continuous phase modulation part i full response signaling the continuous phase modulation cpm signaling scheme has gained interest in recent years because of its attractive spectral properties data symbol pulse shaping has previously been studied with regard to spectra for binary data and modulation index 0 5 in this paper these results have been extended to the m ary case where the pulse shaping is over a one symbol interval the so called full response systems results are given for modulation indexes of practical interest concerning both performance and spectrum comparisons are made with minimum shift keying msk and systems have been found which are significantly better in e b n 0 for a large signal to noise ratio snr without expanded bandwidth schemes with the same bit error probability as msk but with considerably smaller bandwidth have also been found significant improvement in both power and bandwidth are obtained by increasing the number of levels m from 2 to 4

stable gfem sgfem improved conditioning and accuracy of gfem xfem for three dimensional fracture mechanics abstract in this paper we present an extension of the stable generalized fem sgfem for 3 d fracture mechanics problems numerical experiments show that the use of available singular enrichment bases derived from the 2 d asymptotic crack tip solution leads to a severe loss of accuracy in the sgfem an enrichment scheme based on singular bases and linear polynomials is shown to recover the optimal convergence of the sgfem the proposed sgfem for 3 d fractures delivers the same rate of growth in condition number as the standard fem for proper choice of singular enrichment functions the accuracy and conditioning obtained with the sgfem is compared with the generalized fem gfem for different types of singular enrichment bases a fully 3 d fracture mechanics problem is considered to highlight issues that arise only in 3 d problems the convergence of stress intensity factors sifs extracted from gfem and sgfem solutions and the effect of the size of enrichment sub domains on the accuracy of extracted sifs are also studied it is shown that the accuracy of sifs may deteriorate with mesh refinement when the topological enrichment strategy is adopted the proposed sgfem delivers much better accuracy than the gfem for both geometrical and topological enrichment strategies

variationally consistent extended fe model for 3d planar and curved imperfect interfaces abstract we propose an extended finite element method convergent to the asymptotic solution of a thin interface problem for both planar and curved imperfect interfaces in three dimensions the main advantage over standard cohesive zone models is the bulk mesh size independence with respect to standard extended finite element method in the proposed procedure blending and quadrature sub domains are not required the focus is on the evaluation of the accuracy of the proposed approach in solving three dimensional benchmark tests the numerical results are compared with those available from analytical solutions and spring like interface models

a stable and optimally convergent generalized fem sgfem for linear elastic fracture mechanics abstract in this paper we investigate the accuracy and conditioning of the stable generalized fem sgfem and compare it with standard generalized fem gfem for a 2 d fracture mechanics problem the sgfem involves localized modifications of enrichments used in the gfem and the conditioning of the stiffness matrix in this method is of the same order as in the fem numerical experiments show that using the sgfem with only the modified heaviside functions which are used as enrichments in the gfem to approximate the solution of fracture problems in 2 d gives inaccurate results however the sgfem using an additional set of enrichment function yields accurate results while not deteriorating the conditioning of the stiffness matrix rules for the selection of the optimal set of enrichment nodes based on the definition of enrichment functions used in the sgfem are also presented this set leads to optimal convergence rates while keeping the number of degrees of freedom equal to or close to the gfem we show that it is necessary to enrich additional nodes when the crack line is located along element edges in 2 d the selection of these nodes depends on the definition of the enrichment functions at the crack discontinuity a simple and yet generic implementation strategy for the sgfem in an existing gfem xfem software is described the implementation can be used with 2 d and 3 d elements it leads to an efficient evaluation of sgfem enrichment functions

an improved stable xfem is xfem with a novel enrichment function for the computational modeling of cohesive cracks abstract owing to the solution space enriched with a priori known knowledge through the partition of unity the extended or generalized finite element method xfem gfem has been widely applied to the modeling of localized failure in solids as far as cohesive cracks are concerned in this work on the one hand the xfem enriched with heaviside function or the shifted one with respect to nodal values is of optimal accuracy but is prone to the issue of ill conditioned or even singular system matrix for arbitrary crack propagation on the other hand the stable xfem s xfem circumvents the ill conditioning issues by introducing the residual heaviside function with respect to its linear interpolant at the cost of losing accuracy e g spurious stress locking for discontinuities with non uniform displacement jumps aiming to reconcile the incompatibility between accuracy of the solution and conditioning of the system matrix this work addresses a simple yet effective improved stable xfem is xfem with a novel enrichment function both the xfem and s xfem are recovered as its particular cases with different approximation schemes for the bridging scale which incorporates information from both the continuous coarse scale and the discontinuous fine scale in the proposed is xfem as the enrichment basis functions are not contained in the standard polynomial space conditioning of the resulting system matrix is nearly insensitive to the mesh discontinuity configuration even if the crack path gets close to element nodes furthermore the is xfem with a small stabilization parameter is almost of the same accuracy as the xfem particularly pathological numerical results polluted by spurious stress locking exhibited in the s xfem are not observed across a fully softened discontinuity with non uniform displacement jumps as only the enrichment function is modified the proposed is xfem together with appropriate crack propagation criterion and tracking algorithm can be implemented easily in the existing xfem codes several representative numerical simulations of element and structure benchmark tests are presented to validate the proposed is xfem regarding both accuracy of the solution and conditioning of the system matrix

blending in the extended finite element method by discontinuous galerkin and assumed strain methods summary in the extended finite element method xfem errors are caused by parasitic terms in the approximation space of the blending elements at the edge of the enriched subdomain a discontinuous galerkin dg formulation is developed which circumvents this source of error a patch based version of the dg formulation is developed which decomposes the domain into enriched and unenriched subdomains continuity between patches is enforced with an internal penalty method an element based form is also developed where each element is considered a patch the patch based dg is shown to have similar accuracy to the element based dg for a given discretization but requires significantly fewer degrees of freedom the method is applied to material interfaces cracks and dislocation problems for the dislocations a contour integral form of the internal forces that only requires integration over the patch boundaries is developed a previously developed assumed strain as method is also developed further and compared with the dg method for weak discontinuities and linear elastic cracks the dg method is shown to be significantly more accurate than the standard xfem for a given element size and to converge optimally even where the standard xfem does not the accuracy of the dg method is similar to that of the as method but requires less application specific coding copyright q 2007 john wiley sons ltd

qualitative properties of solutions to some nonlinear elliptic equations in r 2 o introduction elliptic equations in this paper we investigate properties of the solutions to the au r x e u x x r 2 for functions r x which are positive near infinity equations of this kind arise from a variety of situations such as from prescribing gaussian curvature in geometry i 2 and from combustion theory in physics 3 recently a series ofworks have been sought to understand the existence and the qualitative properties of the solutions of ni i 5 and ni cheng 4 1 considered the case where r x is nonpositive mcowen 6 1 and aviles 7 investigated the situation where r x 0 in some order as ixl in our previous paper 1 we consider a special case where r is a constant we proved that the solutions are radially symmetric and hence classified all the solutions in this paper we consider more general functions r x first we obtain the asymptotic behavior of the solution near infinity consequently we prove that all the solutions satisfy an identity which is somewhat of a generalization of the well known kazdan warner condition finally using the asymptotic behavior together with the further development of the method employed in our previous paper i 1 we show that all the solutions are radially symmetric provided r is radially symmetric and nonincreasing this part can be viewed as the completion of 1 throughout this paper we assume that the function r x is positive near infinity in 1 we study the asymptotic behavior of the solution u x of let fl 1 2n r2 r x e dx under some appropriate conditions we show that the solutions approach

efficient adaptive integration of functions with sharp gradients and cusps in n dimensional parallelepipeds summary in this paper we study the efficient numerical integration of functions with sharp gradients and cusps an adaptive integration algorithm is presented that systematically improves the accuracy of the integration of a set of functions the algorithm is based on a divide and conquer strategy and is independent of the location of the sharp gradient or cusp the error analysis reveals that for a c0 function derivative discontinuity at a point a rate of convergence of n 1 is obtained in rn two applications of the adaptive integration scheme are studied first we use the adaptive quadratures for the integration of the regularized heaviside function a strongly localized function that is used for modeling sharp gradients then the adaptive quadratures are employed in the enriched finite element solution of the all electron coulomb problem in crystalline diamond the source term and enrichment functions of this problem have sharp gradients and cusps at the nuclei we show that the optimal rate of convergence is obtained with only a marginal increase in the number of integration points with respect to the pure finite element solution with the same number of elements the adaptive integration scheme is simple robust and directly applicable to any generalized finite element method employing enrichments with sharp local variations or cusps in n dimensional parallelepiped elements copyright 2012 john wiley sons ltd

a low complexity iterative phase noise tracker for bit interleaved coded cpm signals in awgn this paper considers iterative detection of bit interleaved coded continuous phase modulation in the presence of both phase noise pn and additive white gaussian noise awgn the proposed receiver iterates between a detection module and an estimation module the detection module operates according to the sum product algorithm and the factor graph framework in order to perform coherent maximum a posteriori bit detection in awgn using a pn estimate provided by the estimation module the latter module which results from the expectation maximization algorithm for maximum likelihood estimation of the unknown pn samples is implemented as a smoothing phase locked loop that uses soft decisions provided by the detector the separation between the detection and the estimation modules allows the use of an off the shelf coherent bit detector the technique is further characterized by a very low computational complexity a small error performance degradation and a small number of overhead symbols

a corrected xfem approximation without problems in blending elements the extended finite element method xfem enables local enrichments of approximation spaces standard finite elements are used in the major part of the domain and enriched elements are employed where special solution properties such as discontinuities and singularities shall be captured in elements that blend the enriched areas with the rest of the domain problems arise in general these blending elements often require a special treatment in order to avoid a decrease in the overall convergence rate a modification of the xfem approximation is proposed in this work the enrichment functions are modified such that they are zero in the standard elements unchanged in the elements with all their nodes being enriched and varying continuously in the blending elements all nodes in the blending elements are enriched the modified enrichment function can be reproduced exactly everywhere in the domain and no problems arise in the blending elements the corrected xfem is applied to problems in linear elasticity and optimal convergence rates are achieved copyright 2007 john wiley sons ltd

the intrinsic xfem a method for arbitrary discontinuities without additional unknowns a new method for treating arbitrary discontinuities in a finite element fe context is presented unlike the standard extended fe method xfem no additional unknowns are introduced at the nodes whose supports are crossed by discontinuities the method constructs an approximation space consisting of mesh based enriched moving least squares mls functions near discontinuities and standard fe shape functions elsewhere there is only one shape function per node and these functions are able to represent known characteristics of the solution such as discontinuities singularities etc the mls method constructs shape functions based on an intrinsic basis by minimizing a weighted error functional thereby weight functions are involved and special mesh based weight functions are proposed in this work the enrichment is achieved through the intrinsic basis the method is illustrated for linear elastic examples involving strong and weak discontinuities and matches optimal rates of convergence even for crack tip applications copyright 2006 john wiley sons ltd

effects of phase noise on ofdm systems with and without pll characterization and compensation in this paper we propose an algorithm for suppressing intercarrier interference due to phase noise in coded orthogonal frequency division multiplexing ofdm systems the algorithm approximates the phase noise waveform by using a fourier series approximation for the current phase noise realization thereby it cancels the effects of the phase noise beyond the standard common phase error correction used in contemporary ofdm standards the algorithm requires that the correlation properties of the intercarrier interference are known we calculate these properties in terms of the phase noise spectral correlation matrix for both wiener and ornstein uhlenbeck phase noise models respectively this modeling corresponds to a free running oscillator as well as a phase locked loop realization of the local oscillator in orthogonal frequency division multiplexing transceivers for both transceiver configurations we investigate the performance of the proposed algorithm it is demonstrated that the new algorithm achieves as much as one order of magnitude better performance in terms of packet bit error rate when compared to a receiver with only the common phase error suppression

fast integration and weight function blending in the extended finite element method two issues in the extended finite element method xfem are addressed efficient numerical integration of the weak form when the enrichment function is self equilibrating and blending of the enrichment the integration is based on transforming the domain integrals in the weak form into equivalent contour integrals it is shown that the contour form is computationally more efficient than the domain form especially when the enrichment function is singular and or discontinuous a method for alleviating the errors in the blending elements is also studied in this method the enrichment function is pre multiplied by a smooth weight function with compact support to allow for a completely smooth transition between enriched and unenriched subdomains a method for blending step function enrichment with singular enrichments is described it is also shown that if the enrichment is not shifted properly the weighted enrichment is equivalent to the standard enrichment an edge dislocation and a crack problem are used to benchmark the technique the influence of the variables that parameterize the weight function is analyzed the resulting method shows both improved accuracy and optimum convergence rates and is easily implemented into existing xfem codes

higher order xfem for curved strong and weak discontinuities the extended finite element method xfem enables the accurate approximation of solutions with jumps or kinks within elements optimal convergence rates have frequently been achieved for linear elements and piecewise planar interfaces higher order convergence for arbitrary curved interfaces relies on two major issues i an accurate quadrature of the galerkin weak form for the cut elements and ii a careful formulation of the enrichment which should preclude any problems in the blending elements for i we employ a strategy of subdividing the elements into subcells with only one curved side reference elements that are higher order on only one side are then used to map the integration points to the real element for ii we find that enrichments for strong discontinuities are easily extended to higher order accuracy in contrast problems in blending elements may hinder optimal convergence for weak discontinuities different formulations are investigated including the corrected xfem numerical results for several test cases involving strong or weak curved discontinuities are presented quadratic and cubic approximations are investigated optimal convergence rates are achieved using the standard xfem for the case of a strong discontinuity close to optimal convergence rates for the case of a weak discontinuity are achieved using the corrected xfem copyright 2009 john wiley sons ltd

modeling holes and inclusions by level sets in the extended finite element method a methodology to model arbitrary holes and material interfaces inclusions without meshing the internal boundaries is proposed the numerical method couples the level set method s osher j a sethian j comput phys 79 1 1988 12 to the extended finite element method x fem n moes j dolbow t belytschko int j numer methods engrg 46 1 1999 131 in the x fem the finite element approximation is enriched by additional functions through the notion of partition of unity the level set method is used for representing the location of holes and material interfaces and in addition the level set function is used to develop the local enrichment for material interfaces numerical examples in two dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique

an effective xfem with equivalent eigenstrain for stress intensity factors of homogeneous plates abstract based on the concept of equivalent eigenstrain a low order accurate extended finite element method xfem is presented the goal is the determination of the stress intensity factors of cracked homogeneous specimens the proposed approach differs from the conspicuous amount of existing contributions on this topic the findings of the present paper highlight aspects so far neglected in the literature such as the mechanical meaning of additional fields and equations specific to the xfem approximation of the displacement field moreover based on the plane strain examples simulated in the present study the proposed xfem is generally computationally more robust and accurate than existing comparable xfems while keeping a minimal implementation effort

decomposition of m ary cpm signals into pam waveforms it is widely known that minimum shift keying msk may be seen as a pam signaling scheme and that the same is true albeit approximately with msk like modulations it is also known perhaps not so widely that any binary continuous phase modulated cpm signal may be exactly decomposed into the sum of a few pam waveforms in this paper we show that this property extends to multilevel cpm signaling features of a pam decomposition are discussed as a function of the alphabet size the modulation index and the frequency response of the system it is found that especially with signaling schemes with a long memory the decomposition has so many terms that it becomes unmanageable for these cases an approximation is proposed with a limited number of terms

on the construction of blending elements for local partition of unity enriched finite elements for computational efficiency partition of unity enrichments are preferably localized to the sub domains where they are needed it is shown that an appropriate construction of the elements in the blending area the regionwhere the enriched elements blend to unenriched elements is often crucial for good performance of local partition of unity enrichments an enhanced strain formulation is developed which leads to good performance the optimal rate of convergence is achieved for polynomial enrichments it is shown that a proper choice of the finite element shape functions and partition of unity shape functions also improves the accuracy and convergence the methods are illustrated by several examples the examples deal primarily with the signed distance function enrichment for treating discontinuous derivatives inside an element but other enrichments are also considered results show that both methods provide optimal rates of convergence

high order extended finite element method for cracked domains the aim of the paper is to study the capabilities of the extended finite element method xfem to achieve accurate computations in non smooth situations such as crack problems although the xfem method ensures a weaker error than classical nite element methods the rate of convergence is not improved when the mesh parameter h is going to zero because of the presence of a singularity the di culty can be overcome by modifying the enrichment of the nite element basis with the asymptotic crack tip displacement solutions as well as with the heaviside function numerical simulations show that the modi ed xfem method achieves an optimal rate of convergence i e like in a standard nite element method for a smooth problem

stable generalized finite element method sgfem abstract the generalized finite element method gfem is a partition of unity method pum where the trial space of standard finite element method fem is augmented with non polynomial shape functions with compact support these shape functions which are also known as the enrichments mimic the local behavior of the unknown solution of the underlying variational problem gfem has been successfully used to solve a variety of problems with complicated features and microstructure however the stiffness matrix of gfem is badly conditioned much worse compared to the standard fem and there could be a severe loss of accuracy in the computed solution of the associated linear system in this paper we address this issue and propose a modification of the gfem referred to as the stable gfem sgfem we show that sgfem retains the excellent convergence properties of gfem does not require a ramp function in the presence of blending elements and the conditioning of the associated stiffness matrix is not worse than that of the standard fem moreover sgfem is very robust with respect to the parameters of the enrichments we show these features of sgfem on several examples

near optimum low complexity smoothing loops for dynamical phase estimation application to bpsk modulated signals this correspondence provides and analyzes a low complexity near optimum fixed interval smoothing algorithm that approaches the performance of an optimal smoother for the price of two low complexity sequential estimators i e two phase locked loops plls based on a linear approximation of the problem a theoretical performance evaluation is given the theoretical results are compared to some simulation results and to the bayesian and hybrid cramer rao bounds they illustrate the good performance of the proposed smoothing pll s pll algorithm

a posteriori analysis of an iterative multi discretization method for reaction diffusion systems abstract this paper is concerned with the accurate computational error estimation of numerical solutions of multi scale multi physics systems of reaction diffusion equations such systems can present significantly different temporal and spatial scales within the components of the model indicating the use of independent discretizations for different components however multi discretization can have significant effects on accuracy and stability we perform an adjoint based analysis to derive asymptotically accurate a posteriori error estimates for a user defined quantity of interest these estimates account for leading order contributions to the error arising from numerical solution of each component an error due to incomplete iteration an error due to linearization and for errors arising due to the projection of solution components between different spatial meshes several numerical examples with various settings are given to demonstrate the performance of the error estimators

a regularized xfem framework for embedded cohesive interfaces this work focuses on xfem modeling of elastodamaging interfaces characterized by regularized kinematics after regularization of the displacement discontinuity a process zone of finite width with continuous strain fields emerges the stress fields are independently energy deduced modeled via specific constitutive laws and subsequently introduced within the virtual work principle the methodology can address cohesive interfaces with vanishing and finite thickness in a unified way two dimensional results for a strain localization problem and several delamination tests are discussed in detail and compared with previous numerical experimental results