the dimensions of some self affine limit sets in the plane and hyperbolic sets in this article we compute the hausdorff dimension and box dimension or capacity of a dynamically constructed model similarity process in the plane with two distinct contraction coefficients these examples are natural generalizations to the plane of the simple markov map constructions for cantor sets on the line some related problems have been studied by different authors however those results are directed toward generic results in quite general situations this paper concentrates on computing explicit formulas in as many specific cases as possible the techniques of previous authors and ours are correspondingly very different in our calculations delicate number theoretic properties of the contraction coefficients arise finally we utilize the results for the model problem to compute the dimensions of some affine horseshoes in n and we observe that the dimensions do not always coincide and their coincidence depends on delicate number theoretic properties of the lyapunov exponents

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

robust fuzzy clustering of relational data popular relational data clustering algorithms relational dual of fuzzy c means rfcm non euclidean rfcm nerfcm both by hathaway et al and fanny by kaufman and rousseeuw are examined a new algorithm which is a generalization of fanny called the fuzzy relational data clustering frc algorithm is introduced having an identical objective functional as rfcm however the frc does not have the restriction of rfcm which is that the relational data is derived from euclidean distance as the measure of dissimilarity between the objects and it also does not have limitations of fanny including the use of a fixed membership exponent or a fuzzifier exponent m the frc algorithm is further improved by incorporating the concept of dave s object data noise clustering nc algorithm done by proposing a concept of noise dissimilarity next based on the constrained minimization which includes an inequality constraint for the memberships and corresponding kuhn tucker conditions a noise resistant frc algorithm is derived which works well for all types of non euclidean dissimilarity data thus it is shown that the extra computations for data expansion spl beta spread transformation required by the nerfcm algorithm are not necessary this new algorithm is called robust non euclidean fuzzy relational data clustering robust ne frc and its robustness is demonstrated through several numerical examples advantages of this new algorithm are faster convergence robustness against outliers and ability to handle all kinds of relational data including non euclidean the paper also presents a new and better interpretation of the noise class

a stabilized mixed finite element method for darcy flow we develop new stabilized mixed finite element methods for darcy flow stability and an a priori error estimate in the stability norm are established a wide variety of convergent finite elements present themselves unlike the classical galerkin formulation which requires highly specialized elements an interesting feature of the formulation is that there are no mesh dependent parameters numerical tests confirm the theoretical results 2002 elsevier science b v all rights reserved

a fast and effective multidimensional scaling approach for node localization in wireless sensor networks given a set of pairwise distance estimates between nodes it is often of interest to generate a map of node locations this is an old nonlinear estimation problem that has recently drawn interest in the signal processing community due to the emergence of wireless sensor networks sensor maps are useful for estimating the spatial distribution of measured phenomena and for routing purposes we propose a two stage algorithm that combines algebraic initialization and gradient descent in particular we borrow an algebraic solution known as fastmap from the database literature adapt it to the sensor network context and motivate the placement of anchor pivot nodes on the edges of the network when all nodes can estimate their distance from the anchors the overall algorithm offers very competitive performance at low complexity quadratic in the number of nodes

additive spectral method for fuzzy cluster analysis of similarity data including community structure and affinity matrices an additive spectral method for fuzzy clustering is proposed the method operates on a clustering model which is an extension of the spectral decomposition of a square matrix the computation proceeds by extracting clusters one by one which makes the spectral approach quite natural the iterative extraction of clusters also allows us to draw several stopping rules to the procedure this applies to several relational data types differently normalized network structure data the first eigenvector subtracted affinity between multidimensional vectors the pseudo inverse laplacian transformation and conventional relational data including in house data of similarity between research topics according to working of a research center the method is experimentally compared with several classic and recent techniques and shown to be competitive

a stabilized mixed finite element method for the incompressible shear rate dependent non newtonian fluids variational multiscale framework and consistent linearization abstract this paper presents a stabilized mixed finite element method for shear rate dependent incompressible fluids the viscosity of the fluid is considered a function of the second invariant of the rate of deformation tensor thus making the shear stress shear strain relation nonlinear the weak form of the generalized navier stokes equations is cast in the variational multiscale vms framework that leads to a two level description of the problem consistent linearization of the fine scale problem with respect to the fine scale velocity field and the use of bubble functions to expand the fine scale trial and test functions lead to an analytical expression for the fine scale velocity along with a definition of the stabilization tensor the ensuing nonlinear stabilized form is presented and the consistent tangent tensor is derived numerical convergence of the proposed method on structured and unstructured meshes that are composed of linear triangles and bilinear quadrilaterals are presented shear thinning and shear thickening effects are investigated via the backward facing step problem and the effects of geometric parameters on the flow characteristics are highlighted time dependent features are investigated via the transient vortex shedding problem and the accuracy and stability properties of the new method are shown

a method of relational fuzzy clustering based on producing feature vectors using fastmap the first stage of organizing objects is to partition them into groups or clusters the clustering is generally done on individual object data representing the entities such as feature vectors or on object relational data incorporated in a proximity matrix this paper describes another method for finding a fuzzy membership matrix that provides cluster membership values for all the objects based strictly on the proximity matrix this is generally referred to as relational data clustering the fuzzy membership matrix is found by first finding a set of vectors that approximately have the same inter vector euclidian distances as the proximities that are provided these vectors can be of very low dimension such as 5 or less fuzzy c means fcm is then applied to these vectors to obtain a fuzzy membership matrix in addition two dimensional vectors are also created to provide a visual representation of the proximity matrix this allows comparison of the result of automatic clustering to visual clustering the method proposed here is compared to other relational clustering methods including nerfcm rouben s method and windhams a p method various clustering quality indices are also calculated for doing the comparison using various proximity matrices as input simulations show the method to be very effective and no more computationally expensive than other relational data clustering methods the membership matrices that are produced by the proposed method are less crisp than those produced by nerfcm and more representative of the proximity matrix that is used as input to the clustering process

on the dimension of deterministic and random cantor like sets symbolic dynamics and the eckmann ruelle conjecture in this paper we unify and extend many of the known results on the dimension of deterministic and random cantor like sets in n and apply these results to study some problems in dynamical systems in particular we verify the eckmann ruelle conjecture for equilibrium measures for holder continuous conformal expanding maps and conformal axiom a topologically hyperbolic homeomorphims we also construct a holder continuous axiom a homeomorphism of positive topological entropy for which the unique measure of maximal entropy is ergodic and has different upper and lower pointwise dimensions almost everywhere this example shows that the non conformal holder continuous version of the eckmann ruelle conjecture is false

interval valued fuzzy relation based clustering with its application to performance evaluation a similarity relation with its partition tree has been applied in the performance evaluation area for obtaining an agglomerative hierarchical clustering these fuzzy relation based methods require a decision maker to perform pair wise comparisons for the similarity among criteria as forming a fuzzy relation matrix the approach is developed based on real membership values of fuzzy relations however interval valued memberships may be better than real membership values to represent higher order imprecision and vagueness for human perception thus in this paper we would like to extend fuzzy relations to interval valued fuzzy relations and then construct interval valued similarity relations for performance evaluation we first give some definitions for these interval valued types of fuzzy relation similarity relation and resolution form we then construct an interval valued fuzzy similarity relation into a hierarchical structure schema it is shown that both of procedures and results for the partition tree derived from interval valued and crisp valued similarity relation matrices have some corresponding relationships and different merits to demonstrate the usefulness of the proposed approach performance evaluations for academic departments of higher education are considered by using actual engineering school data in taiwan

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

relational duals of the c means clustering algorithms abstract the hard and fuzzy c means algorithms are widely used effective tools for the problem of clustering n objects into hard or fuzzy groups of similar individuals when the data is available as object data consisting of a set of n feature vectors in rp however object data algorithms are not directly applicable when the n objects are implicitly described in terms of relational data which consists of a set of n2 measurements of relations between each of the pairs of objects new relational versions of the hard and fuzzy c means algorithms are presented here for the case when the relational data can reasonably be viewed as some measure of distance some convergence properties of the algorithms are given along with a numerical example

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 relationship between stabilized finite element methods and the galerkin method with bubble functions abstract a relation between stabilized finite element methods and the galerkin method employing interpolations with bubble functions is established for the advective diffusive model and for the linearized compressible navier stokes equations the bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy in particular for the advective diffusive model the galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline upwind petrov galerkin supg method in the diffusive limit

a validity measure for fuzzy clustering the authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c partitions without assumptions as to the number of substructures inherent in the data this function depends on the data set geometric distance measure distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used the function is mathematically justified via its relationship to a well defined hard clustering validity function the separation index for which the condition of uniqueness has already been established the performance of this validity function compares favorably to that of several others the application of this validity function to color image segmentation in a computer color vision system for recognition of ic wafer defects which are otherwise impossible to detect using gray scale image processing is discussed

numerical comparison of the rfcm and ap algorithms for clustering relational data we describe and compare two fuzzy clustering algorithms based on optimizing penalty functions of relational data more specifically the ap algorithm of windham is contrasted with the relational fuzzy c means approach through a numerical example on a small artificial data set defined by windham our results indicate that while the two algorithms seem to cluster objects using very different mathematical criteria the numerical results can be quite similar however a second numerical example using a slightly distorted version of windham s data seems to exhibit real differences between clusterings obtained by the two approaches

establishing performance evaluation structures by fuzzy relation based cluster analysis the purpose of this study is to establish hierarchical structures for the performance evaluation of vague humanistic complicated systems to overcome the difficulties due to partial information and the vagueness of human knowledge and recognition a fuzzy relation based clustering method is proposed to model this evaluation first the effects of different max t i compositions on the formation of clusters are discussed then an improved clustering algorithm is developed to produce several partition trees with different levels and clusters according to different t i norm compositions to demonstrate the usefulness of the proposed algorithm the academic departments of higher education were considered using actual engineering school data in taiwan three performance evaluation structures are established by using max t 1 max t 2 and max t 3 compositions the results show that the proposed fuzzy hierarchical approach is useful and practical for performance evaluations of complicated humanistic systems

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

performance evaluation of some clustering algorithms and validity indices in this article we evaluate the performance of three clustering algorithms hard k means single linkage and a simulated annealing sa based technique in conjunction with four cluster validity indices namely davies bouldin index dunn s index calinski harabasz index and a recently developed index i based on a relation between the index i and the dunn s index a lower bound of the value of the former is theoretically estimated in order to get unique hard k partition when the data set has distinct substructures the effectiveness of the different validity indices and clustering methods in automatically evolving the appropriate number of clusters is demonstrated experimentally for both artificial and real life data sets with the number of clusters varying from two to ten once the appropriate number of clusters is determined the sa based clustering technique is used for proper partitioning of the data into the said number of clusters

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

a finite element variational multiscale method for incompressible flow in this paper we present a numerical scheme prove stability existence of solutions uniqueness and convergence of the incompressible navier stokes equations it has the advantage of being defined from strictly algebraic considerations a significant feature of the present method is that the structure of the stabilization term based on the multiscale enrichment and derived from the navier stokes problem itself ample numerical experiments are carried out to confirm the theory and illustrate the effectiveness of the scheme on incompressible fluid

linear fractional multi objective optimization problems subject to fuzzy relational equations with a continuous archimedean triangular norm in this paper linear fractional multi objective optimization problems subject to a system of fuzzy relational equations fres using the max archimedean triangular norm composition are considered first some theorems and results are presented to simplify systems of fuzzy relational equations next the feasible set of the optimization problem is reduced then the linear fractional multi objective optimization problem is converted to a linear one using nykowski and zolkiewski s approach furthermore the efficient solutions are obtained by applying the improved e constraint method in addition we design an algorithm to generate consistent systems of fuzzy relational equations randomly using the covering problem finally the proposed method is effectively tested by solving a randomly generated consistent test problem

identification of overlapping and non overlapping community structure by fuzzy clustering in complex networks this paper proposes a novel method based on fuzzy clustering to detect community structure in complex networks in contrast to previous studies our method does not focus on a graph model but rather on a fuzzy relation model which uses the operations of fuzzy relation to replace a traversal search of the graph for identifying community structure in our method we first use a fuzzy relation to describe the relation between vertices as well as the similarity in network topology to determine the membership grade of the relation then we transform this fuzzy relation into a fuzzy equivalence relation finally we map the non overlapping communities as equivalence classes that satisfy a certain equivalence relation because most real world networks are made of overlapping communities e g in social networks people may belong to multiple communities we can consider the equivalence classes above as the skeletons of overlapping communities and extend our method by adding vertices to the skeletons to identify overlapping communities we evaluated our method on artificial networks with built in communities and real world networks with known and unknown communities the experimental results show that our method works well for detecting these communities and gives a new understanding of network division and community formation

fuzzy relational clustering around medoids a unified view medoid based fuzzy clustering generates clusters of objects based on relational data which records pairwise similarities or dissimilarities among objects compared with single medoid based approaches our recently proposed fuzzy clustering with multiple weighted medoids has shown superior performance in clustering via experimental study in this paper we present a new version of fuzzy relational clustering in this family called fuzzy clustering with multi medoids fmmdd based on the new objective function of fmmdd update equations can be derived more conveniently moreover a unified view of fmmdd and two existing fuzzy relational approaches fuzzy c medoids fcmdd and assignment prototype a p can be established which allows us to conduct further analytical study to investigate the effectiveness and feasibility of the proposed approach as well as the limitations of existing ones the robustness of fmmdd is also investigated our theoretical and numerical studies show that the proposed approach produces good quality of clusters with rich cluster based information and it is less sensitive to noise

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

optimal cluster preserving embedding of nonmetric proximity data for several major applications of data analysis objects are often not represented as feature vectors in a vector space but rather by a matrix gathering pairwise proximities such pairwise data often violates metricity and therefore cannot be naturally embedded in a vector space concerning the problem of unsupervised structure detection or clustering in this paper a new embedding method for pairwise data into euclidean vector spaces is introduced we show that all clustering methods which are invariant under additive shifts of the pairwise proximities can be reformulated as grouping problems in euclidian spaces the most prominent property of this constant shift embedding framework is the complete preservation of the cluster structure in the embedding space restating pairwise clustering problems in vector spaces has several important consequences such as the statistical description of the clusters by way of cluster prototypes the generic extension of the grouping procedure to a discriminative prediction rule and the applicability of standard preprocessing methods like denoising or dimensionality reduction

virtual bubbles and galerkin least squares type methods ga l s abstract the equivalence between stabilized finite element methods or galerkin least squares tyoe methods ga l s and the standard galerkin method with bubble functions is established in an abstract framework the results are applicable to various finite element spaces including high order elements and applications to the advective diffusive model and to the stokes problem are presented illustrating the potential of the abstract theory introduced here

further improvements in feature weighted fuzzy c means in cluster analysis certain features of a given data set may exhibit higher relevance than others to address this issue feature weighted fuzzy c means fwfcm approaches have emerged in recent years however there are certain deficiencies in the existing fwfcms e g the elements in a feature weight vector cannot be adaptively adjusted during the training phase and the update formulas of a feature weight vector cannot be derived analytically in this study an improved fwfcm ifwfcm is proposed to overcome these shortcomings the ifwfcm kd based on the kernelized distance is also proposed experimental results reported for five numerical data sets and the color images show that ifwfcm is superior to the existing fwfcms an interesting conclusion that ifwfcm kd might not improve the performance of ifwfcm is also obtained by applying ifwfcm kd to tackle the above mentioned numerical data sets and color images

nerf c means non euclidean relational fuzzy clustering abstract the relational fuzzy c means rfcm algorithm can be used to cluster a set of n objects described by pair wise dissimilarity values if and only if there exist n points in r n 1 whose squared euclidean distances precisely match the given dissimilarity data this strong restriction on the dissimilarity data renders rfcm inapplicable to most relational clustering problems this paper substantially improves rfcm by generalizing it to the case of arbitrary symmetric dissimilarity data the generalization is obtained using a computationally efficient modification of the existing algorithm that is equivalent to applying a spreading transformation to the dissimilarity data while the method given applies specifically to dissimilarity data a simple transformation can be used to convert similarity relations into dissimilarity data so the method is applicable to any numerical relational data that are positive reflexive or anti reflexive and symmetric numerical examples illustrate and compare the present approach to problems that can be studied with alternatives such as the linkage algorithms

invertible matrices and semilinear spaces over commutative semirings this paper deals with invertible matrices and semilinear spaces over commutative semirings some necessary and sufficient conditions for matrices to be invertible over commutative semirings are obtained the condition under which the cardinality of each basis of semilinear space of n dimensional vectors is n is given in the end the factor rank of matrices over semirings is investigated

revisiting stabilized finite element methods for the advective diffusive equation we give a brief overview of stabilized finite element methods and illustrate the developments applied to the advection diffusion equation this article presents a concise perspective of the developments emanated from the works started in the 1980s through today 2005 elsevier b v all rights reserved pacs 47 11 j

a multiscale finite element method for the incompressible navier stokes equations this paper presents a new multiscale finite element method for the incompressible navier stokes equations the proposed method arises from a decomposition of the velocity field into coarse resolved scales and fine unresolved scales modeling of the unresolved scales corrects the lack of stability of the standard galerkin formulation and yields a method that possesses superior properties like that of the streamline upwind petrov galerkin supg method and the galerkin least squares gls method the multiscale method allows arbitrary combinations of interpolation functions for the velocity and the pressure fields specifically the equal order interpolations that are easy to implement but violate the celebrated babuska brezzi condition a significant feature of the present method is that the structure of the stabilization tensor s appears naturally via the solution of the fine scale problem a family of 2 d elements comprising 3 and 6 node triangles and 4 and 9 node quadrilaterals has been developed convergence studies for the method on uniform skewed as well as composite meshes are presented numerical simulations of the nonlinear steady and transient flow problems are shown that exhibit the good stability and accuracy properties of the method 2005 elsevier b v all rights reserved

application of multi scale finite element methods to the solution of the fokker planck equation abstract this paper presents an application of multi scale finite element methods to the solution of the multi dimensional fokker planck equation the fokker planck or forward kolmogorov equation is a degenerate convective diffusion equation arising in markov process theory it governs the evolution of the transition probability density function of the response of a broad class of dynamical systems driven by gaussian noise and completely describes the response process analytical solutions for the fokker planck equation have been developed for only a limited number of low dimensional systems leading to a large body of approximation theory one such approach successfully applied to the solution of these problems in the past is the finite element method though for systems of dimension three or less in this paper a multi scale finite element method is applied to the fokker planck equation in an effort to develop a formulation that can yield higher accuracy on cruder spatial discretizations thus reducing the computational overhead associated with large scale problems that arise in higher dimensions

modeling subgrid viscosity for advection diffusion problems we analyse the effect of the subgrid viscosity on a finite element discretisation with piecewise linear elements of a linear advection diffusion scalar equation we point out the importance of a proper tune up of the viscosity coefficient and we propose a heuristic method for obtaining reasonable values for it the extension to more general problems is then hinted in the last section

a space time galerkin least squares finite element formulation of the navier stokes equations for moving domain problems a space time galerkin least squares finite element formulation of the navier stokes equations is presented for the analysis of free surface flows moving spatial configurations and deforming fluid structure interfaces the variational equation is based on the time discontinuous galerkin method employing the physical entropy variables the space time elements are oriented in time to accommodate the spatial deformations if the elements are oriented along the particle paths the formulation is lagrangian and if they are fixed in time it is eulerian consequently this formulation is analogous to the arbitrary lagrangian eulerian ale technique a novel mesh rezoning strategy is presented to orient the elements in time and adapt the fluid mesh to the changing spatial configuration numerical results are presented to show the performance of the method

symbolic clustering using a new dissimilarity measure abstract a new dissimilarity measure based on position span and content of symbolic objects is proposed for symbolic clustering the dissimilarity measure is new in the sense that it is not just another aspect of a similarity measure in the proposed hierarchical agglomerative clustering methodology composite symbolic objects are formed using a cartesian join operator whenever a mutual pair of symbolic objects is selected for agglomeration based on minimum dissimilarity the minimum dissimilarity values of different merging levels are used to compute the cluster indicator values and hence to determine the number of clusters in the data the results of the application of the algorithm on numeric data of known number of classes are described first so as to show the efficacy of the method subsequently the results of the experiments on two data sets of assertion type of symbolic objects drawn from the domains of fat oil and microcomputers are presented

on fastmap and the convex hull of multivariate data toward fast and robust dimension reduction fastmap is a dimension reduction technique that operates on distances between objects although only distances are used implicitly the technique assumes that the objects are points in a p dimensional euclidean space it selects a sequence of k spl les p orthogonal axes defined by distant pairs of points called pivots and computes the projection of the points onto the orthogonal axes we show that fastmap uses only the outer envelope of a data set pivots are taken from the faces usually vertices of the convex hull of the data points in the original implicit euclidean space this provides a bridge to results in robust statistics where the convex hull is used as a tool in multivariate outlier detection and in robust estimation methods the connection sheds new light on the properties of fastmap particularly its sensitivity to outliers and provides an opportunity for a new class of dimension reduction algorithms robustmaps that retain the speed of fastmap and exploit ideas in robust statistics

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