a domain decomposition method for domains with holes using a complementary decomposition in this paper a new non conforming domain decomposition method based on fictitious domains is considered for linear elasticity problems on domains with holes existence and uniqueness of the solution of this alternative approach are showed in the continuous and discrete case although the established a priori estimate for the discretization error is not optimal the scheme is of interest in case of moving geometries and in shape optimization to solve the arising coupled linear system we use a block sor method the convergence rate does not depend on the mesh size numerical results illustrate the flexibility of the discretization scheme

mixed boundary integral methods for helmholtz transmission problems in this paper we propose a hybrid between direct and indirect boundary integral methods to solve a transmission problem for the helmholtz equation in lipschitz and smooth domains we present an exhaustive abstract study of the numerical approximation of the resulting system of boundary integral equations by means of galerkin methods some particular examples of convergent schemes in the smooth case in two dimensions are given finally we extend the results to a thermal scattering problem in a half plane with several obstacles and provide numerical results that illustrate the accuracy of our methods depending on the regularity of the interface

nd convolutional codes i performance analysis a noncoherent coded system which incorporates convolutional codes in conjunction of multiple symbol noncoherent detection is presented in this two part paper where part i focuses on the performance analysis of the system and part ii deals with the structural properties of the underlying convolutional codes these convolutional codes are referred to as nd convolutional codes it is shown that nd convolutional codes provide a general framework for various noncoherent coding systems including differential systems two models of the carrier phase are examined and the relationships between them is established for the first one the carrier phase remains constant for l channels signals whereas for the second one it unvaries throughout the transmission period the regular structure of nd codes facilitates the evaluation of a simple upper bound on the pairwise and bit error probabilities as well as a simple expression for the generalized cutoff rate the exponential rate of the error probability which is the single parameter governing the error performance at large signal to noise ratios is identified via large deviations techniques this parameter leads to the interesting conclusion that increasing l does not necessarily monotonically improve the error performance of the noncoherent system the same conclusion is reached by examining upper bounds and computer simulation results of several interesting examples these examples also reveal that optimal codes for coherent detection are not necessarily optimal for noncoherent detection and a search for good codes some of which are tabulated in part ii of the paper is required

properties of some weighted sobolev spaces and application to spectral approximations the weighted sobolev spaces on a square whose weight is a given power of the product of the distances to the edges are introduced trace theorems related to these spaces are proved then a regularity result for the dirichlet problem for the laplace operator is proved next several projection operators with polynomial values are considered for which approximation results in weighted norms are stated finally a collocation spectral method for the dirichlet problem for the laplace operator with inhomogeneous boundary conditions is analyzed this work includes new results on chebyshev approximation

multiple symbol differential detection with interference suppression a multiple symbol differential detector is formulated for m ary differential phase shift keying modulation where the channel state information is unknown to the receiver the maximum likelihood decision statistic is derived for the detector and its performance is demonstrated by analysis and simulation under the gaussian assumption for the aggregate interference plus noise an exact expression for the symbol pairwise error probability is developed for m ary differential phase shift keying modulation over a diversity slow fading rayleigh channel in the presence of an interference source a simpler expression of the pairwise error probability is developed for the asymptotic case of large signal to noise ratio and small signal to interference ratio it is shown that with an increasing observation interval the performance of the differential detector over an unknown channel approaches that of optimum combining with known channel

on the ranks of toeplitz matrices over finite fields abstract let t be a skew symmetric toeplitz matrix with entries in a finite field for all positive integers n let t n be the upper n n corner of t with nullity n t n the sequence n n n satisfies a unimodality property and is eventually periodic if the entries of t satisfy a periodicity condition we compute the maximum value and the period of the nullity sequence for toeplitz matrices of finite bandwidth this sequence satisfies a certain symmetry condition about its maximal values these results apply to give some information about the ranks of general skew symmetric toeplitz matrices with eventually periodic entries

spectral element discretization of the maxwell equations on considere un probleme variationnel equivalent aux equations de l electromagnetisme avec conditions aux limites absorbantes sur une partie de la frontiere qu on prouve etre bien pose puis on propose une discretisation de ce probleme par schema aux differences finies en temps et elements spectraux en espace et on etablit des estimations d erreur entre solutions exacte et approchee

analysis of the kleiser schumann method the kleiser schumann algorithm for the approximation of the stokes problem by fourier legendre polynomials is analized stability when the degree of the polynomials increases is established whereas error estimates in sobolev spaces are proven

staggered grids hybrid dual spectral element method for second order elliptic problems application to high order time splitting methods for navier stokes equations abstract this paper is a presentation of a mixed spectral element method based on staggered grids strategy used for the discretization of second order elliptic problems set under hybrid dual formulation a numerical analysis is performed proving the expected optimality and some numerical tests are described to confirm the predicted convergence rates the second part deals with a high order time splitting spectral scheme for the simulation of unsteady incompressible navier stokes flows we show how to use such a solver as a filtering tool to obtain divergence free discrete velocity some computational examples are reported which quantify the improvements induced by such a filter we have observed a strengthening of the stability and of the accuracy

noncoherent coded modulation trellis coded modulation with two or multidimensional signal constellations together with coherent maximum likelihood detection is considered an attractive solution for communications over the additive white gaussian noise awgn channel in this paper a new noncoherent communication system is introduced called noncoherent coded modulation ncm as an alternative to coherent coded modulation ncm achieves almost the same power efficiency without bandwidth expansion or an extensive increase in complexity as a noncoherent system the method does not need carrier phase estimation nonetheless differential encoding is not required high performance noncoherent detection is achieved by using multiple symbol observations unlike previous approaches a sliding window for the observations is used with each observation covering several branches of the trellis such that the observations are time overlapped we define a new type of noncoherent maximum likelihood sequence estimator mlse and analyze its performance over the awgn channel by numerical calculation of the union bound we perform a computerized search and present new codes for noncoherent detection with their performance the new codes cover many useful rates and complexities and achieve higher performance than existing codes for noncoherent detection the method can also be used for multiple symbol demodulation of mdpsk with better results than existing methods

squeeze flow of a piezoviscous fluid we investigate squeeze flow of piezoviscous fluids presence of contact line leads to strong pressure variations strong pressure variations induce strong viscosity variations in piezoviscous fluid squeeze flow characteristics are influenced by piezoviscosity of the fluid we investigate the squeeze flow of a piezoviscous fluid the classical navier stokes fluid model and the no slip boundary condition on the plate fluid interface implies the presence of the pressure singularity at the contact line it can be conjectured that the same behaviour is present even for piezoviscous fluids consequently the pressure variation in the fluid could be large and the pressure dependent viscosity could be important even if the piezoviscous coefficient is apparently small we investigate this conjecture by means of numerical simulation based on a variant of the spectral collocation method the numerical simulations indicate that the effects due to pressure dependent viscosity are for certain range of parameter values significant

codes based on a trellis cut set transformation ii codes for noncoherent detection for pt i see ibid vol 46 p 610 20 1998 we continue the study of cut set trellis section t sub cb codes begun in part i and show that such codes are well suited for use with multiple symbol noncoherent detection and conventional two symbol differential detection the information bit assignment for a cut set trellis section can be modified to make the resulting code noncatastrophic for noncoherent detection by this procedure many existing two dimensional 2 d and multidimensional mpsk and qam trellis codes designed for coherent detection can be easily converted into codes for both coherent and noncoherent detection compared to m dpsk trellis codes it is shown that 2 d mpsk cut set trellis section codes have improved performance for multiple symbol noncoherent detection and comparable performance for conventional two symbol differential detection thus cut set trellis section codes are a class of universal channel codes since a single encoder performs well for coherent detection multiple symbol noncoherent detection and conventional two symbol differential detection

inf sup conditions for the mortar spectral element discretization of the stokes problem summary the aim of this paper is to prove some babuska brezzi type conditions which are involved in the mortar spectral element discretization of the stokes problem for several cases of nonconforming domain decompositions

noncoherent demodulation techniques for trellis coded m dpsk signals considers noncoherent decoding of trellis coded m dpsk transmission and attempts to unify and contrast the approaches to this problem which have been previously reported in the second part of the paper the maximum likelihood block decoders for the awgn channel are outlined first assuming that the decoder has no knowledge of the state of the encoder at the beginning of the block and then assuming that it knows the state because these exhaustive decoders suffer from an exponential growth in complexity with block length two simplified decoders are proposed that approach the performance of the exhaustive decoders with a much more manageable complexity through a union bound analysis and computer simulations it is shown that it is possible to achieve large gains over uncoded systems with a very reasonable decoder complexity

on sequences of toeplitz matrices over finite fields abstract for each non negative integer n let a n be an n 1 by n 1 toeplitz matrix over a finite field f and suppose for each n that a n is embedded in the upper left corner of a n 1 we study the structure of the sequence n n z where n null a n is the nullity of a n for each n z and each nullity pattern 0 1 n we count the number of strings of toeplitz matrices a 0 a 1 a n with this pattern as an application we present an elementary proof of a result of d e daykin on the number of n n toeplitz matrices over g f 2 of any specified rank

tcm with differential encoding set partitioning trellis designs and distance analysis differential encoding de is a classical technique at the transmitter that allows simple noncoherent detection at the receiver on the other hand trellis coded modulation tcm is a bandwidth efficient technique which offers reliable data transmission in this paper we aim to find the best concatenation order of tcm and de for channel phase coherence over n 2 symbols besides the well known tcm followed by de called tcm de we propose a new trellis coding extension of de which extends our earlier work called differential trellis coded modulation dtcm dtcm is tcm with de defined in states where distinct states may have distinct de functions we propose design methods of de functions for noncoherently non catastrophic dtcm for both tcm de and dtcm we propose additive distance measures and set partitioning based on the proposed set partitioning trellis codes are designed or searched for both tcm de and dtcm both minimum distances and simulation results show that tcm de outperforms dtcm and the obtained new codes are better than the original codes

analysis of spectral projectors in one dimensional domains in this paper we analyze a class of projection operators with values in a subspace of polynomials these projection operators are related to the hubert spaces involved in the numerical analysis of spectral methods they are in the first part of the paper the standard sobolev spaces and in the second part some weighted sobolev spaces the weight of which is related to the orthogonality relation satisfied by the chebyshev polynomials these results are used to study the approximation of a model fourth order problem

noncoherent sequence detection new noncoherent sequence detection algorithms for combined demodulation and decoding of coded linear modulations transmitted over additive white gaussian noise channels possibly affected by intersymbol interference are presented optimal sequence detection in the presence of a random rotation of the signal phase assumed to be constant during the entire transmission requires a receiver complexity exponentially increasing with the duration of the transmission based on proper approximations simple suboptimal detection schemes based on the viterbi algorithm are presented whose performance approaches that of coherent detection in a companion paper by colavolpe and raheli see ibid vol 47 no 9 p 1303 7 1999 noncoherent sequence detection is extended to continuous phase modulations in the proposed schemes the tradeoff between complexity and performance is simply controlled by a parameter referred to as implicit phase memory and the number of states of a trellis diagram besides being realizable these schemes have the convenient feature of allowing us to remove the constant phase assumption and encompass time varying phase models the proposed schemes compare favorably with other solutions previously proposed in the technical literature

a discontinuous petrov galerkin method with lagrangian multipliers for second order elliptic problems we present a discontinuous petrov galerkin dpg method for the finite element discretization of second order elliptic boundary value problems the novel approach emanates from a one element weak formulation of the differential problem this procedure which is typical of discontinuous galerkin dg methods is based on introducing variables defined in the interior and on the boundary of the element the interface variables are suitable lagrangian multipliers that enforce interelement continuity of the solution and of its normal derivative thus providing the proper connection between neighboring elements the internal variables can be eliminated in favor of the interface variables using static condensation to end up with a system of reduced size in the sole lagrangian multipliers a stability and convergence analysis of the novel formulation is carried out and its connection with mixed hybrid and dg methods is explored numerical tests on several benchmark problems are included to validate the convergence performance and the flux conservation properties of the dpg method

finite element approximations of viscous flows with varying density this paper deals with the equations of a stationary viscous flow when the density is a given function of the space variable two formulations are studied according to whether the unknowns are the velocity and the pressure or the momentum and the pressure in both cases when the variation of the density is not too strong the well posedness of the problem and of its approximation by several standard finite elements is proved and estimates for the error between the exact and discrete solutions are given some numerical tests which are in complete agreement with these results are presented

the performance of trellis coded mdpsk with multiple symbol detection the idea of using a multiple more than two symbol observation interval to improve error probability performance is applied to differential detection of trellis coded multiple phase shift keying mpsk over an additive white gaussian noise awgn channels an equivalent euclidean distance measure per trellis branch is determined for this detection scheme this is used to define an augmented larger multiplicity trellis code whose distance measure is the conventional squared euclidean distance typical of conventional trellis coded modulation on the awgn such an augmented multiple trellis code is a convenient mathematical tool for simplifying the analysis results are obtained by a combination of analysis and computer simulation it is shown that only a slight increase e g one symbol in the length of the observation interval will provide a significant improvement in bit error probability performance

moments of the complex multivariate normal distribution abstract moments of the complex multivariate normal distribution are obtained by differentiating its characteristic function applying the differential operators for the differentiation of functions of complex vectors a recurrence relation for the derivatives of the characteristic function is derived and explicit expressions for the moments are obtained moments up to order 6 are expressed in terms of hermitian matrices moments of hermitian quadratic forms up to order 3 are also obtained

impact of diversity reception on fading channels with coded modulation ii differential block detection for pt i see ibid vol 45 no 6 p 563 572 1997 we study coded modulation with block differential detection in an arbitrarily correlated rician fading channel with space diversity coded differential q psk is included in our analysis as a special case a metric is chosen that is optimum for perfect interleaving slow fading and independent diversity branches for slow fading we compare the the cutoff rates of the channels resulting from different choices of block length n and diversity index m specifically we show that block detection with diversity may or may not generate a better coding channel than usual differential detection according to the code selected and the combination of values of m and n in particular for low diversity orders m 1 2 and for low to medium code rates differential detection is still an optimal or near optimal solution while for high diversity orders m spl ges 2 and medium to high code rates up to uncoded modulation block detection with n 2 can provide a significant gain an error floor always exists when fading is fast it decreases exponentially with the product of code diversity and space diversity so that the latter emerges as a very effective technique for lowering the error floor of a system affected by fast fading performance examples based on actual coding schemes are also shown

high order direct stokes solvers with or without temporal splitting numerical investigations of their comparative properties a recently proposed direct stokes solver which decouples the velocity and pressure operators without calling for a temporal scheme is numerically analyzed in comparison first with the splitting scheme proposed by g karniadakis m israeli and s orszag in j comput phys 97 1991 pp 414 443 and with the unique grid bbb p n bbb p n 2 uzawa approach for the space accuracy and computational costs the chebyshev collocation approximation is used to analyze the spectra of the continuous temporal evolution operators and their discrete time versions from the first to the fourth order an explicit boundary condition is also involved in the proposed stokes solver and it is numerically shown that the trace of bf delta bf u on the boundary must be evaluated through its bf nabla times bf nabla times contribution only otherwise the ellipticity is lost before proceeding to the time discretization the explicit evaluation of the rotational boundary term does not prevent the first and second order in time schemes from being unconditionally stable while the schemes built at the next two higher orders are limited by the usual explicit cal o n 4 stability criterion on the time step the proposed bf u p decoupling gives this limitation a less restrictive coefficient and supplies the expected temporal orders on the whole explored range of time step sizes the effective accuracy obtained for the navier stokes 2d solutions has been measured for the re 1000 lid driven cavity problem and has been found equivalent to what is supplied by the much more expensive uzawa decoupling method

a connection between subgrid scale eddy viscosity and mixed methods we consider a new mixed method related to the evss method in computational viscoelasticity for the convection dominated convection diffusion equation in which stabilization is added then removed through the extra mixed variables this consistent stabilization is equivalent to an artificial viscosity operator acting only on the fluctuations in u h by suitable choice of the mixed spaces a method of guermond is recovered exactly we show that for a different natural choice a new method results with global error estimates similar to both guermond s method and the streamline diffusion supg method

spectral tau approximation of the two dimensional stokes problem we analyse the spectral tau method for the approximation of the stokes system on a square with dirichlet boundary conditions we provide an error estimate in the norm of the sobolev spaceh s for the approximation of a divergence free vector field with polynomial divergence free vector fields we apply this result to prove some convergence estimates for the solution of the discrete stokes problem

on multidimensional coded modulations having uniform error property for generalized decoding and flat fading channels we consider the problem of uniform error property uep for a coded modulation with constant energy multidimensional symbols transmitted over the additive white gaussian noise awgn or fading channels and received by a broad class of decoders this class includes coherent partially coherent double differential and noncoherent decoders decoders designed for fading channels decoders using one or multiple symbol observations and many more these decoders are described as special cases of a general decoder model this decoder operates by maximizing an arbitrary likelihood function that its arguments are front end correlator matched filter outputs a group code structure that guarantees uep is developed by using the theory of geometrically uniform codes and applying it to the general decoder these codes are defined over groups commonly nonbinary with isometric mapping to channel symbols we show the code construction for the specific case of lth dimensional m ary phase shift keying mpsk an additional interesting property of these general uniform error codes is related to the case of noncoherent decoding we show that when using codes of this family if a code is noncoherently catastrophic then it is also rotationally invariant then the use of preceding of the input such that the code becomes rotationally transparent will also make it noncatastrophic

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

stabilized finite elements for a reaction dispersion saddle point problem with nonconstant coefficients we consider a system of two reaction dispersion equations with nonconstant parameters both equations are coupled through the boundary conditions we propose a mixed variational formulation that leads to a nonsymmetric saddle point problem we prove its well posedness then we develop a stabilized mixed finite element discretization of this problem and establish optimal a priori error estimates

mathematical analysis and numerical approximation of a general linearized poro hyperelastic model abstract we describe the behavior of a deformable porous material by means of a poro hyperelastic model that has been previously proposed in chapelle and moireau 2014 under general assumptions for mass and momentum balance and isothermal conditions for a two component mixture of fluid and solid phases in particular we address here a linearized version of the model based on the assumption of small displacements we consider the mathematical analysis and the numerical approximation of the problem more precisely we carry out firstly the well posedness analysis of the model then we propose a numerical discretization scheme based on finite differences in time and finite elements for the spatial approximation stability and numerical error estimates are proved particular attention is dedicated to the study of the saddle point structure of the problem that turns out to be interesting because velocities of the fluid phase and of the solid phase are combined into a single quasi incompressibility constraint our analysis provides guidelines to select the componentwise polynomial degree of approximation of fluid velocity solid displacement and pressure to obtain a stable and robust discretization based on taylor hood type finite element spaces interestingly we show how this choice depends on the porosity of the mixture i e the volume fraction of the fluid phase

mixed variational formulations in locally convex spaces the main purpose of this paper is to extend to the setting of locally convex spaces the study of the mixed variational formulation of some elliptic boundary value problems the so called babuska brezzi theory this study consists of characterizing the existence of a solution and giving conditions that guarantee the stability of the corresponding galerkin method

stabilization of spectral methods by finite element bubble functions abstract we show that a standard spectral collocation scheme can be stabilized by adding extra trial test functions with local support bubbles applications are given to a scalar advection diffusion problem and to the stokes problem

existence uniqueness and approximation for generalized saddle point problems extensions of the well known results of brezzi on saddle point problems are presented the class of problems is generalized to include the unsymmetric case and the known stability and approximation results are strengthened and applied to the generalized problem an application to the solution of certain exterior interface problems is indicated

multiple symbol differentially detected multilevel codes for the rayleigh fading channel conventional differential detection is known to perform poorly on the fast fading rayleigh fading channel due to the rapid variation of the channel state the technique of multiple symbol differential detection msdd improves the error performance by detecting over a sequence of symbols and exploiting the inherent correlation of the fading process to further reduce the error rate we need to introduce some form of coding successful coding for the rayleigh fading channel requires interleaving to decorrelate the channel a conflicting requirement to msdd we propose a solution consisting of interleaving blocks of l m ary phase shift keying mpsk symbols that are multiple symbol differentially detected the blocks are treated as elements of an m sup l symbol alphabet over which a multilevel code based on geometrically uniform partitions is defined

spectrally efficient noncoherent communication this paper considers noncoherent communication over a frequency nonselective channel in which the time varying channel gain is unknown a priori but is approximately constant over a coherence interval unless the coherence interval is large coherent communication which requires explicit channel estimation and tracking prior to detection incurs training overhead which may be excessive especially for multiple antenna communication in contrast noncoherent detection may be viewed as a generalized likelihood ratio test glrt which jointly estimates the channel and the data and hence does not require separate training the main results in this paper are as follows 1 we develop a signal space criterion for signal and code design for noncoherent communication in terms of the distances of signal points from the decision boundaries 2 the noncoherent metric thus obtained is used to guide the design of signals for noncoherent communication that are based on amplitude phase constellations these are significantly more efficient than conventional differential phase shift keying psk especially at high signal to noise ratio snr also known results on the high snr performance of multiple symbol demodulation of differential psk are easily inferred from the noncoherent metric 3 the glrt interpretation is used to obtain near optimal low complexity implementations of noncoherent block demodulation in particular this gives an implementation of multiple symbol demodulation of differential psk which is of linear complexity in the block length and whose degradation from the exact exponential complexity implementation can be made as small as desired

multiple phase codes for detection without carrier phase reference we consider the construction and analysis of linear block codes for m ary phase shift keying that can be decoded without carrier phase synchronization under these circumstances the function that has a significant impact on performance is the noncoherent distance analogous to the euclidean distance for the coherent case the major difficulty in constructing and analyzing such codes lies in the fact that the noncoherent distance is not a true metric for this reason prior work mainly relies on numerical approaches to search for good codes and to determine the corresponding minimum noncoherent distance we first present a theorem that links the noncoherent distance with the euclidean and lee 1958 distances this theorem allows us to construct good codes and determine their minimum noncoherent distances analytically based on this theorem we classify the codes whose duals consist of a cyclic group these codes are of minimum redundancy we further investigate codes with the flavor of hamming and shortened hamming codes many of these new codes provide significantly larger coding gains than previously known codes linear codes derived from code division multiple access cdma sequences are considered as well these codes in general provide rather large coding gains finally an algorithm is introduced that can be appended to any suboptimal decoding technique to enhance the performance

multiple trellis coded modulation mtcm the authors demonstrate a trellis coded modulation technique referred to as multiple trellis coded modulation mtcm wherein more than one channel symbol per trellis branch is transmitted they have found simple two state trellis codes for symmetric mpsk multiple phase shift keying and am modulations that can achieve 3 db gain over uncoded modulation at very high signal to noise ratios without bandwidth expansion or reduction in information bit rate the gain of these codes with respect to previously reported two state trellis codes is between 1 and 2 db at very high signal to noise ratios depending on the number of bits per hertz transmitted these gains are achieved for those of the equivalent conventional trellis codes with the same number of states in the trellis diagram the authors note that additional computations per branch are needed for the multiple trellis coding scheme the concept can be extended to a higher number of states and other types of modulations

multiple symbol differential detection of mpsk a differential detection technique for mpsk multiple phase shift keying which uses a multiple symbol observation interval is presented and its performance is analyzed and simulated the technique makes use of maximum likelihood sequence estimation of the transmitted phases rather than symbol by symbol detection as in the conventional differential detection thus the performance of this multiple symbol detection scheme fills the gap between conventional two symbol observation differentially coherent detection of mpsk and ideal coherent of mpsk with differential encoding the amount of improvement gained over conventional differential detection depends on the number of phases m and the number of additional symbol intervals added to the observation what is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation the analysis and simulation results presented are for uncoded mpsk

spectral method solution of the stokes equations on nonstaggered grids abstract the stokes equations are solved using spectral methods with staggered and nonstaggered grids numerous ways to avoid the problem of spurious pressure modes are presented including new techniques using the pseudospectral method and a method solving the weak form of the governing equations a variation on the spectral element method developed by patera the pseudospectral methods using nonstaggered grids are simpler to implement and have comparable or better accuracy than the staggered grid formulations three test cases are presented a formulation with an exact solution a formulation with homogeneous boundary conditions and the driven cavity problem the solution accuracy is shown to be greatly improved for the driven cavity problem when the analytical solution of the singular flow behavior in the upper corners is separated from the computational solution

finite dimensional approximation of nonlinear problems in the first two papers of this series 4 5 we have studied a general method of approximation of nonsingular solutions and simple limit points of nonlinear equations in a banach space we derive here general approximation results of the branches of solutions in the neighborhood of a simple bifurcation point the abstract theory is applied to the galerkin approximation of nonlinear variational problems and to a mixed finite element approximation of the von karman equations

theoretical analysis and performance limits of noncoherent sequence detection of coded psk a theoretical performance analysis of noncoherent sequence detection schemes previously proposed by the authors for combined detection and decoding of coded m ary phase shift keying m psk is presented a method for the numerical evaluation of the pairwise error probability for which no closed form expressions exist is described the classical union bound is computed and results are compared with computer simulations an upper bound on this pairwise error probability is also presented this upper bound may be effectively used for the definition of an equivalent distance which may be useful in exhaustive searches for optimal codes using this bound it is proven that in the general coded case the considered noncoherent decoding schemes perform as close as desired to an optimal coherent receiver when a phase memory parameter is sufficiently large in the case of differentially encoded m psk a simple expression of the asymptotic bit error probability is derived which is in agreement with simulations for high as well as low signal to noise ratio snr

legendre and chebyshev spectral approximations of burgers equation we give error estimates for both legendre and chebyshev spectral approximations of the steady state burgers problem u xx lambda uu x f 0 in i 1 1 u 1 u 1 0 to do that we prove some abstract approximation properties of orthogonal projection operators in some weighted sobolev spacesh s i for both legendre and chebyshev weights

polynomial approximation of divergence free functions etude de la meilleure approximation d une fonction sans divergence par un polynome algebrique ou trigonometrique sans divergence etablissement d une estimation optimale

an overview of projection methods for incompressible flows a series of numerical issues related to the analysis and implementation of fractional step methods for incompressible flows are addressed in this paper these methods are often referred to in the literature as projection methods and can be classified into three classes namely the pressure correction methods the velocity correction methods and the consistent splitting methods for each class of schemes theoretical and numerical convergence results available in the literature are reviewed and open questions are discussed the essential results are summarized in a table which could serve as a useful reference to numerical analysts and practitioners published by elsevier b v msc 65n35 65n22 65f05 35j05

on the constrained capacity of block differential modulation and detection in this paper we consider block differential modulation bdm to tackle the phase slip problem in digital communication systems when the received signal phase can drift the synchronizer can suddenly choose a wrong reference phase e g adding multiples of 2 m in case of m ary phase shift keying phase slips are detrimental for any coherent system since they cause long error bursts till an opposite phase slip occurs bdm is a generalization of differential modulation dm neither of them relies on the absolute carrier phase however bdm differentially encodes information between small blocks of symbols and exploits couples of adjacent blocks to decode this allows simple and practical demapping without sacrificing capacity we show that for low and moderate phase slip probabilities bdm approaches the constrained capacity of coherent transmission in particular at high spectral efficiencies we provide closed form results for the constrained capacity in absence of phase slips for phase shift keying and quadrature amplitude modulation and we evaluate numerically the constrained capacity through an efficient monte carlo method when phase slips occur besides we provide simple upper and lower bounds

stability of a cartesian grid projection method for zero froude number shallow water flows in this paper a godunov type projection method for computing approximate solutions of the zero froude number incompressible shallow water equations is presented it is second order accurate and locally conserves height mass and momentum to enforce the underlying divergence constraint on the velocity field the predicted numerical fluxes computed with a standard second order method for hyperbolic conservation laws and applied to an auxiliary system are corrected in two steps first a mac type projection adjusts the advective velocity divergence in a second projection step additional momentum flux corrections are computed to obtain new time level cell centered velocities which satisfy another discrete version of the divergence constraint the scheme features an exact and stable second projection it is obtained by a petrov galerkin finite element ansatz with piecewise bilinear trial functions for the unknown height and piecewise constant test functions the key innovation compared to existing finite volume projection methods is a correction of the in cell slopes of the momentum by the second projection the stability of the projection is proved using a generalized theory for mixed finite elements in order to do so the validity of three different inf sup conditions has to be shown the results of preliminary numerical test cases demonstrate the method s applicability on fixed grids the accuracy is improved by a factor four compared to a previous version of the scheme

an extended hu washizu formulation for elasticity a class of new mixed formulations for elasticity is developed and analysed the formulations are based on the discrete evss method introduced in the context of incompressible viscoelastic flows by a fortin m fortin and co workers a key feature is a stabilization term that renders coercive a problem that might not otherwise be so the focus in this work is on behaviour in the incompressible limit and the goal is that of obtaining formulations that are uniformly stable and convergent concrete examples are presented of element choices that lead to unstable formulations in the classical formulation and which are stable for the formulations introduced here a selection of numerical results illustrates in a comparative way the behaviour of the elements introduced

a variational spectral method for the two dimensional stokes problem abstract a spectral galerkin scheme for solving the two dimensional stationary stokes problem is considered in vorticity stream function formulation the stokes problem is reduced to a biharmonic one a new formulation for the decomposition of the biharmonic operator is introduced main difficulty in this decomposition is to find the trace of the vorticity using the adjoint of the composition of trace operator and green s operator a variational form is obtained for computing the boundary value of the vorticity the discrete variational form preserves the properties such as coercivity and continuity of the continuous case which are important for our convergence analysis convergence of our scheme is proved and numerical experiments are performed for the steady driven cavity problem

a spectral numerical method for the navier stokes equations with applications to taylor couette flow a new spectral method for solving the incompressible navier stokes equations in a plane channel and between concentric cylinders is presented the method uses spectral expansions which inherently satisfy the boundary conditions and the continuity equation and yield banded matrices which are efficiently solved at each time step in addition the number of dependent variables is reduced resulting in a reduction in computer memory requirements several test problems have been computed for the channel flow and for flow between concentric cylinders including taylor couette flow with axisymmetric taylor vortices and wavy vortices in all cases agreement with available experimental and theoretical results is very good

role of the lbb condition in weak spectral projection methods 405 this paper investigates the relevance of the ladyshenskaya babuska brezzi con dition in spectral projection methods we consider the stability and convergence properties for a first order nonincremental projection method and a second order incremental projection method both based on a spectral galerkin legendre spatial discretization we show that the convergence of both projection methods is controlled by the ability of the spectral framework to approximate correctly the steady stokes problem c 2001 elsevier science

a model for two coupled turbulent fluids part ii numerical analysis of a spectral discretization we consider a system of equations that models the stationary flow of two immiscible turbulent fluids on adjacent subdomains the equations are coupled by nonlinear boundary conditions on the interface which is here a fixed given surface we propose a spectral discretization of this problem and perform its numerical analysis the convergence of the method is proven in the two dimensional case together with optimal error estimates

multiple symbol trellis coded modulation applied to noncoherent continuous phase frequency shift keying this paper considers a maximum likelihood ml noncoherent detection scheme for multiple full response continuous phase frequency shift keying cpfsk waveforms and introduces a trellis coded modulation tcm scheme for this noncoherent modulation by utilizing a gaussian approximation for rician random variables we express the pairwise error probability as a function of the equivalent normalized squared distance ensd ensd plays the same role as normalized squared euclidean distance when evaluating error probability performance for coherent detection we derive an analytical approximation on the bit error probability by employing ensd for both the coded system and the uncoded system for the uncoded system we show that the bit error probability of noncoherent detection approaches that of coherent symbol by symbol detection in the limit as the multiplicity of the symbol goes to infinity for large signal to noise ratio snr we determine specific optimal trellis encoders for binary and 4 ary cpfsk with modulation index 1 2 and 1 4 respectively by application of ungerboeck s 1982 set partitioning approach

nullities for a class of skew symmetric toeplitz band matrices abstract for all n k 1 we give formulas for the nullity n n k of the n n skew symmetric toeplitz band matrix whose first k superdiagonals have all entries 1 and whose remaining superdiagonals have all entries 0 this is accomplished by counting the number of cycles in certain directed graphs as an application for each fixed integer z 0 and large fixed k we give an asymptotic formula for the percentage of n k satisfying n n k z for the purpose of rapid computation an algorithm is devised that quickly computes n n k even for extremely large values of n and k

nd convolutional codes ii structural analysis for pt i see ibid vol 43 no 2 p 558 75 1997 the structural properties of a noncoherent coded system which incorporates convolutional codes in conjunction with multiple symbol noncoherent detection is presented in this second part of a two part paper where the performance analysis was provided in part i these convolutional codes are referred to as nd convolutional codes and they provide a general framework for various noncoherent coding systems including differential systems for several practical models of the carrier phase the exponential rate in which the error probability decays to zero derived in part i of the paper is used here to obtain the free equivalent distance of nd codes which is the single parameter dominating the error performance at large signal to noise ratios the free equivalent distance is upper bounded by the free nd distance which constitutes a more convenient and practical parameter to work with and it is the basis for a computer search for optimal nd codes the resultant codes of the computer search are compared to codes which are optimal for coherent detection and it is verified that the latter codes are not necessarily optimal for noncoherent detection since they exhibit in many cases a relatively small nd distance the ambiguity problem inherent to noncoherent systems is also treated in this paper in the general framework of nd catastrophic codes and necessary and sufficient conditions for catastrophic error propagation are identified

iterative decision feedback differential demodulation of bit interleaved coded mdpsk for flat rayleigh fading channels a simple receiver structure previously proposed by the authors for convolutional coded m ary differential phase shift keying transmission over flat rayleigh fading channels without channel state information is analyzed in detail we present a thorough discussion of the iterative decoding procedure which is referred to as iterative decision feedback differential demodulation iterative df dm the convergence behavior of iterative df dm is theoretically examined the analysis supports the observation that the iterative decoding scheme works well for target bit error rates which are usually of interest furthermore the associated cut off rate for error free decision feedback is studied judging from this performance parameter remarkable gains in power efficiency compared to conventional differential demodulation are indicated while the computational complexity of the decoding remains low the results from information theory are in good agreement with the given simulation results

generalized inf sup conditions for chebyshev spectral approximation of the stokes problem a mixed problem and its approximation in an abstract framework are considered they are proved to be well posed if and only if several inf sup conditions are satisfied these results are applied to the stokes equations in a square formulated in chebyshev weighted sobolev spaces and their approximations two kinds of spectral discretizations are analyzed a galerkin method and a collocation method at the chebyshev nodes

spectral approximation of the periodic nonperiodic navier stokes equations in order to approximate the navier stokes equations with periodic boundary conditions in two directions and a no slip boundary condition in the third direction by spectral methods we justify by theoretical arguments an appropriate choice of discrete spaces for the velocity and the pressure the compatibility between these two spaces is checked via an infsup condition we analyze a spectral and a collocation pseudo spectral method for the stokes problem and a collocation pseudo spectral method for the navier stokes equations we derive error bounds of spectral type i e which behave likem wherem depends on the number of degrees of freedom of the method and represents the regularity of the data

finite element approximation of elliptic problems with dirac measure terms in weighted spaces applications to one and three dimensional coupled problems in this work we study the stability and the convergence rates of the finite element approximation of elliptic problems involving dirac measures using weighted sobolev spaces and weighted discrete norms our approach handles both the cases where the measure is simply a right hand side and where it represents an additional term i e solution dependent in the formulation of the problem the main motivation of this study is to provide a methodological tool to treat elliptic problems in fractured domains where the coupling terms are seen as dirac measures concentrated on the fractures we first establish a decomposition lemma which is our fundamental tool for the analysis of the considered problems in the nonstandard setting of weighted spaces then we consider the stability of the galerkin approximation with finite elements in weighted norms with uniform and graded meshes we introduce a discrete decomposition lemma that extends the continuous one and allows us to derive discrete inf sup conditions in weighted norms then we focus on the convergence of the finite element method due to the lack of regularity the convergence rates are suboptimal for uniform meshes we show that using graded meshes optimal rates are recovered our theoretical results are supported by several numerical experiments finally we show how our theoretical results apply to certain coupled problems involving fluid flow in porous three dimensional media with one dimensional fractures that are found in the analysis of microvascular flows

maximum likelihood differential detection of uncoded and trellis coded amplitude phase modulation over awgn and fading channels spl minus metrics and performance this paper derives metrics for maximum likelihood differential detection of uncoded and trellis coded mpsk and qam transmitted over rayleigh and rician fading channels receiver structures based on these metrics are proposed and their error probability performance analyzed and or simulated the results represent a generalization of the notion of multiple symbol differential detection previously introduced by the authors for mpsk over an awgn to the fading channel and other modulations for the coded cases ideal interleaving deinterleaving is assumed and furthermore the presence or absence of channel state information an interesting side result is that for a constant envelope modulation transmitted over a fading channel with unknown but rapidly varying phase error the other extreme to the slowly varying phase error case normally assumed for differential detection under certain practical assumptions it is shown that the optimum receiver is of the limiter discriminator type

nonlinear complementarity functions for plasticity problems with frictional contact in this paper a unifying framework for the numerical treatment of frictional contact in combination with elastoplasticity with hardening is presented both kinds of problems lead to the mathematical structure of variational inequalities which are discretized by introducing additional variables for the contact stresses or the deviatoric stresses leading to a mixed formulation by defining a family of nonlinear complementarity functions which can be applied to both frictional and plastic yield conditions these inequality constraints are reformulated as equalities combined with the equilibrium equations a system of nonlinear equations is obtained that is solved in terms of a semismooth newton method to obtain a larger domain of convergence and better stability properties the introduction of additional scaling parameters is motivated and their benefit to the convergence of the scheme is demonstrated due to the locality of the contact and plastic constraints the resulting method can be interpreted as a primal dual active set strategy furthermore for linear hardening laws our method is a generalization of the well known radial return algorithm which is obtained for a special suboptimal choice of the plastic scaling parameters the efficiency and the generality of the proposed quasi newton scheme is demonstrated by several numerical examples including the simulation of a three dimensional contact problem with several elastoplastic bodies exponential isotropic hardening and coulomb friction

numerical analysis of the modified evss method abstract in this paper we present a proof of the stability of a new mixed finite element method introduced recently by the authors 9 within the context of viscoelastic fluids the mixed formulation is related to the evss elastic viscous split stress method proposed by rajagopalan et al 14 and is based on the introduction of the rate of deformation tensor as an additional unknown the proof applies to the stokes flow and some linearized constitutive equations of slow viscoelastic flows existence and uniqueness of the continuous and the discrete problems are derived from a generalized brezzi babuska theory it is shown that no additional compatibility condition is required between the various variables except the usual one for the velocity and the pressure fields this result allows to choose low order finite element for the stress several numerical experiments on the 4 1 contraction stokes flow will be presented which will confirm the improved stability obtained with this new formulation