development of high order taylor galerkin schemes for les in this paper we describe the implementation and development of a new taylor galerkin finite element scheme within an unstructured hybrid parallel solver the scheme has been specifically conceived for unsteady les it is third order in space and time and has a low dissipative error minimal additional cpu costs are achieved by using a new approximation of the finite element integrals and a simple iterative method for the approximate inversion of the modified mass matrix basic convective tests are carried out in 2 and 3 dimensions for arbitrary elements numerical estimates of the order of convergence are presented on regular and perturbed grids finally test cases that are relevant to les are carried out and these clearly demonstrate the important improvements that our new scheme offers relative to a selection of existing methods

an adaptive finite element method for transient compressible flows with moving boundaries a description is given of an adaptive finite element method for the simulation of two dimensional compressible flows with moving boundaries the method is implemented on an unstructured triangular grid and the mesh adaptation is achieved by local grid regeneration using an error estimation procedure coupled to an automatic triangular mesh generator two numerical examples are included to illustrate the numerical performance of the method

a characteristic finite element algorithm for time dependent 3 d advection dominated transport using unstructured grids abstract an algorithm based on operator splitting has been successfully implemented for solving unsteady advection dominated transport problems in 3 d specifically the general operator integration factor splitting method of maday et al is applied to the unsteady advection diffusion equation with source sink terms the algorithm incorporates a 3 d characteristic galerkin scheme to treat advection and a standard galerkin treatment of the diffusion and source sink terms up to third order operator splitting was implemented and validated against several analytical solutions the algorithm showed the expected error behaviour and good performance in modeling advection dominated transport problems the practical utility and effectiveness of the proposed numerical scheme was further demonstrated by solving the graetz nusselt problem i e high peclet number mass heat transport in a fully developed pipe flow

quadratic inequalities deduced from the theory of reproducing kernels abstract a typical result given in this paper is as follows for an n x n positive definite hermitian matrix a and for any vector x c we obtain the inequality expx exp a 1 1 expx exp x ax where for x x 1 x 2 x n t expx exp x 1 exp x 2 exp x n t and for a a exp a exp a we deal with inequalities of this type in a more general situation by using the theory of reproducing kernels

neuro fuzzy system with learning tolerant to imprecision in this paper a new learning method tolerant to imprecision is introduced and used in neuro fuzzy modeling this method can be called e insensitive learning where in order to fit the fuzzy model to real data a weighted e insensitive loss function is used the proposed method makes it possible to exclude an intrinsic inconsistency of neuro fuzzy modeling where zero tolerance learning is used to obtain a fuzzy model tolerant to imprecision the e insensitive learning leads to a model with the minimal vapnik chervonenkis dimension complexity which results in improving generalization ability of this system and its robustness to outliers finally numerical examples are given to demonstrate the validity of the introduced method

switching regression models and fuzzy clustering a family of objective functions called fuzzy c regression models which can be used too fit switching regression models to certain types of mixed data is presented minimization of particular objective functions in the family yields simultaneous estimates for the parameters of c regression models together with a fuzzy c partitioning of the data a general optimization approach for the family of objective functions is given and corresponding theoretical convergence results are discussed the approach is illustrated by two numerical examples that show how it can be used to fit mixed data to coupled linear and nonlinear models

gaussian clustering method based on maximum fuzzy entropy interpretation abstract a new method of fuzzy clustering is proposed this is a complete gaussian membership function derived by means of the maximum entropy interpretation compared to the traditional fuzzy c means fcm method our approach exhibits the following two advantages 1 having clearer physical meaning and well defined mathematical features 2 having an optimal choice for feature parameter in theory moreover we also review some existing measures of uncertainty of fuzzy sets and redefine fuzzy entropy as analogous to probabilistic entropy

the isometric identities and inversion formulas of complex continuous wavelet transforms abstract the reproducing kernel function of the image space of a family of complex wavelet transforms is presented an admissible wavelet is obtained by convolution computation next the correlative characterisation of the image space of the family of complex wavelet transforms is provided when the scale is fixed furthermore the isometric identities and inversion formulas are obtained which provide a theoretic basis for investigating the image space of the general wavelet transform

high resolution finite element analysis of shallow water equations in two dimensions abstract we present in this study the taylor galerkin finite element model to stimulate shallow water equations for bore wave propagation in a domain of two dimensions to provide the necessary precision for the prediction of a sharply varying solution profile the generalized taylor galerkin finite element model is constructed through introduction of four parameters this paper also presents the fundamental theory behind the choice of free parameters one set of parameters is theoretically determined to obtain the high order accurate taylor galerkin finite element model the other set of free parameters is determined using the underlying discrete maximum principle to obtain the low order monotonic taylor galerkin finite element model theoretical study reveals that the higher order scheme exhibits dispersive errors near the discontinuity while lower order scheme dissipates the discontinuity a scheme which has a high resolution shock capturing ability as a built in feature is thus needed in the present study notice that lumping of the mass matrix equations is invoked in the low order scheme to allow simulation of the hydraulic problem with discontinuities we check the prediction accuracy against suitable test problems preferably ones for which exact solutions are available based on numerical results it is concluded that the taylor galerkin flux corrected transport tg fct finite element method can render the technique suitable for solving shallow water equations with sharply varying solution profiles

an adaptive finite element procedure for compressible high speed flows abstract a two step explicit finite element procedure for obtaining time accurate solutions to the compressible euler equations is described the method is coupled with an adaptive mesh refinement process which enables steady state solutions of improved quality to be obtained

an axiomatic approach to soft learning vector quantization and clustering this paper presents an axiomatic approach to soft learning vector quantization lvq and clustering based on reformulation the reformulation of the fuzzy c means fcm algorithm provides the basis for reformulating entropy constrained fuzzy clustering ecfc algorithms according to the proposed approach the development of specific algorithms reduces to the selection of a generator function linear generator functions lead to the fcm and fuzzy learning vector quantization algorithms while exponential generator functions lead to ecfc and entropy constrained learning vector quantization algorithms the reformulation of lvq and clustering algorithms also provides the basis for developing uncertainty measures that can identify feature vectors equidistant from all prototypes these measures are employed by a procedure developed to make soft lvq and clustering algorithms capable of identifying outliers in the data set this procedure is evaluated by testing the algorithms generated by linear and exponential generator functions on speech data

generalized fuzzy c means clustering strategies using l sub p norm distances fuzzy c means fcm is a useful clustering technique modifications of fcm using l sub 1 norm distances increase robustness to outliers object and relational data versions of fcm clustering are defined for the more general case where the l sub p norm p spl ges 1 or semi norm 0 0 in order to facilitate the empirical examination of the object data models both object and relational approaches are included in a numerical study

on robust fuzzy c regression models one of the most popular clustering methods based on minimization of a criterion function is the fuzzy c means one its generalization by application of hyperplane shaped prototypes of the clusters is known as the fuzzy c regression models fcrm method although with this generalization many new applications of clustering emerged it appeared to be rather sensitive to poor initialization and to the presence of noise and outliers in data in this paper we introduce a new objective function using the huber s m estimators and the yager s owa operators to overcome the disadvantages of the approach considered we derive and describe an algorithm for minimization of the objective function defined we have called it the fuzzy c ordered regression models fcorm clustering algorithm the algorithm is compared to a few other important reference ones to this end experiments on synthetic data with various types of noise and different numbers of outliers are carried out we investigate the methods performance in the conditions that can be encountered in signal analysis large scale simulations demonstrate the competitiveness and usefulness of the method proposed

the use of domain splitting with an explicit hyperbolic solver abstract a method of splitting the solution domain in order to allow faster computation of practical first order hyperbolic problems is described results are presented which show the performance of the method in both one and two dimensions an indication is also given of the likely saving in computer time which can be achieved by using the method

fuzzy clustering with structural constraints abstract in this paper we propose a generalization of the standard clustering problem which we call structural constrained clustering scc problem in scc problem the cluster interconnections are given by a binary relation r if this relation is empty then scc problem reduces to the standard classification problem the cluster structure imposed by r may be described by the covering graph of r for example if this graph is a rooted tree then a hierarchical structure is imposed to the clusters we formulate scc as a fuzzy clustering problem with prototype inter relation a general algorithm to solve this problem is proposed for three particular distance measures squared euclidean and l1 metric we compute the prototypes by solving a particular multifacility location problem

k version of finite element method in gas dynamics higher order global differentiability numerical solutions in this paper we consider and examine alternate finite element computational strategies for time dependent navier stokes equations describing high speed compressible flows with shocks in a viscous and conducting medium with the ultimate objective of establishing the desired features of a general mathematical and computational framework for such initial value problems ivp in which a the numerically computed solutions are in agreement with the physics of evolution described by the governing differential equations gdes i e the ivp b the solutions are admissible in the non discretized form of the gdes in the pointwise sense i e anywhere and everywhere in the entire space time domain and hence in the integrated sense as well c the numerical approximations progressively approach the same global differentiability in space and time as the theoretical solutions d it is possible to time march the solutions this is essential for efficiency as well as ensuring desired accuracy of the computed solution for the current increment of time i e to minimize the error build up in the time marching process e the computational process is unconditionally stable and non degenerate regardless of the choice of discretization nature of approximations and their global differentiability and the dimensionless parameters influencing the physics of the process f there are no issues of stability cfl number limitations and g the mathematical and computational methodology is independent of the nature of the space time differential operators we consider one dimensional compressible flow in a viscous and conducting medium with shocks as model problems to illustrate various features of the general mathematical and computational framework used here and to demonstrate that the proposed framework is general and is applicable to all ivp the riemann shock tube with a single diaphragm serves as a model problem the specific details presented in the paper discuss 1 choice of the form of the gdes i e strong form or weak form 2 various choices of variables the paper establishes and considers density velocity and temperature as variables of choice 3 details of the space time least squares ls integral forms meritorious over all others in all aspects are presented and choice of approximation spaces are discussed 4 in all numerical studies we consider a viscous and conducting medium with ideal gas law however results are also presented for non conducting medium extension of this work to real gas models will be presented in a separate paper it is worth noting that when the medium is viscous and conducting the solutions of gas dynamics equations are analytic 5 it is also significant to note that upwinding methods based on addition of artificial diffusion such as supg supg dc supg dc ls and their many variations are neither needed nor used in this present work 6 numerical studies are aimed at resolving the localized details of the shock structure i e shock relations shock width shock speed etc as well as the over all global behaviour of the solution in the entire space time domain 7 numerical studies are presented for riemann shock tube for high mach number flows with special emphasis also on time accuracy of the evolution which is ensured by requiring that the approximations for each increment of time satisfy non discretized form of the gdes in the pointwise sense and hence in the integrated sense as well 8 comparisons are made with published results as well as theoretical solutions when possible it is established that space time least squares processes are the only processes that yield variationally consistent space time integral forms and hence unconditionally non degenerate space time computational processes which when considered in higher order scalar product spaces provide the desired mathematical framework in which progressively higher order global differentiability solutions in space and time yield the same characteristics as the theoretical solutions of the ivp in all aspects copyright 2006 john wiley sons ltd

application of entropy and energy measures of fuzziness to processing of ecg signal the paper deals with the application of entropy and energy measure of fuzziness to processing of ecg signal after formulation of the problem the notion of entropy measure of fuzziness is recalled next the idea of a fuzzy signal created from the original signal is proposed and the entropy measure of fuzziness determined for each sample is calculated the application of this measure to building a detection function of ecg signal is presented the theoretical considerations have been illustrated with digital processing of the real ecg signal

a time domain constrained fuzzy clustering method and its application to signal analysis this paper introduces a new fuzzy clustering method with time domain constraints which is used to signal analysis proposed method makes it possible to include natural constraints for signal analysis using fuzzy clustering that is the neighboring samples of signal belong to the same cluster this method can be called time domain constrained fuzzy clustering this paper introduces two approaches to include the above kind of constraints the first approach leads to the time domain constrained fuzzy c regression models method the second approach leads to the insensitive version of the above method which results in additional robustness for outliers and non gaussian noise finally simulations on synthetic as well as real life signals are realized to evaluate the performance of the time domain constrained fuzzy clustering methods a comparison with the traditional fuzzy c regression models is also made large scale simulations demonstrate the competitiveness of the proposed methods for signal analysis with respect to the traditional fuzzy clustering methods

mercer kernel based clustering in feature space the article presents a method for both the unsupervised partitioning of a sample of data and the estimation of the possible number of inherent clusters which generate the data this work exploits the notion that performing a nonlinear data transformation into some high dimensional feature space increases the probability of the linear separability of the patterns within the transformed space and therefore simplifies the associated data structure it is shown that the eigenvectors of a kernel matrix which defines the implicit mapping provides a means to estimate the number of clusters inherent within the data and a computationally simple iterative procedure is presented for the subsequent feature space partitioning of the data

adaptive fuzzy c shells clustering and detection of ellipses several generalizations of the fuzzy c shells fcs algorithm are presented for characterizing and detecting clusters that are hyperellipsoidal shells an earlier generalization the adaptive fuzzy c shells afcs algorithm is examined in detail and is found to have global convergence problems when the shapes to be detected are partial new formulations are considered wherein the norm inducing matrix in the distance metric is unconstrained in contrast to the afcs algorithm the resulting algorithm called the afcs u algorithm performs better for partial shapes another formulation based on the second order quadrics equation is considered these algorithms can detect ellipses and circles in 2d data they are compared with the hough transform ht based methods for ellipse detection existing ht based methods for ellipse detection are evaluated and a multistage method incorporating the good features of all the methods is used for comparison numerical examples of real image data show that the afcs algorithm requires less memory than the ht based methods and it is at least an order of magnitude faster than the ht approach

a streamline upwind full galerkin method for space time convection dominated transport problems an original space time finite element approach for the solution of the diffusion convection equation is proposed in this paper a slight manipulation of the differential equation suggests that transient transport problems may in fact be seen as steady state space time transport problems accurately and easily soluble by the standard galerkin technique however concerning convective transport involving sharp fronts or coarse discretization it is shown that implementation of dissipation along space time trajectories significantly improves the solutions classical comparative test problems are run to establish the performances of this method and to show the limits of the more sophisticated petrov and taylor galerkin schemes evocation of a possible space time anisotropy generated by usual finite difference time stepping procedures as well as comparative analysis of amplification matrices help to understand the accuracy and the robustness of the proposed approach

on the stabilization parameter in the subgrid scale approximation of scalar convection diffusion reaction equations on distorted meshes abstract in this paper we revisit the definition of the stabilization parameter in the finite element approximation of the convection diffusion reaction equation the starting point is the decomposition of the unknown into its finite element component and a subgrid scale that needs to be approximated in order to incorporate the distortion of the mesh into this approximation we transform the equation for the subgrid scale within each element to the shape regular reference domain the expression for the subgrid scale arises from an approximate fourier analysis and the identification of the wave number direction where instabilities are most likely to occur the final outcome is an expression for the stabilization parameter that accounts for anisotropy and the dominance of either convection or reaction terms in the equation

quadratic inequalities associated with integrals of reproducing kernels abstract quadratic inequalities with positive definite matrices which are derived from integrals of reproducing kernels are examined and applied to obtain a new class of inequalities for functions in functional hilbert spaces

clustering algorithms based on volume criteria clustering algorithms such as the k means algorithm and the fuzzy c means algorithm are based on the minimization of the trace of the fuzzy within fluster scatter matrix in this paper we explore the use of determinant volume criteria for clustering we derive an algorithm called the minimum scatter volume msv algorithm that minimizes the scatter volume and another algorithm called the minimum cluster volume mcv that minimizes the sum of the volumes of the individual clusters the behavior of msv is shown to be similar to that of k means whereas mcv is more versatile

a new possibilistic clustering algorithm for line detection in real world imagery though promising in nature line detection algorithms based on fuzzy clustering suffer from excessive sensitivity to noise and non linear structures a new detection scheme is proposed here which is suitable for the processing of real world images possibilistic clustering is used instead of fuzzy clustering to achieve a higher immunity to noise whereas a set of criteria to eliminate non linear clusters is provided to take into account the presence of curved lines merging of segments is possible due to a fuzzy reasoning module exploiting human perception considerations the number of parameters to be set is kept to a minimum thus ensuring generality and robustness tests confirm the ability of the proposed system in interpreting the linear structures present in the image

an integrated approach to fuzzy learning vector quantization and fuzzy c means clustering derives an interpretation for a family of competitive learning algorithms and investigates their relationship to fuzzy c means and fuzzy learning vector quantization these algorithms map a set of feature vectors into a set of prototypes associated with a competitive network that performs unsupervised learning derivation of the new algorithms is accomplished by minimizing an average generalized distance between the feature vectors and prototypes using gradient descent a close relationship between the resulting algorithms and fuzzy c means is revealed by investigating the functionals involved it is also shown that the fuzzy c means and fuzzy learning vector quantization algorithms are related to the proposed algorithms if the learning rate at each iteration is selected to satisfy a certain condition

numerical experiments with the osher upwind scheme for the euler equations the osher algorithm for solving the euler equations is an upwind finite difference procedure that is derived by combining the salient features of the theory of conservation laws and the mathematical theory of characteristi cs for hyperbolic systems of equations a first order accurate version of the numerical method was derived by osher circa 1980 for the one dimensional non isentropic euler equations in cartesian coordinates in this paper the extension of the scheme to arbitrary two dimensional geometries is explained results are then presented for several example problems in one and two dimensions future work will include extension of the method to second order accuracy and the development of implicit time differencing for the osher algorithm

a finite element formulation of compressible flows using various sets of independent variables abstract this paper presents a finite element method for the simulation of compressible flows the navier stokes and euler equations are solved in the conservation form using various sets of independent variables a variational formulation is developed based upon a variant of the petrov galerkin method and uses a shock capturing operator an adaptive algorithm based on a particular residual norm is proposed several numerical examples are presented to demonstrate the performances of each set of variables in solving compressible high speed flows

fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation ii shell clustering algorithms are ideally suited for computer vision tasks such as boundary detection and surface approximation particularly when the boundaries have jagged or scattered edges and when the range data is sparse this is because shell clustering is insensitive to local aberrations it can be performed directly in image space and unlike traditional approaches it does assume dense data and does not use additional features such as curvatures and surface normals the shell clustering algorithms introduced in part i of this paper assume that the number of clusters is known however which is not the case in many boundary detection and surface approximation applications this problem can be overcome by considering cluster validity we introduce a validity measure called surface density which is explicitly meant for the type of applications considered in this paper we show through theoretical derivations that surface density is relatively invariant to size and partiality incompleteness of the clusters we describe unsupervised clustering algorithms that use the surface density measure and other measures to determine the optimum number of shell clusters automatically and illustrate the application of the proposed algorithms to boundary detection in the case of intensity images and to surface approximation in the case of range images

on some recent adventures into improved finite element cfd methods for convective transport abstract the quest continues for computational fluid dynamics cfd algorithms that are accurate and efficient for convection dominated applications including shocks travelling fronts and wall layers the boundary value optimal galerkin weak statement invariably requires manipulation either in the test space or in an augmented form for the conservation law system to handle the disruptive character introduced by the discretized first order convection term an incredible variety of methodologies have been derived and examined to address this issue in particular seeking achievement of accurate and monotone discrete approximate solutions in an efficient implementation the utk cfd research group continues its search on examining the breadth of approaches leading to development of a consistent encompassing theoretical statement exhibiting quality performance included herein are adventures into generalized taylor series lax wendroff methods characteristic euler flux resolutions sub grid embedded high degree lagrange bases with static condensation and assembled stencil fourier analysis optimization for finite element weak statement implementations for appropriate model problems including steady convection diffusion and pure unsteady convection and benchmark navier stokes definitions recent advances have lead to candidate accurate monotone methods with linear basis efficiency this contribution highlights the theoretical developments and presents quantitative documentation of achievable high quality solutions

shallow water problems a general explicit formulation this paper gives a general formulation for shallow water equations which is capable of solving problems of induced harbour oscillation tidal flow tsunami propagation dispersion of pollutant etc the shallow water equations are written in a novel fully conservative form the solution algorithm is based on an explicit time integration procedure which exploits the conservative properties of the governing equations and incorporates accurate treatment of convective terms without introduction of artificial damping its accuracy and low cost of computation make it attractive with regard to existing procedures

robust clustering methods a unified view clustering methods need to be robust if they are to be useful in practice in this paper we analyze several popular robust clustering methods and show that they have much in common we also establish a connection between fuzzy set theory and robust statistics and point out the similarities between robust clustering methods and statistical methods such as the weighted least squares technique the m estimator the minimum volume ellipsoid algorithm cooperative robust estimation minimization of probability of randomness and the epsilon contamination model by gleaning the common principles upon which the methods proposed in the literature are based we arrive at a unified view of robust clustering methods we define several general concepts that are useful in robust clustering state the robust clustering problem in terms of the defined concepts and propose generic algorithms and guidelines for clustering noisy data we also discuss why the generalized hough transform is a suboptimal solution to the robust clustering problem

soft learning vector quantization and clustering algorithms based on ordered weighted aggregation operators this paper presents the development and investigates the properties of ordered weighted learning vector quantization lvq and clustering algorithms these algorithms are developed by using gradient descent to minimize reformulation functions based on aggregation operators an axiomatic approach provides conditions for selecting aggregation operators that lead to admissible reformulation functions minimization of admissible reformulation functions based on ordered weighted aggregation operators produces a family of soft lvq and clustering algorithms which includes fuzzy lvq and clustering algorithms as special cases the proposed lvq and clustering algorithms are used to perform segmentation of magnetic resonance mr images of the brain the diagnostic value of the segmented mr images provides the basis for evaluating a variety of ordered weighted lvq and clustering algorithms

least squares characteristics and finite elements for advection dispersion simulation the method of characteristics is combined with the method of least squares to solve the advection equation within the finite element framework fourier mode analysis shows that the numerical scheme is stable and accurate even when a linear basis function is used however in practical application the involvement of using numerical quadrature in this method can produce numerical instability depending on the value of the courant number used it is found that using c1 continuous hermitian cubic basis functions in the scheme reduces the degree of instability significantly and produces high accuracy when being used in a split operator approach this method combines naturally with the standard finite element method and results in a highly accurate scheme for advection dispersion simulation

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

modeling incompressible flows at low and high reynolds numbers via a finite calculus finite element approach we present a formulation for incompressible flows analysis using the finite element method fem the necessary stabilization for dealing with convective effects and the incompressibility condition is modeled via the finite calculus fic method the stabilization terms introduced by the fic formulation allow to solve a wide range of fluid flow problems for low and high reynolds numbers flows without the need for a turbulence model examples of application of the fic fem formulation to the analysis of 2d and 3d incompressible flows with moderate and large reynolds numbers are presented

a space time coupled p version least squares finite element formulation for unsteady fluid dynamics problems this paper presents a p version least squares finite element formulation for unsteady fluid dynamics problems where the effects of space and time are coupled the dimensionless form of the differential equations describing the problem are first cast into a set of first order differential equations by introducing auxiliary variables this permits the use of c element approximation the element properties are derived by utilizing p version approximation functions in both space and time and then minimizing the error functional given by the space time integral of the sum of squares of the errors resulting from the set of first order differential equations this results in a true space time coupled least squares minimization procedure a time marching procedure is developed in which the solution for the current time step provides the initial conditions for the next time step the space time coupled p version approximation functions provide the ability to control truncation error which in turn permits very large time steps what literally requires hundreds of time steps in uncoupled conventional time marching procedures can be accomplished in a single time step using the present space time coupled approach for non linear problems the non linear algebraic equations resulting from the least squares process are solved using newton s method with a line search this procedure results in a symmetric hessian matrix equilibrium iterations are carried out for each time step until the error functional and each component of the gradient of the error functional with respect to nodal degrees of freedom are below a certain prespecified tolerance the generality success and superiority of the present formulation procedure is demonstrated by presenting specific formulations and examples for the advection diffusion and burgers equations the results are compared with the analytical solutions and those reported in the literature the formulation presented here is ideally suited for space time adaptive procedures the element error functional values provide a mechanism for adaptive h p or hp refinements the work presented in this paper provides the basis for the extension of the space time coupled least squares minimization concept to two and three dimensional unsteady fluid flow

computational algorithms for transient analysis the burden of weight and consequences towards formalizing discrete numerically assigned dna algorithmic markers wp family abstract different from the way we have been looking in the past at developments encompassing modal type and a wide class of step by step time stepping approaches for transient and dynamic field problems and significantly different from the way these have been developed and described in standard text books over the years this paper outlines the theoretical ideas and basis towards providing a generalized methodology and formulations leading to integral and a wide class of integration operators for the resulting solution of these transient equation systems it is herein postulated that integral operators and a wide class of integration operators pertain to and emanate from the same family with the burden which is being carried by a virtual field or weighted function field specifically introduced for the time discretization is strictly enacted in a mathematically consistent manner so as to first permit obtaining the adjoint operator of the original semi discretized equation system subsequently the selection or burden carried by the virtual or weighted function fields originally introduced to facilitate the time discretization process determines the formal development and outcome of exact integral operators approximate integral operators and a wide class of integration operators thus the present developments not only serve as a prelude towards the formal developments for exact integral operators but also demonstrate that the resulting approximate integral operators and a wide class of integration operators and known methods are simply subsets of the generalizations of a standardized w p family and emanate from the principles presented herein the burden of weight and the resulting consequences towards subsequently enabling a formal basis for the selection of discrete numerically assigned dna algorimmic markers to particularly identitfy a wide class of algorithms is described for transient field problems and dynamic field problems respectively

positive definite hermitian matrices and reproducing kernels abstract some quadratic identities associated with positive definite hermitian matrices are derived by use of the theory of reproducing kernels for example the following identity is obtained let aj mj 1 be n n positive definite hermitian matrices then for any complex vector x c n we have the identity x j 1 m a 1 j 1 x min j 1 m x j a j x j the minimum is taken here over all the decompositions x mj 1xj this identity gives in a sense a precise converse for an inequality which was derived by t ando moreover this paper shows that the sum of two reproducing kernels is naturally related to the harmonic arithmetic mean inequality for matrices and also that the geometric arithmetic mean inequality for matrices can be naturally interpreted in terms of tensor product spaces

fuzzy order statistics and their application to fuzzy clustering the median and the median absolute deviation mad are robust statistics based on order statistics order statistics are extended to fuzzy sets to define a fuzzy median and a fuzzy mad the fuzzy c means fcm clustering algorithm is defined for any p norm pfcm including the l sub 1 norm 1fcm the 1fcm clustering algorithm is implemented via the alternating optimization ao method and the clustering centers are shown to be the fuzzy median the resulting ao 1fcm clustering algorithm is called the fuzzy c medians fcmed clustering algorithm an example illustrates the robustness of the fcmed

a finite element formulation for a convection diffusion equation based on cattaneo s law a number of contributions have been made during the last decades to model pure diusive transport problems by using the so called hyperbolic diusion equa on problems based on a cattaneo type law the finite element solution of the proposed equations is addressed the performance of the algorithm is verified by solving some 2d test cases some interesting features of the proposed model can be observed from these examples and we conclude that the proposal is a feasible alternative to the parabolic model for real engineering simulations

efficient implementation of high order methods for the advection diffusion equation abstract a new approach to designing high order defined here to exceed third accurate methods has been developed and tested for a linear advection diffusion equation in one and two dimensions the systematic construction of progressively higher order spatial approximations is achieved via a modified equation analysis which allows one to determine the computational stencil coefficients appropriate for a desired accuracy order a distinguishing desirable property of the developed method is solution matrix bandwidth containment i e bandwidth always remains equal to that of the second order discretization numerical simulations compare performance of the developed fourth and sixth order methods to that of the linear and bilinear basis galerkin weak statement formulations in one and two dimensions respectively uniform mesh refinement convergence results confirm the order of truncation error for each method high order approximations are shown to require significantly fewer nodes to accurately resolve solution gradients for convection dominated problems

adaptive explicit and implicit finite element methods for transient thermal analysis the application of adaptive finite element methods to the solution of transient heat conduction problems in two dimensions is investigated the computational domain is represented by an unstructured assembly of linear triangular elements and the mesh adaptation is achieved by local regeneration of the grid using an error estimation procedure coupled to an automatic triangular mesh generator two alternative solution procedures are considered in the first procedure the solution is advanced by explicit timestepping with domain decomposition being used to improve the computational efficiency of the method in the second procedure an algorithm for constructing continuous lines which pass only once through each node of the mesh is employed the lines are used as the basis of a fully implicit method in which the equation system is solved by line relaxation using a block tridiagonal equation solver the numerical performance of the two procedures is compared for the analysis of a problem involving a moving heat source applied to a convectively cooled cylindrical leading edge

comparison of some finite element methods for solving the diffusion convection reaction equation abstract in this paper we describe several finite element methods for solving the diffusion convection reaction equation none of them is new although the presentation is non standard in an effort to emphasize the similarities and differences between them in particular it is shown that the classical supg method is very similar to an explicit version of the characteristic galerkin method whereas the taylor galerkin method has a stabilization effect similar to a sub grid scale model which is in turn related to the introduction of bubble functions

numerical solution of the incompressible navier stokes equations with coriolis forces based on the discretization of the total time derivative in this paper we present a numerical formulation to solve the incompressible navier stokes equations written in a rotating frame of reference the method is based on a finite difference discretization in time and a finite element discretization in space when the viscosity is very small numerical oscillations may appear due both to the high reynolds number and to the presence of the coriolis forces to overcome these oscillations a special discretization in time is proposed the idea is to discretize the total time derivative in an inertial basis rather than only the partial time derivative in the rotating reference system after this is done a further high order approximation is introduced leading to a problem posed in the rotating frame of reference and in spatial coordinates in contrast with the straightforward discretization of the original equations some additional terms appear that enhance the stability of the numerical scheme in the absence of coriolis forces the method is a generalization of the characteristic galerkin technique for convection dominated flows

towards a robust fuzzy clustering fuzzy clustering helps to find natural vague boundaries in data the fuzzy c means method fcm is one of the most popular clustering methods based on minimization of a criterion function however one of the greatest disadvantages of this method is its sensitivity to presence of noise and outliers in data this paper introduces a new e insensitive fuzzy c means efcm clustering algorithm as a special case this algorithm includes the well known fuzzy c medians method fcmed also methods with insensitivity control named fcm and fcm are introduced performance of the new clustering algorithm is experimentally compared with the fcm method using synthetic data with outliers and heavy tailed and overlapped groups of data in background noise

stability analysis of the forward euler scheme for the convection diffusion equation using the supg formulation in space the stability and accuracy of the forward euler scheme for the semidiscrete problem arising from the space discretization of the convection diffusion equation using the supg formulation are analysed both linear and quadratic finite elements are considered the stability limits are derived for the one dimensional problem and a heuristic criterion is proposed for the multidimensional equation some numerical experiments are conducted in order to assess the performance of different finite elements

least squares finite element formulation for hydrodynamic modeling of semiconductor devices a least squares finite element formulation is presented for the hydrodynamic modeling of semiconductor devices the formulation results in a symmetric and positive definite algebraic system its capability of adopting equal order interpolations for all unknown variables makes it simple to formulate and easy to program the semiconductor hydrodynamic equations coupled with the poisson equation are formulated as one unified equation system in this least squares finite element scheme the developed method is examined on 1 d and 2 d deep submicron semiconductor device structures to demonstrate its capability of handling the large gradients of variables and highly nonlinear source terms in the semiconductor hydrodynamic equations

high order finite volume methods for viscoelastic flow problems in this paper accurate and stable finite volume schemes for solving viscoelastic flow problems are presented two contrasting finite volume schemes are described a hybrid cell vertex scheme and a pure cell centred counterpart both schemes employ a time splitting algorithm to evolve the solution through time towards steady state in the case of the hybrid scheme a semi implicit formulation is employed in the momentum equation based on the taylor galerkin approach with a pressure correction step to enforce incompressibility the basis of the pure finite volume approach is a backward euler scheme with a semi lagrangian step to treat the convection terms in the momentum and constitutive equations two distinct finite volume schemes are presented for solving the systems of partial differential equations describing the flow of viscoelastic fluids the schemes are constructed to be second order accurate in space the issue of stability is also addressed with respect to the treatment of convection numerical examples are presented illustrating the performance of these schemes on some steady and transient problems that possess analytical solutions

simulation for viscoelastic flow by a finite volume element method stability of a second order finite element finite volume fe fv hybrid scheme is investigated on the basis of flows with increasing weissenberg number fes are used to discretise the balances of mass and momentum for the stress equation a fv method is used based on the recent development with fluctuation distribution schemes for pure convection problems examples considered include a start up channel flow flow past a cylinder and the non smooth 4 1 contraction flow for an oldroyd b fluid a considerable gain in efficiency per time step can be obtained compared to an alternative pure fe implementation a distribution based on the flux terms is unstable for higher weissenberg numbers and this is also true for a distribution based on source terms alone the instability is identified as being caused by the interaction of the balance equations and stress equation a combination of distribution schemes based on flux and source terms however gives a considerable improvement to the hybrid fe fv implementation with respect to limiting weissenberg number attenuation the hybrid scheme is more stable than the pure fe alternative for the smooth flow past a cylinder but less so for the non smooth contraction flow the influence of additional strain rate stabilisation techniques is also analysed and found to be beneficial

meshfree iterative stabilized taylor galerkin and characteristic based split cbs algorithms for incompressible n s equations abstract this paper presents two stabilized schemes of the fractional step algorithm using characteristic based split and taylor galerkin like based split respectively in the meshfree context an iterative procedure which makes the convective term satisfy the momentum conservation equation in an implicit sense is introduced into the two schemes to allow much larger time step sizes a modified version of finite increment calculus process for incompressibility stabilization is developed to avoid the calculation of high order spatial derivatives numerical experiments demonstrate the capability and stability of the proposed schemes of the meshfree based fractional step method in the simulation of incompressible flows

incompressibility without tears how to avoid restrictions of mixed formulation the severe restrictions of the babuska brezzi stability criteria permit only a limited number of interpolations for velocities displacements and pressure to be used for incompressible behaviour these restrictions preclude the use of many useful elements we show in this paper how such difficulties can be side stepped by seeking the steady state solution through the use of various time marching schemes this permits a simple iterative approach to incompressible or nearly incompressible problems of fluid mechanics or solid mechanics and provides a stimulus for the use of such procedures in metal forming flow etc

the fuzzy c spherical shells algorithm a new approach the fuzzy c spherical shells fcss algorithm is specially designed to search for clusters that can be described by circular arcs or generally by shells of hyperspheres a new approach to the fcss algorithm is presented this algorithm is computationally and implementationally simpler than other clustering algorithms that have been suggested for this purpose an unsupervised algorithm which automatically finds the optimum number of clusters is not known it uses a cluster validity measure to identify good clusters merges all compatible clusters and eliminates spurious clusters to achieve the final results experimental results on several data sets are presented

fuzzy c varieties elliptotypes clustering in reproducing kernel hilbert space abstract fuzzy clustering algorithms are successfully applied to a wide variety of problems such as pattern recognition image analysis modeling and so on the fuzzy c means fcm method is one of the most popular clustering methods based on the minimization of a criterion function however the performance of the fcm method is good only when a data set contains clusters that are approximately the same size and shape in this paper a simple idea will be used to overcome this problem the original input data space will be mapped into the high possibly infinite dimensional feature space f through some nonlinear mapping in this space the data structures will be modeled by the linear varieties or elliptotypes this method is called kernel fuzzy c varieties elliptotypes clustering algorithm performance of the new clustering algorithm is experimentally compared with fcm and fuzzy c varieties elliptotypes methods using synthetic datasets and real life datasets

l 1 norm based fuzzy clustering abstract the paper presents the l1 version of the well known fuzzy clustering method namely fuzzy isodata proposed by bezdek and dunn due to their robustness l1 norm based methods gained much attention in statistics the presented fuzzy clustering problem uses the distance between observations and location parameter vectors which is based on the l1 norm instead of the inner product induced norm used in classical fuzzy isodata two alternative methods to solve the l1 fuzzy clustering problem are derived in practice both membership grades and location parameter vectors are unknown the paper presents two iterative algorithms each the implementation of the derived method finally numerical examples are presented one of them refers to famous iris data

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