adaptive computations of a posteriori finite element output bounds a comparison of the hybrid flux approach and the flux free approach two different domain decomposition approaches for the a posteriori finite element output bound method with adaptive subdomain refinement are investigated for the three dimensional convection diffusion equation the bound method provides relevant inexpensive rigorous lower and upper bounds for output linear functionals of partial differential equation pde associated with a fine mesh at a fraction of the computational cost of the fine mesh solution to achieve a desired bound gap i e difference between upper and lower output bounds at the lowest cost an adaptive subdomain refinement technique is used to refine subdomains only where needed the bound method based on a finite element domain decomposition technique requires two global calculations and a multitude of subdomain computations there are two main approaches to decompose a global domain into local subdomains for the subdomain based output bound method a hybrid flux elemental neumann subdomain approach and a flux free nodal neumann subdomain approach in this paper the two different domain decomposition approaches are briefly described and compared linear and quadratic finite element discretizations for the hybrid flux and flux free approaches are developed and validated for a convergence test and an adaptive subdomain refinement example the comparison of the hybrid flux and flux free approaches is presented in terms of numerical accuracy and computational cost

performance analysis of coded modulation with generalized selection combining in rayleigh fading we consider coded modulation with generalized selection combining gsc for bandwidth efficient coded modulation over rayleigh fading channels our results show that reception diversity with generalized selection combining can conveniently trade off system complexity versus performance we provide a number of new results by calculating the cutoff rate and by deriving analytical upper bounds on symbol interleaved trellis coded modulation tcm and bit interleaved coded modulation bicm with gsc all are verified by simulation we show that our new bounds on tcm with gsc which includes maximum ratio combining and selection combining as special cases are tighter than the previously derived bounds a new asymptotic analysis on the pairwise error probability which can be used as a guideline for designing coded modulation over gsc channels is also given finally we show that bicm with iterative decoding bicm id can achieve significant coding gain over conventional coded modulation in a multiple receiving antenna channel

acoustic design by topology optimization abstract to bring down noise levels in human surroundings is an important issue and a method to reduce noise by means of topology optimization is presented here the acoustic field is modeled by helmholtz equation and the topology optimization method is based on continuous material interpolation functions in the density and bulk modulus the objective function is the squared sound pressure amplitude first room acoustic problems are considered and it is shown that the sound level can be reduced in a certain part of the room by an optimized distribution of reflecting material in a design domain along the ceiling or by distribution of absorbing and reflecting material along the walls we obtain well defined optimized designs for a single frequency or a frequency interval for both 2d and 3d problems when considering low frequencies second it is shown that the method can be applied to design outdoor sound barriers in order to reduce the sound level in the shadow zone behind the barrier a reduction of up to 10 db for a single barrier and almost 30 db when using two barriers are achieved compared to utilizing conventional sound barriers

shape design sensitivity analysis for the radiated noise from the thin body abstract many industrial applications generally use thin body structures in their design to calculate the radiated noise from vibrated structure including thin bodies the conventional boundary element method bem using the helmholtz integral equation is not an effective resolution thus many researchers have studied to resolve the thin body problem in various physical fields no major study in the design sensitivity analysis dsa fields for thin body acoustics however has been reported a continuum based shape dsa method is presented for the radiated noise from the thin body the normal derivative integral equation is employed as an analysis formulation and for the acoustic shape design sensitivity formulation the equation is differentiated directly by using material derivative concept to solve the normal derivative integral equation the normal velocities on the surface should be calculated in the acoustic shape sensitivity formulation not only the normal velocities on the surface are required but also derivative coefficients of the normal velocities structural shape design sensitivity are also required as the input hence the shape design sensitivity of structural velocities on the surface with respect to the shape change should be calculated in this research the structural shape design sensitivities are also obtained by using a continuum approach and both a modified interpolation function and the cauchy principle value are used to regularize the singularities generated from the acoustic shape design sensitivity formulation a simple annular disk is considered as a numerical example to validate the accuracy and efficiency of the shape design sensitivity equations derived in this research the commercial bem code sysnoise is utilized to confirm the results of the developed in house code based on a normal derivative integral equation to validate the calculated design sensitivity results central finite difference method fdm is employed the error between fdm and the analytical result are less than 3 this comparison demonstrates that the proposed design sensitivities of the radiated pressure are very accurate

new closed form bounds on the performance of coding in correlated rayleigh fading new simple bounds are presented for the probability of error in a binary hypothesis test for communications using diversity signaling in correlated rayleigh fading the bounds are developed in the context of pairwise error event probabilities in decoding an error correction code a long standing conjecture regarding the form of worst case error events in exponentially correlated rayleigh fading is also proven the utility of the results is illustrated by their application to transfer function bounds on the probability of bit error for a system using a convolutional code the closed form transfer function bounds are shown to be tighter than previously developed transfer function bounds for communications in exponentially correlated rayleigh fading

a local a posteriori error estimator based on equilibrated fluxes we present and analyze a new a posteriori error estimator for lowest order conforming finite elements it is based on raviart thomas finite elements and can be obtained locally by a postprocessing technique involving for each vertex a local subproblem associated with a dual mesh under certain regularity assumptions on the right hand side we obtain an error estimator where the constant in the upper bound for the true error tends to one replacing the conforming finite element solution by a postprocessed one the error estimator is asymptotically exact the local equivalence between our estimator and the standard residual based error estimator is established numerical results illustrate the performance of the error estimator

a finite element boundary element method for large displacement fluid structure interaction with potential flow this work concerns the interaction of light membrane structures enclosing incompressible fluids large displacements and collapsed boundaries initially slender subdomains are characteristic of this class of problems a finite element boundary element fe be coupled discretization is presented as an enabling technology addressing these challenges by avoiding volumetric meshing as required by arbitrary lagrangian eulerian or immersed boundary type methods the presented formulation includes a compatibility condition to which a physical interpretation is given and a regularizing bending stiffness observed to be necessary from both the theoretical well posedness and numerical stability point of view a cheap contact load is designed to deal with possibly complex geometries reusing already computed discrete boundary element kernels numerical experiments show the capabilities of the proposed scheme

structural acoustic optimum design of shell structures in open closed space based on a free form optimization method abstract noise reduction by structural geometry optimization has attracted much attention among designers in the present work we propose a free form optimization method for the structural acoustic design optimization of shell structures to reduce the noise of a targeted frequency or frequency range in an open or closed space the objective of the design optimization is to minimize the average structural vibration induced sound pressure at the evaluation points in the acoustic field under a volume constraint for the shape design optimization we carry out structural acoustic coupling analysis and adjoint analysis to calculate the shape gradient functions then we use the shape gradient functions in velocity analysis to update the shape of shell structures we repeat this process until convergence is confirmed to obtain the optimum shape of the shell structures in a structural acoustic coupling system the numerical results for the considered examples showed that the proposed design optimization process can significantly reduce the noise in both open and closed spaces

thickness optimization of a multilayered structure on the coupling surface between a structure and an acoustic cavity this paper describes a new design method to optimize thickness distribution of a multilayered structure which is located on the coupling surface between a structure and an acoustic cavity the design method is based on the concept of the density approach in topology optimization incorporating a transfer matrix for a multilayered structure that includes a poroelastic media layer the one dimensional transfer matrix adopted here is an approximate representation addressing vibro acoustic effects inherent in a multilayered structure and balances calculation resources and desired accuracy applying the transfer matrix representation as boundary conditions on the coupling surface between a structure and an acoustic cavity the modified equilibrium equation of the vibro acoustic system is derived which is approximately but efficiently solved by the modal approach in this study the problem of minimizing the acoustic pressure within the cavity over the prescribed frequency range is formulated under the volume constraint of the poroelastic media layer the continuous approximation of thickness distribution is assumed and the thickness of the poroelastic media layer at each nodal point is chosen as design variables numerical results show that an acoustic response is significantly reduced by the optimal thickness distribution having a total weight equal to or less than that in the initial uniform thickness these demonstrate that the proposed method is effective to design the optimal thickness distribution of a multilayered structure

error estimate procedure in the finite element method and applications statically and kinematically admissible fields are explicitly derived from the finite element solution of the primal form of linear models the error on constitutive law for these fields yields an expression of the finite element error moreover the contribution of each element to this error allows to implement an automatic mesh refinement procedure leading to a uniform distribution of a given accuracy

shape optimization of an acoustic horn the shape of an acoustic horn is optimized with respect to its ability to provide impedance matching to the surrounding air the resulting minimization problem is solved using a bfgs quasi newton algorithm the wave propagation is modeled by a finite element approximation of the helmholtz equation and the necessary objective function gradient is calculated from the solution of the associated adjoint equation local solutions to the optimization problem corresponding to irregular horn contours are avoided by using a filtering technique that applies smoothing to the design updates and the gradient the method converges fast to a smooth solution and the resulting horn has good impedance properties throughout the entire frequency band of interest

achievable performance over the correlated rician channel the correlated rician channel is a useful model for a slowly fading channel in which the complex fading process is composed of two quadrature gaussian processes with a given autocorrelation function for slow fading the correlation between adjacent symbols is relatively high the authors investigate the achievable error probabilities over the channel employing coherent detection and ideal side information on the realization of the fading processes at the receiver an underlying decoding delay constraint which precludes the use of ideal interleaving is assumed coded bpsk performance is addressed both with and without the piecewise constant approximation according to which the fading value remains constant during the symbol duration for the latter case that is no piecewise constant approximation the analysis relies on the fredholm determinant associated with the fading process autocorrelation function the authors focus on the exponentially correlated channel the worst case pairs of codewords are identified the exponential behavior of the error probability with random coding and i i d gaussian inputs is analyzed and the behavior of the cut off rate and capacity is addressed the results enhance the insight to the effect of the basic parameters governing the performance and these are examined in view of previous works and compared to relevant performance results for the block fading channel model

topology optimization for the radiation and scattering of sound from thin body using genetic algorithms abstract many industrial applications generally use thin body structures in their design to calculate the radiation and scattering of sound from a thin body structure the conventional boundary element method bem using the helmholtz integral equation is not an effective resolution especially if the structure including a thin body is not fully closed the conventional bem fails to yield a reliable solution unfortunately most applications requiring the noise prediction generally have some openings because of cooling and so on therefore many researchers have studied to resolve the thin body problem in various fields in engineering optimization fields even though several studies have been made on the design optimization to improve the acoustic characteristic of a closed structure by using the conventional bem no study has been yet reported for the design of the holes on the thin body using topology optimization in this research the normal derivative integral equation is used to solve the acoustic problem of a thin body structure also based on the normal derivative integral equation the topology optimization of the thin body has been studied for the design of the holes an in house code actop is developed and implemented for the acoustical topology optimization using a genetic algorithm by using a simple box example the utility of actop is validated the results of examples show that actop can provide very good initial design for acoustic problems therefore the proposed topology optimization technique should be attractive for a design engineer in acoustic fields

local error estimators for finite element linear analysis local error estimators on stresses displacements etc are derived from constitutive relation error estimators examples show that they can be considered as an upper bound

local error estimates of fem for displacements and stresses in linear elasticity by solving local neumann problems in this paper we present two types of local error estimators for the primal finite element method fem by duality arguments they are first derived from the explicit residual error estimation method rem and then as a new contribution from the implicit posterior equilibrium method pem using improved boundary tractions gained by local post processing with local neumann problems with applications in elastic problems for the displacements a local error estimator with an upper bound is derived and also a local estimator for stresses furthermore for better numerical efficiency the residua are projected energy invariant onto reference elements where the local neumann problems have to be solved comparative examples between rem and pem type local estimators show superior effectivity indices for the latter one copyright 2001 john wiley sons ltd

variations on the gallager bounds connections and applications there has been renewed interest in deriving tight bounds on the error performance of specific codes and ensembles based on their distance spectrum we discuss many reported upper bounds on the maximum likelihood ml decoding error probability and demonstrate the underlying connections that exist between them in addressing the gallager bounds and their variations we focus on the duman and salehi see ieee trans commun vol 46 p 717 723 1998 variation which originates from the standard gallager bound a large class of efficient bounds or their chernoff versions is demonstrated to be a special case of the generalized second version of the duman and salehi bounds implications and applications of these observations are pointed out including the fully interleaved fading channel resorting to either matched or mismatched decoding the proposed approach can be generalized to geometrically uniform nonbinary codes finite state channels bit interleaved coded modulation systems and it can be also used for the derivation of upper bounds on the conditional decoding error probability

evaluation of the exact union bound for trellis coded modulations over fading channels an analytical technique is presented for computing the exact union bound on the average bit error probability of trellis coded modulation schemes over rayleigh rician or shadowed rician fading channels to this end an integral expression is derived for the pairwise error event probability pep existing bounds can be obtained as special cases of this expression it turns out that a gauss chebyshev quadrature rule offers excellent accuracy for this integral by extension the exact union bound i e the weighted sum of an exact peps of a code can readily be evaluated this method has the same complexity as the union chernoff bound and a few examples are given to show its application

natural element approximation of reissner mindlin plate for locking free numerical analysis of plate like thin elastic structures abstract a rotation free mixed natural element approximation of reissner mindlin plate for the locking free numerical analysis of plate like thin elastic structures is presented motivated by the rotation free approximation for plate and shell like elastic structures and the high smoothness of laplace interpolation functions used in natural element method the mid surface deflection and the rotation of shear are directly approximated using laplace interpolation functions while the voronoi polygon wise constant curvatures and bending moments are indirectly computed by area averaging the boundary integrals of deflection derivatives and rotation of shear the present approximation of the deflection and rotation of shear of discretized reissner mindlin plate bending problem is formulated according to the modified mixed hu washizu principle through the numerical results it is verified that the rotation free mixed natural element approximation of only the deflection and rotation of shear successfully prevents shear locking in the numerical analysis of plate like thin elastic structures

error estimation of stress intensity factors for mixed mode cracks this paper presents an a posteriori error estimator for mixed mode stress intensity factors in plane linear elasticity a surface integral over an arbitrary crown is used for the separate calculation of the combined mode s stress intensity factors the error in the quantity of interest is based on goal oriented error measures and estimated through an error in the constitutive relation copyright 2006 john wiley sons ltd

bounds on the error performance of coding for nonindependent rician fading channels new upper bounds on the error performance of coded systems for rician channels are presented the fading channels need not be fully interleaved to obtain meaningful performance results these bounds hold for coherent differentially coherent and noncoherent demodulation of binary signals they provide a useful analytical approach to the evaluation of the error performance of convolutional or block coding and they may be generalized to m ary signals and trellis modulation the approach allows for complex bounds using the fine structure of the code for simpler bounds similar to those on memoryless channels and finally for a random coding bound using the cutoff rate of the channel the analysis thus permits a step by step evaluation of coded error performances for rician fading channels

goal oriented a posteriori error estimates in linear elastic fracture mechanics goal oriented a posteriori error estimators are presented in this paper for the error obtained while approximately evaluating the j integral in linear elastic fracture mechanics using the finite element method the j integral provides a criterion for crack propagation of a pre existing crack therefore its reliable and accurate evaluation is of considerable importance in engineering applications to prevent failure of structures this can be achieved by goal oriented adaptive finite element methods based on the well established strategy of solving an auxiliary dual problem in order to control the error of a non linear functional here the j integral in this paper two principally different goal oriented adaptive strategies are presented the first strategy rests upon equilibrated residual error estimators based on local neumann problems whereas the second one makes use of averaging techniques the paper is concluded by a numerical example that illustrates our theoretical results

tight analytical and asymptotic upper bound for the ber and fer of linear codes over exponentially correlated generalized fading channels in this paper the upper bound and asymptotical approximation for the bit error rate ber as well as for the frame error rate of linear block codes under maximum likelihood decoding operating over exponentially correlated ec generalized fading channels are proposed particularly our analysis takes the convolutional codes as an example and three different fading scenarios are considered namely rice nakagami m and weibull fading such scenarios have a common property that is spherically invariant random process sirp our analysis relies on the derivation of new lower bounds per each eigenvalue since the ber as well as the fer expressions are written in terms of the pairwise error probability which by its turn depends on the eigenvalues of the channel covariance matrix based on that the upper bounds and asymptotic expressions of the considered metrics subject to the three above fading models are derived which show to be tighter than the previous results published elsewhere in the literature especially for the high signal to noise ratio regions

the post processing approach in the finite element method part 2 the calculation of stress intensity factors abstract in the context of a model problem the authors describe post processing techniques for the calculation of generalized stress intensity factors they discuss two broad classes of methods one involving an influence function and the other related to the well known energy release principle of fracture mechanics an error analysis is sketched and two numerical examples are given to illustrate the effectivity of the techniques this is the second in a series of three papers author

some new twists to problems involving the gaussian probability integral using an alternate form of the gaussian probability integral discovered a number of years ago it is shown that the solution to a number of previously considered communication problems can be simplified and in some cases made more accurate i e exact rather than bounded these problems include the evaluation of 1 the bit error probability of uncoded phase shift keying psk with costas loop tracking 2 word error probability of antipodal modulation in the presence of fading 3 bit error probability of coded m ary psk mpsk over the memoryless fading channel with given channel state information 4 conditional symbol error probability of mpsk in the presence of carrier synchronization error and 5 the average error probability for the binary additive white gaussian noise awgn intersymbol interference channel also obtained is a generalization of this new alternate form to the case of a two dimensional gaussian probability integral with arbitrary correlation which can be used to evaluate the symbol error probability of mpsk with i q unbalance

local problems on stars a posteriori error estimators convergence and performance a new computable a posteriori error estimator is introduced which relies on the solution of small discrete problems on stars it exhibits built in flux equilibration and is equivalent to the energy error up to data oscillation without any saturation assumption a simple adaptive strategy is designed which simultaneously reduces error and data oscillation and is shown to converge without mesh pre adaptation nor explicit knowledge of constants numerical experiments reveal a competitive performance show extremely good effectivity indices and yield quasi optimal meshes

subdomain based flux free a posteriori error estimators a new residual type flux free error estimator is presented it estimates upper and lower bounds of the error in energy norm the proposed approach precludes the main drawbacks of standard residual type estimators circumvents the need of flux equilibration and results in a simple implementation that uses standard resources available in finite element codes this is specially interesting for 3d applications where the implementation of this technique is as simple as in 2d recall that on the contrary the complexity of the flux equilibration techniques increases drastically in the 3d case the bounds for the energy norm of the error are used to produce upper and lower bounds of linear functional outputs representing quantities of engineering interest the presented estimators demonstrate their efficiency in numerical tests producing sharp estimates both for the energy and the quantities of interest

tailoring static deformation of frame structures based on a non parametric shape size optimization method abstract in this study a non parametric shape size optimization method is developed for tailoring the static deformation of large scale frame structures this deformation control design is one of the important problems in the stiffness design of frame structures and enables us to create a smart or a high performance structure for a specific ability of deformation as the objective functional we introduce the sum of squared error norms for achieving the desired displacements on specified members and assume that each frame member varies in the off axis direction with changing cross sections the shape gradient function the size gradient function and the optimality conditions for this problem are theoretically derived with the lagrange multiplier method the material derivative method and the adjoint variable method the optimal shape size variations that minimize the objective functional are determined by using the h1 gradient method for frame structures with the proposed method the optimal arbitrarily formed frame structures with the optimal cross sections can be obtained without any shape and size parameterization while maintaining their smoothness the validity and practical utility of this method for tailoring the static deformation of frame structures are verified through design examples

a constitutive relation error estimator based on traction free recovery of the equilibrated stress a new methodology for recovering equilibrated stress fields is presented which is based on traction free subdomains computations it allows a rather simple implementation in a standard finite element code compared with the standard technique for recovering equilibrated tractions these equilibrated stresses are used to compute a constitutive relation error estimator for a finite element model in 2d linear elasticity a lower bound and an upper bound for the discretization error are derived from the error in the constitutive relation these bounds in the discretization error are used to build lower and upper bounds for local quantities of interest copyright 2008 john wiley sons ltd

on goal oriented error estimation for elliptic problems application to the control of pointwise errors a method to estimate and control pointwise errors in finite element approximations of elliptic problems is presented as an application of the more general theory of goal oriented error estimation in the latter the accuracy of numerical approximations is assessed in terms of measures that are of practical interest to engineers rather than the classical global energy norm goal oriented error estimation requires the solution of a problem dual to the original problem and the computation of several global error estimates the performance of the method is carefully tested in the particular case of estimation and control of pointwise errors on a one dimensional problem

a posteriori estimation and adaptive control of the error in the quantity of interest part i a posteriori estimation of the error in the von mises stress and the stress intensity factor in this paper we address the problem of a posteriori estimation of the error in an engineering quantity of interest which is computed from a finite element solution as an example we consider the plane elasticity problem with the von mises stress and the stress intensity factor as the quantities of interest the estimates of the error in the von mises stress at a point are obtained by partitioning the error into two components with respect to the element which includes the point the local and the pollution errors and by constructing separate estimates for each component the estimates of the error in the stress intensity factors are constructed by employing an extraction method we demonstrate that our approach gives accurate estimates for rather coarse meshes and elements of various degrees in part ii we will address the problem of the adaptive control of the error in the quantity of interest the goal of the computation and the construction of goal adaptive meshes for one or multiple goals

evaluation of the local quality of stresses in 3d finite element analysis this article deals with the local quality on stresses produced during finite element analysis in 3d linear elasticity we use an estimation technique based on the concept of error in constitutive relation which yields excellent estimates of the local errors without requiring the approximate calculation of green functions