s type a pml damping function performs best for k pml 1 extensive numerical experiments reveal an optimal range of pml thicknesses i opt for k pml i opt the error is small and insensitive to change choosing k pml from anywhere within i opt yields a parameter free pml method

locally conformal fdtd for anisotropic conductive interfaces locally conformal discretizations have been developed for the finite difference time domain fdtd method to mitigate staircasing errors that arise in the modeling of arbitrary e g curved slanted interfaces by regular orthogonal grids in particular locally conformal algorithms based on the computation of effective material parameters in partially filled fdtd cells are attractive because they are simple to implement and maintain the basic conditional stability of fdtd with only minor changes on the courant limit in this paper we propose a new locally conformal implementation for fdtd tailored for anisotropic conductive interfaces instead of employing arithmetic or geometrical averages we invoke the quasi static relationship between the current density and the electric field to derive the effective conductivities of partially filled fdtd cells

a survey of finite element methods for time harmonic acoustics many of the current issues and methodologies related to finite element methods for time harmonic acoustics are reviewed the effective treatment of unbounded domains is a major challenge most prominent among the approaches that have been developed for this purpose are absorbing boundary conditions infinite elements and absorbing layers standard computational methods are unable to cope with wave phenomena at short wave lengths due to resolutions required to control dispersion and pollution errors leading to prohibitive computational demands since computation naturally separates the scales of a problem according to the mesh size multiscale considerations provide a useful framework for viewing these difficulties and developing methods to counter them other issues addressed are related to the efficient solution of systems of specialized algebraic equations and inverse problems of acoustics the tremendous progress that has been made in all of the above areas in recent years will surely continue leading to many more exciting developments

constructing free energy approximations and generalized belief propagation algorithms important inference problems in statistical physics computer vision error correcting coding theory and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs the belief propagation bp algorithm is an efficient way to solve these problems that is exact when the factor graph is a tree but only approximate when the factor graph has cycles we show that bp fixed points correspond to the stationary points of the bethe approximation of the free energy for a factor graph we explain how to obtain region based free energy approximations that improve the bethe approximation and corresponding generalized belief propagation gbp algorithms we emphasize the conditions a free energy approximation must satisfy in order to be a valid or maxent normal approximation we describe the relationship between four different methods that can be used to generate valid approximations the bethe method the junction graph method the cluster variation method and the region graph method finally we explain how to tell whether a region based approximation and its corresponding gbp algorithm is likely to be accurate and describe empirical results showing that gbp can significantly outperform bp

on the numerical solution of the three dimensional inverse obstacle scattering problem abstract the inverse problem under consideration is to determine the shape of an impenetrable sound soft obstacle from the knowledge of a time harmonic incident plane acoustic wave and far field or near field measurements of the scattered wave we present a method for the approximate solution which avoids the solution of the corresponding direct problem and stabilizes the ill posed inverse problem by reformulating it as a nonlinear optimization problem the numerical implementation of the method is described and some three dimensional examples of reconstructions are given

the three dimensional inverse scattering problem for acoustic waves abstract we consider the inverse scattering problem for an acoustically soft obstacle in r 3 by assuming a priori that the unknown scattering obstacle is starlike and has its boundary lying in a compact family of holder continuously differentiable surfaces it is shown that an optimal solution can be constructed which depends continuously on the measured far field data remarks are made on the numerical approximation of the optimal solution

recent developments in inverse acoustic scattering theory we survey some of the highlights of inverse scattering theory as it has developed over the last 15 years with emphasis on uniqueness theorems and reconstruction algorithms for time harmonic acoustic waves included in our presentation are numerical experiments using real data and numerical examples of the use of inverse scattering methods to detect buried objects

perfectly matched layers for transient elastodynamics of unbounded domains one approach to the numerical solution of a wave equation on an unbounded domain uses a bounded domain surrounded by an absorbing boundary or layer that absorbs waves propagating outward from the bounded domain a perfectly matched layer pml is an unphysical absorbing layer model for linear wave equations that absorbs almost perfectly outgoing waves of all non tangential angles of incidence and of all non zero frequencies in a recent work computer methods in applied mechanics and engineering 2003 192 1337 1375 the authors presented inter alia time harmonic governing equations of pmls for anti plane and for plane strain motion of visco elastic media this paper presents a corresponding time domain displacement based governing equations of these pmls and b displacement based finite element implementations of these equations suitable for direct transient analysis the finite element implementation of the anti plane pml is found to be symmetric whereas that of the plane strain pml is not numerical results are presented for the anti plane motion of a semi infinite layer on a rigid base and for the classical soil structure interaction problems of a rigid strip footing on i a half plane ii a layer on a half plane and iii a layer on a rigid base these results demonstrate the high accuracy achievable by pml models even with small bounded domains

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

finite difference time domain modeling of curved surfaces em scattering the finite difference time domain fdtd method is generalized to include the accurate modeling of curved surfaces this generalization the contour path cp method accurately models the illumination of bodies with curved surfaces yet retains the ability to model corners and edges cp modeling of two dimensional electromagnetic wave scattering from objects of various shapes and compositions is presented

on the solution of a class of large body problems with full or partial circular symmetry by using the finite difference time domain fdtd method this paper presents an efficient method to accurately solve large body scattering problems with partial circular symmetry the method effectively reduces the computational domain from three to two dimensions by using the reciprocity theorem it does so by dividing the problem into two parts a larger 3 d region with circular symmetry and a smaller 2 d region without circular symmetry an finite difference time domain fdtd algorithm is used to analyze the circularly symmetric 3 d case while a method of moments mom code is employed for the nonsymmetric part of the structure the results of these simulations are combined via the reciprocity theorem to yield the radiation pattern of the composite system the advantage of this method is that it achieves significant savings in computer storage and run time in performing an equivalent 2 d as opposed to a full 3 d fdtd simulation in addition to enhancing computational efficiency the fdtd algorithm used in this paper also features one improvement over conventional fdtd methods a conformal approach for improved accuracy in modeling curved dielectric and conductive surfaces the accuracy of the method is validated via a comparison of simulated and measured results

a generalized finite element method for solving the helmholtz equation in two dimensions with minimal pollution when using the galerkin fem for solving the helmholtz equation in two dimensions the error of the corresponding solution differs substantially from the error of the best approximation and this effect increases with higher wave number k in this paper we will design a generalized finite element method gfem for the helmholtz equation such that the pollution effect is minimal

shannon theoretic approach to a gaussian cellular multiple access channel we obtain shannon theoretic limits for a very simple cellular multiple access system in our model the received signal at a given cell site is the sum of the signals transmitted from within that cell plus a factor spl alpha 0 spl les spl alpha spl les 1 times the sum of the signals transmitted from the adjacent cells plus ambient gaussian noise although this simple model is scarcely realistic it nevertheless has enough meat so that the results yield considerable insight into the workings of real systems we consider both a one dimensional linear cellular array and the familiar two dimensional hexagonal cellular pattern the discrete time channel is memoryless we assume that n contiguous cells have active transmitters in the one dimensional case and that n sup 2 contiguous cells have active transmitters in the two dimensional case there are k transmitters per cell most of our results are obtained for the limiting case as n spl rarr spl infin the results include the following 1 we define c sub n c spl circ sub n as the largest achievable rate per transmitter in the usual shannon theoretic sense in the one and two dimensional cases respectively assuming that all signals are jointly decoded we find expressions for limn spl rarr spl infin c sub n and limn spl rarr spl infin c spl circ sub n 2 as the interference parameter spl alpha increases from 0 c sub n and c spl circ sub n increase or decrease according to whether the signal to noise ratio is less than or greater than unity 3 optimal performance is attainable using tdma within the cell but using tdma for adjacent cells is distinctly suboptimal 4 we suggest a scheme which does not require joint decoding of all the users and is in many cases close to optimal

on the symmetric information rate of two dimensional finite state isi channels we derive a pair of bounds upper and lower on the symmetric information rate of a two dimensional finite state intersymbol interference isi channel model for channels with small impulse response support they can be estimated via a modified forward recursion of the bahl cocke jelinek raviv bcjr algorithm the convergence of the bounds is also analyzed to relax the constraint on the size of the impulse response a new upper bound is proposed which allows the tradeoff of the computational complexity and the tightness of the bound these bounds are further extended to d dimensional d 2 isi channels

markov processes asymptotically achieve the capacity of finite state intersymbol interference channels recent progress in capacity evaluation has made it possible to compute a sequence of lower bounds on the capacity of a finite state intersymbol interference isi channel by finding a sequence of optimized markov input processes with increasing order for which the state of the process is the previous input symbols in this correspondence we prove that as the order goes to infinity the sequence of optimized markov sources asymptotically achieves the capacity of the channel the conclusion is extended to two dimensional finite state isi channels the binary symmetric channel bsc with constrained inputs and general indecomposable finite state channels with a mild constraint

application of an ultra weak variational formulation of elliptic pdes to the two dimensional helmholtz problem a new technique to solve elliptic linear pdes called ultra weak variational formulation uwvf in this paper is introduced in b despres c r acad sci paris 318 1994 pp 939 944 this paper is devoted to an evaluation of the potentialities of this technique it is applied to a model wave problem the two dimensional helmholtz problem the new method is presented in three parts following the same style of presentation as the classical one of the finite elements method even though they are definitely conceptually different methods the first part is committed to the variational formulation and to the continuous problem the second part defines the discretization process using a galerkin procedure the third part actually studies the efficiency of the technique from the order of convergence point of view this is achieved using theoretical proofs and a series of numerical experiments in particular it is proven and shown the order of convergence is lower bounded by a linear function of the number of degrees of freedom an application to scattering problems is presented in a fourth part

the intersymbol interference channel lower bounds on capacity and channel precoding loss the discrete time additive gaussian intersymbol interference isi channel with i i d not necessarily gaussian input signals is considered several new and old lower bounds on the capacity are derived in a unified manner by assuming different front end receiver filters in particular the sampled whitened matched filter swmf and the minimum mean squared error decision feedback equalizer mmse dfe filter the features of the bounds are demonstrated and compared in several examples with binary and quaternary input signals it is also shown that the effect of an ideal post cursor or tail cancellation in an information preserving context depends primarily on the front end filter while as is well known ideal post cursor cancellation at the output of the swmf decreases the information the opposite trend is seen when an mmse dfe front filter is considered this observation reflects the basic theoretical obstacles in precoding i e ideal post cursor cancellation in the presence of a pre cursor it is used to assess the inherent loss in terms of information rates as compared to the rates achievable with the hypothetical ideal post cursor cancellation associated with any post cursor cancellation technique such as precoding dfe or other variants when operating in synergy with the mmse dfe front end filter the effect of the front end filter on an ideally interleaved precoded coded modulation system is also addressed

a residual based finite element method for the helmholtz equation a new residual based finite element method for the scalar helmholtz equation is developed this method is obtained from the galerkin approximation by appending terms that are proportional to residuals on element interiors and inter element boundaries the inclusion of residuals on inter element boundaries distinguishes this method from the well known galerkin least squares method and is crucial to the resulting accuracy of this method in two dimensions and for regular bilinear quadrilateral finite elements it is shown via a dispersion analysis that this method has minimal phase error numerical experiments are conducted to verify this claim as well as test and compare the performance of this method on unstructured meshes with other methods it is found that even for unstructured meshes this method retains a high level of accuracy copyright 2000 john wiley sons ltd

an improved thin wire representation for fdtd computations we have shown that finite difference time domain fdtd electromagnetic computations for a conductor system having a radius smaller than 0 15deltar or larger than 0 65 deltar deltar is the lateral side length of cells employed modeled using arbitrary radius wire representations proposed so far with a time increment determined from the upper limit of courant s stability condition result in numerical instability a primary factor causing this numerical instability is that the speed of waves propagating in the radial direction from the wire in the immediate vicinity of the wire exceeds the speed of light and therefore courant s condition is not satisfied there it is further shown that for these cases the arbitrary radius wire representation can be improved by modifying the material parameters for the axial field components closest to the wire as well as those for the radial electric and circulating magnetic field components the improved wire representation is effective in representing a wire whose radius ranges from 0 0001deltar to 0 9deltar

the design and analysis of the generalized finite element method abstract in this paper we introduce the generalized finite element method gfem as a combination of the classical finite element method fem and the partition of unity method pum the standard finite element spaces are augmented by adding special functions which reflect the known information about the boundary value problem and the input data e g the singular functions obtained from the local asymptotic expansion of the exact solution in the neighborhood of a corner point etc the special functions are multiplied with the partition of unity corresponding to the standard linear vertex shape functions and pasted together with the existing finite element basis to construct an augmented conforming finite element space in this way the local approximability afforded by the special functions is included in the approximation while maintaining the existing infrastructure of finite element codes the major features of the gfem are 1 the essential boundary conditions can be imposed exactly as in the standard fem unlike other partition of unity based methods where this is a major issue 2 the accuracy of the numerical integration of the entries of the stiffness matrix and load vector is controlled adaptively so that the errors in integration of the special functions do not affect the accuracy of the constructed approximation this issue also has not been sufficiently addressed in other implementations of partition of unity or meshless methods and 3 linear dependencies in the system of equations are resolved by employing an easy modification of the direct linear solver the power of the gfem for solving problems in domains with complex geometry with less error and less computer resources than the standard fem is illustrated by numerical examples

reduction restrictions of darboux and laplace transformations for the goursat equation we study darboux and laplace transformations of the solutions and potentials of the goursat equation which is equivalent to one of the lax pair equations for the 2d mkdv hierarchy the reduction restrictions for these transformations are considered the derived reduction equations are generalizations of the liouville and sinh gordon equation the integrability of these equations by the st method is proved the binary darboux transformation for the goursat equation is suggested we find exact rational nonsingular solutions of the 2d mkdv equations via the moutard transformation for the goursat equation

lattice electromagnetic theory from a topological viewpoint the language of differential forms and topological concepts are applied to study classical electromagnetic theory on a lattice it is shown that differential forms and their discrete counterparts cochains provide a natural bridge between the continuum and the lattice versions of the theory allowing for a natural factorization of the field equations into topological field equations i e invariant under homeomorphisms and metric field equations the various potential sources of inconsistency in the discretization process are identified distinguished and discussed a rationale for a consistent extension of the lattice theory to more general situations such as to irregular lattices is considered

bubble functions prompt unusual stabilized finite element methods a second order linear scalar differential equation including a zero th order term is approximated using first the standard galerkin method enriched with bubble functions static condensation of the bubbles suggest an unusual stabilized finite element method for which we establish a convergence study and obtain successful numerical simulations the method is generalized to allow for a convection operator in the equation this work may be employed as a starting point for simulation of nonlinear equations governing turbulence phenomena flows with chemical reactions and other important problems

the performance of spheroidal infinite elements a number of spheroidal and ellipsoidal infinite elements have been proposed for the solution of unbounded wave problems in the frequency domain i e solutions of the helmholtz equation these elements are widely believed to be more effective than conventional spherical infinite elements in cases where the radiating or scattering object is slender or flat and can therefore be closely enclosed by a spheroidal or an ellipsoidal surface the validity of this statement is investigated in the current article the radial order which is required for an accurate solution is shown to depend strongly not only upon the type of element that is used but also on the aspect ratio of the bounding spheroid and the non dimensional wave number the nature of this dependence can partially be explained by comparing the non oscillatory component of simple source solutions to the terms available in the trial solution of spheroidal elements numerical studies are also presented to demonstrate the rates at which convergence can be achieved in practice by unconjugated burnett and conjugated astley leis type elements it will be shown that neither formulation is entirely satisfactory at high frequencies and high aspect ratios

optimum estimation via gradients of partition functions and information measures a statistical mechanical perspective in continuation to a recent work on the statistical mechanical analysis of minimum mean square error mmse estimation in gaussian noise via its relation to the mutual information the i mmse relation here we propose a simple and more direct relationship between optimum estimation and certain information measures e g the information density and the fisher information which can be viewed as partition functions and hence are amenable to analysis using statistical mechanical techniques the proposed approach has several advantages most notably its applicability to general sources and channels as opposed to the i mmse relation and its variants which hold only for certain classes of channels e g additive white gaussian noise channels we then demonstrate the derivation of the conditional mean estimator and the mmse in a few examples two of these examples turn out to be generalizable to a fairly wide class of sources and channels for this class the proposed approach is shown to yield an approximate conditional mean estimator and an mmse formula that has the flavor of a single letter expression we also show how our approach can easily be generalized to situations of mismatched estimation

a fast method for solving acoustic scattering problems in frequency bands abstract we present a methodology for computing efficiently scattered fields in a frequency band the main feature of this methodology is the construction of a series of discrete problems that differ only by their right hand sides rather than by both their left and right hand sides its key steps are a the reformulation of the acoustic scattering problem in a bounded domain using any preferred absorbing boundary condition b the characterization of the repeated derivatives with respect to the frequency of the scattered field as solutions of scattering type problems with different source terms and boundary conditions and c the reconstruction of a scattered field by either the pade approximants or wynn s algorithm we report on several multifrequency acoustic scattering examples that illustrate the accuracy and computational efficiency of the proposed solution methodology

perfectly matched layers for time harmonic elastodynamics of unbounded domains theory and finite element implementation abstract one approach to the numerical solution of a wave equation on an unbounded domain uses a bounded domain surrounded by an absorbing boundary or layer that absorbs waves propagating outwards from the bounded domain a perfectly matched layer pml is an unphysical absorbing layer model for linear wave equations that absorbs almost perfectly outgoing waves of all non tangential angles of incidence and of all non zero frequencies this paper develops the pml concept for time harmonic elastodynamics in cartesian coordinates utilising insights obtained with electromagnetics pmls and presents a novel displacement based symmetric finite element implementation of the pml for time harmonic plane strain or three dimensional motion the pml concept is illustrated through the example of a one dimensional rod on elastic foundation and through the anti plane motion of a two dimensional continuum the concept is explored in detail through analytical and numerical results from a pml model of the semi infinite rod on elastic foundation and through numerical results for the anti plane motion of a semi infinite layer on a rigid base numerical results are presented for the classical soil structure interaction problems of a rigid strip footing on a i half plane ii layer on a half plane and iii layer on a rigid base the analytical and numerical results obtained for these canonical problems demonstrate the high accuracy achievable by pml models even with small bounded domains

mutual information and minimum mean square error in gaussian channels this paper deals with arbitrarily distributed finite power input signals observed through an additive gaussian noise channel it shows a new formula that connects the input output mutual information and the minimum mean square error mmse achievable by optimal estimation of the input given the output that is the derivative of the mutual information nats with respect to the signal to noise ratio snr is equal to half the mmse regardless of the input statistics this relationship holds for both scalar and vector signals as well as for discrete time and continuous time noncausal mmse estimation this fundamental information theoretic result has an unexpected consequence in continuous time nonlinear estimation for any input signal with finite power the causal filtering mmse achieved at snr is equal to the average value of the noncausal smoothing mmse achieved with a channel whose snr is chosen uniformly distributed between 0 and snr

optimizing the perfectly matched layer the berenger perfectly matched layer or pml 4 3 is used in computational electromagnetism as a sponge layer to terminate finite element approximations of scattering problems an infinite perfectly matched layer creates no reflection for incident waves of any frequency or any incident direction and the waves decay exponentially in magnitude into the layer this property is lost when the layer is truncated since the truncation boundary generates a reflected wave discretization of the differential equations further changes the reflection coefficient of the layer in this talk we shall describe the pml in the simple case of a two dimensional electromagnetic problem the first part of this abstract is expository we shall show how to derive the layer using a change of variable approach 5 9 6 after this derivation we describe some new analysis to show the effects of truncating and discretizing the pml 9 we end by showing how to compute an optimal layer and make some remarks about pml for the full maxwell system

a statistical mechanics approach to large system analysis of cdma multiuser detectors we present a theory based on statistical mechanics to evaluate analytically the performance of uncoded fully synchronous randomly spread code division multiple access cdma multiuser detectors with additive white gaussian noise awgn channel under perfect power control and in the large system limit application of the replica method a tool developed in the literature of statistical mechanics allows us to derive analytical expressions for the bit error rate as well as the multiuser efficiency of the individually optimum io and jointly optimum jo multiuser detectors over the whole range of noise levels the information theoretic capacity of the randomly spread cdma channel and the performance of decorrelating and linear minimum mean square error mmse detectors are also derived in the same replica formulation thereby demonstrating validity of the statistical mechanical approach

higher dimensional darboux transformations abstract we give conditions for a first order partial differential operator to serve as an n dimensional darboux transformation between two second order partial differential operators we show that some of these conditions are given by first order nonlinear partial differential equations which may be solved using the method of characteristics we also discuss the well known example of the boiti leon pempinelli equation and some others

conformal fdtd methods to avoid time step reduction with and without cell enlargement during the last decades there have been considerable efforts to develop accurate and yet simple conformal methods for modelling curved boundaries within the finite difference time domain fdtd algorithm in an earlier publication we proposed the uniformly stable conformal usc approach as a general three dimensional extension of fdtd without the need to reduce the maximum stable time step the main idea of usc is the usage of virtually enlarged cells near to the boundary leading to an increased implementation effort in this paper we review the usc method and introduce a new simple and accurate conformal scheme which does not use such enlarged cells this simplified conformal sc scheme has the same number of operations and algorithmic logic as the standard staircase method and thus is easily realizable in existing fdtd codes like usc it leads to accurate results without time step reduction showing a nearly second order convergence in practice the method is verified and compared to other approaches by means of several numerical 2d and 3d examples

mapped wave envelope elements for acoustical radiation and scattering wave envelope elements provide an alternative to boundary element methods for the solution of exterior wave problems applications to date have been to axisymmetric geometries and have involved the use of large but finite wave envelope meshes compatibly matched to denser near field meshes of conventional elements in the present paper the wave envelope idea is extended by the inclusion of an element mapping taken directly from infinite element methodology and by modifications to the residual formulation taken in conjunction these two measures permit the outer boundary of the wave envelope region to be moved to infinity while preserving the boundedness of the acoustic mass and stiffness integrals the present formulation is developed initially with reference to a simple one dimensional model and is then applied in two and three dimensions comparisons between computed results and those obtained from analytic solutions where applicable and from boundary element codes demonstrate the effectiveness of the method

low frequency finite difference time domain modeling of a pec sphere based on a quasi analytical coupled dipole approximation a computational formulation is presented for the low frequency single cell finite difference time domain fdtd modeling of a perfectly electric conducting pec sphere the approach is based on the fact that the scattered field from electrically small objects can be expressed in terms of an electric and magnetic dipole these dipoles can be decomposed with respect to the dipole moments that can be defined along the discrete field components that comprise the cell wherein the pec sphere is inscribed the dipole moment components couple to each other and this mechanism is quantified by a quasi analytical coupled dipole approximation cda the quasi analyticity requires to substitute the involved dyadic green s function dgf terms in the cda formula by their numerically computed fdtd compatible equivalents the material properties of the equivalent electric and magnetic spheres are derived using the quasi analytical cda that leads to expressions that resemble the claussius mossotti mixing formula the theoretically derived results are supported by numerical simulations

on accuracy conditions for the numerical computation of waves abstract the helmholtz equation k 2 n 2 u f with a variable index of refraction n and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems such problems can be solved numerically by first truncating the given unbounded domain imposing a suitable outgoing radiation condition on an artificial boundary and then solving the resulting problem on the bounded domain by direct discretization for example using a finite element method in practical applications the mesh size h and the wave number k are not independent but are constrained by the accuracy of the desired computation it will be shown that the number of points per wavelength measured by kh 1 is not sufficient to determine the accuracy of a given discretization for example the quantity k 3 h 2 is shown to determine the accuracy in the l 2 norm for a second order discretization method applied to several propagation models

a two level domain decomposition method for the iterative solution of high frequency exterior helmholtz problems summary we present a lagrange multiplier based two level domain decomposition method for solving iteratively large scale systems of equations arising from the finite element discretization of high frequency exterior helmholtz problems the proposed method is essentially an extension of the regularized feti finite element tearing and interconnecting method to indefinite problems its two key ingredients are the regularization of each subdomain matrix by a complex interface lumped mass matrix and the preconditioning of the interface problem by an auxiliary coarse problem constructed to enforce at each iteration the orthogonality of the residual to a set of carefully chosen planar waves we show numerically that the proposed method is scalable with respect to the mesh size the subdomain size and the wavenumber we report performance results for a submarine application that highlight the efficiency of the proposed method for the solution of high frequency acoustic scattering problems discretized by finite elements

on an improved unusual stabilized finite element method for theadvective reactive diffusive equation an improved unusual finite element method is studied herein for a second order linear scalar differential equation including a zero order term the method consists in subtracting from the standard galerkin method a mesh dependent term suggested by static condensation of the bubbles based on this idea a new stabilized parameter is constructed which improves accuracy of the solution several numerical tests attest the efficiency of the present method and an error analysis is perfomed

an ellipsoidal acoustic infinite element abstract in previous papers the authors presented new 3 d time harmonic prolate and oblate spheroidal acoustic infinite elements based on new prolate and oblate spheroidal multipole expansions for modeling acoustic fields in unbounded domains here we present the development of an ellipsoidal infinite element which is the logical generalization of those elements this development is also based on a new multipole expansion as well as a new system of ellipsoidal coordinates the element stiffness radiation damping and mass matrices are developed and presented in sufficient detail to enable their software implementation both the new coordinate system and the new element include the previous spheroidal coordinate systems and spheroidal elements as limiting cases therefore all the previously reported performance data for the spheroidal elements apply to this ellipsoidal element when used in spheroidal form since the three axes of an ellipsoid can be chosen independently an ellipsoid can circumscribe any structural shape at least as closely and generally more closely than a prolate or oblate spheroid the resulting reduction in size of the finite computational domain will result in even greater computational speeds than those already reported for the spheroidal elements the element may be used to model problems in free space 4 steradians half space 2 quarter space or eighth space 2 since this infinite element provides maximum computational efficiency for structures of all shapes software element libraries would need only this one element for all problems in unbounded domains

h adaptive finite element computation of time harmonic exterior acoustics problems in two dimensions abstract in this paper we carry out adaptive finite element computations of the helmholtz equation in two dimensions in the context of time harmonic exterior acoustics the purpose is to demonstrate potentially significant cost savings engendered through adaptivity for propagating solutions at moderate wave numbers ka 2 4 the computations are performed on meshes of linear triangles and are adapted to the solution by locally changing element sizes h refinement the adaptive procedure involves applying an explicit residual based a posteriori error estimator and an h adaptive strategy which were derived in a previous paper the adaptive meshes are then obtained through global mesh regeneration using an advancing front mesh generator two different finite element formulations are considered the galerkin and galerkin least squares gls methods the infinite physical domain is truncated by an artificial exterior boundary on which a fully coupled dirichlet to neumann dtn boundary condition is applied two different problems are computed plane wave scattering by a rigid infinite surface circular and square cross sections and nonuniform radiation from an infinite circular cylinder detailed cost studies with respect to an active column direct solver are performed for the nonuniform radiation problem the adaptive mesh is twenty times more cost effective than a uniform mesh for galerkin when coupled with the gls formulation the adaptive mesh is forty times more efficient than galerkin computations on a uniform mesh

discrete input two dimensional gaussian channels with memory estimation and information rates via graphical models and statistical mechanics discrete input two dimensional 2d gaussian channels with memory represent an important class of systems which appears extensively in communications and storage in spite of their widespread use the workings of 2d channels are still very much unknown in this work we try to explore their properties from the perspective of estimation theory and information theory at the heart of our approach is a mapping of a 2d channel to an undirected graphical model and inferring its a posteriori probabilities apps using generalized belief propagation gbp the derived probabilities are shown to be practically accurate thus enabling optimal maximum a posteriori map estimation of the transmitted symbols also the shannon theoretic information rates are deduced either via the vector wise shannon mcmillan breiman smb theorem or via the recently derived symbol wise guo shamai verdu gsv theorem our approach is also described from the perspective of statistical mechanics as the graphical model and inference algorithm have their analogues in physics our experimental study based on common channel settings taken from cellular networks and magnetic recording devices demonstrates that under nontrivial memory conditions the performance of this fully tractable gbp estimator is almost identical to the performance of the optimal map estimator it also enables a practically accurate simulation based estimate of the information rate rationalization of this excellent performance of gbp in the 2 d gaussian channel setting is addressed