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

numerical solution of a system of fuzzy polynomials by fuzzy neural network in this paper a new approach for solving systems of fuzzy polynomials based on fuzzy neural network fnn is presented this method can also lead to improve numerical methods in this work an architecture of fuzzy neural networks is also proposed to find a real root of a system of fuzzy polynomials if exists by introducing a learning algorithm finally we illustrate our approach by numerical examples

newton s method for solving a system of fuzzy nonlinear equations abstract in this paper we propose the numerical solution for a system of fuzzy nonlinear equations by newton s method the fuzzy quantities are presented in parametric form some numerical illustrations are given to show the efficiency of algorithm

efficient computation of the sound fields above a layered porous ground an efficient computation of sound fields due to a monopole source placed above a porous layer is presented this paper examines an improved scheme whereby the steepest descent path is selected for the numerical evaluation of the sommerfeld integral along the steepest descent path a standard gaussian hermite quadrature can be used to calculate the sound fields effectively the suggested numerical scheme is accurate at all frequencies except in the very near field the proposed method is more numerically efficient than other computational schemes especially at long ranges and high source frequencies

the variational multiscale method a paradigm for computational mechanics abstract we present a general treatment of the variational multiscale method in the context of an abstract dirichlet problem we show how the exact theory represents a paradigm for subgrid scale models and a posteriori error estimation we examine hierarchical p methods and bubbles in order to understand and ultimately approximate the fine scale green s function which appears in the theory we review relationships between residual free bubbles element green s functions and stabilized methods these suggest the applicability of the methodology to physically interesting problems in fluid mechanics acoustics and electromagnetics

a stabilized finite element method for generalized stationary incompressible flows abstract in this paper we describe a finite element formulation for the numerical solution of the stationary incompressible navier stokes equations including coriolis forces and the permeability of the medium the stabilized method is based on the algebraic version of the sub grid scale approach we first describe this technique for general systems of convection diffusion reaction equations and then we apply it to the linearized flow equations the important point is the design of the matrix of stabilization parameters that the method has this design is based on the identification of the stability problems of the galerkin method and a scaling of variables argument to determine which coefficients must be included in the stabilization matrix this together with the convergence analysis of the linearized problem leads to a simple expression for the stabilization parameters in the general situation considered in the paper the numerical analysis of the linearized problem also shows that the method has optimal convergence properties

a multiscale stabilized finite element method for the advection diffusion equation this paper presents a multiscale method that yields a stabilized finite element formulation for the advection diffusion equation the multiscale method arises from a decomposition of the scalar field into coarse resolved scale and fine unresolved scale the resulting stabilized formulation possesses superior properties like that of the supg and the gls methods a significant feature of the present method is that the definition of the stabilization term appears naturally and therefore the formulation is free of any user designed or user defined parameters another important ingredient is that since the method is residual based it satisfies consistency ab initio based on the proposed formulation a family of 2 d elements comprising 3 and 6 node triangles and 4 and 9 node quadrilaterals has been developed numerical results show the good performance of the method on uniform skewed as well as composite meshes and confirm convergence at optimal rates 2004 elsevier b v all rights reserved

a simple subgrid scale stabilized method for the advection diffusion reaction equation abstract a subgrid scale method has been developed for the advection diffusion reaction equation with a simple intrinsic time scale parameter the proposed formulation combines very good accuracy and stability in all the physical regimes of the equation that is in the exponential regime for both negative and positive source terms and in the propagation regime numerical examples confirm the robustness and accuracy of the method

variational subgrid scale formulations for the advection diffusion reaction equation abstract the exact variational multiscale vms and the subgrid scale sgs methods have been developed for the advection reaction and the advection diffusion reaction equations from the element green s function approximate intrinsic time scale parameters have been derived for these cases and are shown to be similar to other expressions obtained in the literature out of the maximum principle and convergence error analysis the methods have been compared with typical stabilized finite element methods as expected the vms is nodally exact for the one dimensional case

stabilized finite element methods for steady advection diffusion with production abstract finite element methods for solving equations of steady advection diffusion with production are constructed employing a linear source to model production the galerkin method requires relatively fine meshes to retain an acceptable degree of accuracy for wide ranges of values of the physical coefficients numerous criteria for improved accuracy via galerkin least squares are proposed and examined in the entire parameter space of these several provide the lowest error in nodal amplification factors each in a certain range of ratios of physical coefficients guidelines for required mesh resolutions are presented for galerkin and galerkin least squares showing that in large parts of the parameter space substantial savings may be obtained by employing galerkin least squares galerkin least squares gradient least squares a new variation of the galerkin method is designed to provide exact nodal amplification factors offering accurate solutions at any resolution numerical tests validate these conclusions

analysis of approximation of continuous fuzzy functions by multivariate fuzzy polynomials for the given fuzzy valued function j rn f0 r the fuzzy valued bernstein polynomial is introduced to show the fact that continuous fuzzy valued functions can be approximately represented as the fuzzy valued polynomials on any compact set u rn some equivalent condition for the continuous fuzzy function f f0 r n f0 r that can be approximated to any degree of accuracy by fuzzy polynomials on arbitrary compact set u f0 r n are presented

deduction of ground impedance from measurements of excess attenuation spectra an efficient numerical method of deducing ground surface impedance from measurements of short range propagation from a point source is proposed the method involves finding the root of a complex equation and uses the fact that the classical approximation for the spherical wave reflection coefficient near grazing incidence is an analytic function of the impedance examples of fitting measured excess attenuation spectra are given methods for ensuring the uniqueness of the resulting impedance fits are discussed subsequent deductions of parameters in a two parameter impedance model are also considered and exemplified

a stabilized finite element method based on sgs models for compressible flows abstract we present an appropriate extension of the stabilized finite element formulation introduced in a corsini f rispoli a santoriello a variational multiscale high order finite element formulation for turbomachinery flow computations comput methods appl mech engrg 194 2005 4797 4823 for the prediction of incompressible flows aimed at compressible flows the stabilized formulation is the so called variable subgrid scale method v sgs based on an approximation of the class of subgrid scale models sgs derived from the hughes variational multiscale method hughes vms introduced in t j r hughes multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods comput methods appl mech engrg 127 1995 387 401 it is characterized by a variable stabilization parameter within the domain of element we also propose an innovative procedure for computing the stabilization parameter by using the one dimensional element green s functions corresponding to an advective diffusive differential operator the stabilization parameter is defined as the sum of two components the first providing its mean value and the second its element wise space dependency on this basis the present work proposes the stabilization matrix for the multidimensional advective diffusive system of equations governing compressible flows the procedure developed for computing the stabilization parameter can be applied to other differential operators as it has been shown in a corsini f rispoli a santoriello a variational multiscale high order finite element formulation for turbomachinery flow computations comput methods appl mech engrg 194 2005 4797 4823 the proposed stabilization device is validated by simulation of inviscid and viscous supersonic flow configurations

neural net solutions to fuzzy problems the quadratic equation abstract this paper continues our research on using neural nets to solve fuzzy equations after outlining our general method of employing neural nets to solve fuzzy problems we concentrate on solving the fuzzy quadratic equation we show how neural nets can produce both real and complex fuzzy number solutions

applications of the pseudo residual free bubbles to the stabilization of convection diffusion problems abstract residual free bubbles have been recently introduced in order to compute optimal values for the stabilization methods a la hughes franca however unless in very special situations one dimensional problems limit cases etc they require the actual solution of pde problems the bubble problems in each element thus they are very difficult to be used in practice in this paper we present for the special case of convection dominated elliptic problems a cheap way to compute approximately the solution of the bubble problem in each element this provides as a consequence a cheap way to compute good approximations for the optimal values of the stabilization parameters

heuristic approximations for sound fields produced by spherical waves incident on locally and non locally reacting planar surfaces the classic weyl van der pol wvdp formula is a well known asymptotic solution for accurately predicting sound fields above a locally reacting ground surface however the form of the wvdp formula is inadequate for predicting sound fields in the vicinity of non locally reacting surfaces a correction term is often required in the formula to provide accurate numerical solutions even with this correction there is a singularity in the diffraction wave term when the source is located directly above or below the receiver this paper explores a heuristic method to remove this singularity and suggests an analytical form comparable to the wvdp formula this improved formula offers a physically interpretable solution and allows for accurate predictions of the total sound field above locally and non locally reacting surfaces for all geometrical configurations

numerical approximation of fuzzy functions by fuzzy polynomials one of the interesting important and attractive problems in applied mathematics is how to best approximate a function in a given space in this paper the problem of best approximation is considered for fuzzy functions by optimization to obtain a fuzzy polynomial

a flexible inner outer preconditioned gmres algorithm a variant of the gmres algorithm is presented that allows changes in the preconditioning at every step there are many possible applications of the new algorithm some of which are briefly discussed in particular a result of the flexibility of the new variant is that any iterative method can be used as a preconditioner for example the standard gmres algorithm itself can be used as a preconditioner as can cgnr or cgne the conjugate gradient method applied to the normal equations however the more appealing utilization of the method is in conjunction with relaxation techniques possibly multilevel techniques the possibility of changing preconditioners may be exploited to develop efficient iterative methods and to enhance robustness a few numerical experiments are reported to illustrate this fact

genetically optimized fuzzy polynomial neural networks with fuzzy set based polynomial neurons in this paper we propose and investigate a new category of neurofuzzy networks fuzzy polynomial neural networks fpnn endowed with fuzzy set based polynomial neurons fspns we develop a comprehensive design methodology involving mechanisms of genetic optimization and genetic algorithms gas in particular the conventional fpnns developed so far are based on the mechanisms of self organization fuzzy neurocomputing and evolutionary optimization the design of the network exploits the fspns as well as the extended group method of data handling gmdh let us stress that in the previous development strategies some essential parameters of the networks such as the number of input variables the order of the polynomial the number of membership functions and a collection of the specific subset of input variables being available within the network are provided by the designer in advance and kept fixed throughout the overall development process this restriction may hamper a possibility of developing an optimal architecture of the model the design proposed in this study addresses this issue the augmented and genetically developed fpnn gfpnn results in a structurally optimized structure and comes with a higher level of flexibility in comparison to the one we encounter in the conventional fpnns the ga based design procedure being applied at each layer of the fpnn leads to the selection of the most suitable nodes or fspns available within the fpnn in the sequel two general optimization mechanisms are explored first the structural optimization is realized via gas whereas the ensuing detailed parametric optimization is carried out in the setting of a standard least square method based learning the performance of the gfpnn is quantified through experimentation in which we use a number of modeling benchmarks synthetic and experimental data being commonly used in fuzzy or neurofuzzy modeling the obtained results demonstrate the superiority of the proposed networks over the models existing in the references

fuzzy integral based perceptron for two class pattern classification problems the single layer perceptron with single output node is a well known neural network for two class classification problems furthermore the sigmoid or logistic function is usually used as the activation function in the output neuron a critical step is to compute the sum of the products of the connection weights with the corresponding inputs which indicates the assumption of additivity among individual variables unfortunately because the input variables are not always independent of each other an assumption of additivity may not be reasonable enough in this paper the inner product can be replaced with an aggregation value obtained by a useful fuzzy integral by viewing each of the connection weights as a value of a l fuzzy measure for the corresponding variable a genetic algorithm is then employed to obtain connection weights by maximizing the number of correctly classified training patterns and minimizing the errors between the actual and desired outputs of individual training patterns the experimental results further demonstrate that the proposed method outperforms the traditional single layer perceptron and performs well in comparison with other fuzzy or non fuzzy classification methods

a learning algorithm of fuzzy neural networks with triangular fuzzy weights abstract in this paper first we propose an architecture of fuzzy neural networks with triangular fuzzy weights the proposed fuzzy neural network can handle fuzzy input vectors as well as real input vectors in both cases outputs from the fuzzy neural network are fuzzy vectors the input output relation of each unit of the fuzzy neural network is defined by the extension principle of zadeh next we define a cost function for the level sets i e cuts of fuzzy outputs and fuzzy targets then we derive a learning algorithm from the cost function for adjusting three parameters of each triangular fuzzy weight finally we illustrate our approach by computer simulations on numerical examples

numerical solution of fuzzy polynomials by fuzzy neural network in this paper an architecture of fuzzy neural networks is proposed to find a real root of fuzzy polynomials if exists by introducing a learning algorithm we proposed a learning algorithm from the cost function for adjusting of crisp weights finally we illustrated our approach by numerical examples

impedance measurements around grazing incidence for nonlocally reacting thin porous layers for locally reacting materials with a constant surface impedance a classical method based on the work of chien and soroka j sound vib 43 9 20 1975 for measuring this impedance in situ around grazing incidence is currently used a generalization of this work to include thin nonlocally reacting materials with a surface impedance noticeably dependent on the angle of incidence is performed it is shown that the model by chien and soroka can be used though the constant surface impedance must be replaced by the impedance at grazing incidence for the evaluation of the numerical distance measurements performed on a thin porous layer using this method are compared with measurements performed using the near field acoustical holography method m tamura j acoust soc am 88 2259 2264 1990 other measurements performed on a fibrous layer are in good agreement with the predicted values of the impedance at grazing incidence

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

ranking of fuzzy numbers by sign distance several different strategies have been proposed for ranking of fuzzy numbers these include methods based on the coefficient of variation cv index distance between fuzzy sets centroid point and original point and weighted mean value each of these techniques has been shown to produce non intuitive results in certain cases in this paper we propose a modification of the distance based approach called the sign distance which is both efficient to evaluate and able to overcome the shortcomings of the previous techniques the calculation of the proposed method is far simpler than the other approaches

solving linear and quadratic fuzzy equations abstract we present necessary and sufficient conditions for some linear and quadratic equations to have a solution when the parameters are either real or complex fuzzy numbers the solution will be a real or complex fuzzy number applications in chemistry economics finance and physics are presented for these types of equations

fuzzy data processing using polynomial bidirectional hetero associative network abstract this investigation presents a novel method of fuzzy data processing using polynomial bidirectional hetero associative network pbhan this has a higher capacity for pattern pair storage than that of the conventional bidirectional associative memories bams and fuzzy memories in addition a new energy function is defined the pbhan takes advantage of fuzzy characteristics in evolution equations such that the signal noise ratio snr is significantly increased the energy of the pbhan defined by the proposed energy function decreases as the recall process proceeds thereby ensuring the stability of the system in this work we prove the stability of fuzzy data processing using pbhan the increase of snr consequently enhances the capacity of the pbhan the capacity of the fuzzy data processing using pbhan in the worst case is also estimated

a petrov galerkin formulation for advection reaction diffusion problems abstract in this work we present a new method called su c pg to solve advection reaction diffusion scalar equations by the finite element method fem the supg for streamline upwind petrov galerkin method is currently one of the most popular methods for advection diffusion problems due to its inherent consistency and efficiency in avoiding the spurious oscillations obtained from the plain galerkin method when there are discontinuities in the solution following this ideas tezduyar and park treated the more general advection reaction diffusion problem and they developed a stabilizing term for advection reaction problems without significant diffusive boundary layers in this work an supg extension for all situations is performed covering the whole plane represented by the peclet number and the dimensionless reaction number the scheme is based on the extension of the super convergence feature through the inclusion of an additional perturbation function and a corresponding proportionality constant both proportionality constants that one corresponding to the standard perturbation function from supg and the new one introduced here are selected in order to verify the super convergence feature i e exact nodal values are obtained for a restricted class of problems uniform mesh no source term constant physical properties it is also shown that the su c pg scheme verifies the discrete maximum principle dmp that guarantees uniform convergence of the finite element solution moreover it is shown that super convergence is closely related to the dmp motivating the interest in developing numerical schemes that extend the super convergence feature to a broader class of problems

separated flow computations with the k e v2 model tlirbulent separated flows over a backstep in a plane diffuser and around a triangular cylinder are computed with the k e v2 model these provide examples of massive separation of smooth separation and of unsteady vortex shedding it is shown that to accurately predict the time averaged properties of bluff body flow it is necessary to resolve the coherent vortex shedding the near wall treatment of the v2 22 system of equations is able to cope with both the massive and smooth separations good agreement between experiment and prediction is found in all

spatial fourier transform method of measuring reflection coefficients at oblique incidence i theory and numerical examples a new method using spatial fourier transform has been developed to measure reflection coefficients at oblique incidence the method involves the measurement of complex pressure distributions on two parallel planes lying close to the surface of a test material and decomposing each of the complex pressure distributions into plane wave components by using two dimensional spatial fourier transform the incident and reflected plane wave components on the surface of the test material can be mathematically separated by the use of plane wave propagation theory this separation leads to the determination of reflection coefficients at arbitrary angles of incidence investigation has been made into the error due to the finite size of the measurement area to show that the magnitude of the error can be reduced by using a dipole source instead of a monopole source numerical examples are given to illustrate the validity of the method

an approach to causal modeling in fuzzy environment and its application abstract this paper suggests an approach to building a causal model in fuzzy environment the fuzzy vector autoregressive fvar model is defined and a causality definition in the fuzzy environment is provided three types of causality namely nonfuzzy non causality nonfuzzy causality and fuzzy causality are defined based on the fuzzy causality relation introduced in this paper necessary and sufficient conditions for the three types of causality are also provided when fuzzy parameters have triangular membership functions a procedure to implement the fuzzy causal modeling is also suggested we applied the procedure to real data and compared it with other conventional empirical studies

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

a variational multiscale higher order finite element formulation for turbomachinery flow computations abstract the variational multiscale approach for finite elements addresses the inclusion of the effect of fine scales of the solution in the coarse problem in this framework advective diffusive reactive equations modelling turbomachinery flows feature both advection and reaction induced instabilities to be tackled to this end this work deals with a new method called v sgs variable subgrid scale designed for quadratic elements with a variable intrinsic time parameter two dimensional tests have been considered to compare v sgs against supg and other stabilization devices including the flow around a naca 4412 airfoil to assess its reliability in the handling of advanced turbulence closures on cruder meshes

a multiscale finite element method for the helmholtz equation it is well known that when the standard galerkin method is applied to the helmholtz equation it exhibits an error in the wavenumber and the solution does not therefore preserve the phase characteristics of the exact solution improvements on the galerkin method including galerkin least squares gls methods have been proposed however these approaches rely on a dispersion analysis of the underlying difference stencils in order to reduce error in the solution in this paper we propose a multiscale finite element for the helmholtz equation the method employs a multiscale variational formulation which leads to a subgrid model in which subgrid scales are incorporated analytically through appropriate green s functions it is shown that entirely new and accurate methods emerge and that gls methods can be obtained as special cases of the more general subgrid model

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100