approximation of cahn hilliard diffuse interface models using parallel adaptive mesh refinement and coarsening with c1 elements a variational formulation and c1 finite element scheme with adaptive mesh refinement and coarsening are developed for phase separation processes described by the cahn hilliard diffuse interface model of transport in a mixture or alloy the adaptive scheme is guided by a laplacian jump indicator based on the corresponding term arising from the weak formulation of the fourth order non linear problem and is implemented in a parallel solution framework it is then applied to resolve complex evolving interfacial solution behavior for 2d and 3d simulations of the classic spinodal decomposition problem from a random initial mixture and to other phase transformation applications of interest simulation results and adaptive performance are discussed the scheme permits efficient robust multiscale resolution and interface characterization copyright 2008 john wiley sons ltd

isogeometric structural shape optimization an old dilemma in structural shape optimization is the needed tight link between design model or geometric description and analysis model the intention of this paper is to show that isogeometric analysis offers a potential and promising way out of this dilemma to this end we show a structural shape optimization framework based on the isogeometric analysis approach with the discretization based on non uniform rational b splines nurbs the analysis model represents the structural geometry exactly furthermore nurbs enable efficient geometry control together with smooth boundaries they are the de facto standard in cad systems but are also widely used in a shape optimal design context to define the geometry representation and the design variables with the presented isogeometric approach to shape optimization the analysis model is inherently merged with the design model omitting the typically involved interplay between both we derive analytical sensitivities for nurbs discretizations which allow application of efficient gradient based optimization algorithms the present contribution is restricted to two dimensional problems of linear elasticity but the extension to three dimensions and other problem classes is straightforward some representative examples demonstrate and validate the methodology further the potential of boundary continuity control within isogeometric structural shape optimization is explored to trigger smooth or less smooth angular designs

recovery based error estimation and adaptivity using high order splines over hierarchical t meshes abstract an adaptive higher order method based on a generalization of polynomial rational splines over hierarchical t meshes pht rht splines is introduced while most problems considered in isogeometric analysis can be solved efficiently when the solution is smooth many non trivial simulations have rough solutions this can be caused for example by the presence of re entrant corners in the domain for such problems a tensor product basis is less suitable for resolving the singularities that appear as refinement propagates throughout the computational domain hierarchical bases and adaptivity allow for a more efficient way of dealing with singularities by adding more degrees of freedom only where they are necessary to improve the approximation in order to drive the adaptive refinement an efficient recovery based error estimator is proposed in this work the estimator produces a recovered solution which is a more accurate approximation than the computed numerical solution several 2d and 3d numerical investigations with pht splines of higher order and greater continuity show good performance compared to uniform refinement in terms of degrees of freedom and computational cost

isogeometric analysis using t splines we explore t splines a generalization of nurbs enabling local refinement as a basis for isogeometric analysis we review t splines as a surface design methodology and then develop it for engineering analysis applications we test t splines on some elementary two dimensional and three dimensional fluid and structural analysis problems and attain good results in all cases we summarize the current status of t splines their limitations and future possibilities

local refinement of analysis suitable t splines we develop a local refinement algorithm for analysis suitable t splines which does not produce excessive propagation of control points we then demonstrate its use as an adaptive framework for isogeometric analysis analysis suitable t splines are a class of t splines which are linearly independent and form a partition of unity these properties coupled with local refinement make this class of t splines appealing as a basis for isogeometric analysis

dimensions of spline spaces over t meshes a t mesh is basically a rectangular grid that allows t junctions in this paper we propose a method based on bezier nets to calculate the dimension of a spline function space over a t mesh when the order of the smoothness is less than half of the degree of the spline functions a dimension formula is derived which involves only the topological quantities of the t mesh the construction of basis functions is briefly discussed furthermore the dimension formulae for t meshes after mesh operations such as edge insertion and mesh merging are also obtained

analysis of parameter selection for gustafson kessel fuzzy clustering using jacobian matrix in fuzzy clustering the fuzzy c means fcm is the most known algorithm several extensions and variations of fcm had been proposed in the literature the first important extension to fcm was proposed by gustafson and kessel gk in the gk fuzzy clustering they considered the effect of different cluster shapes except for spherical shapes by replacing the euclidean distance of the fcm objective function with the mahalanobis distance the gk algorithm has become one of the most frequently used clustering algorithms just like fcm the fuzziness index m is a parameter in which the value will greatly influence the performance of the gk algorithm however there is no theoretical work on the parameter selection for the fuzziness index m of gk in this paper we reveal the relation between the stable fixed points of the gk algorithm and the datasets using jacobian matrix analysis and then provide a theoretical base for selecting the fuzziness index m in the gk algorithm some experimental results verify the effectiveness of our theoretical results

characterization of t splines with reduced continuity order on t meshes abstract the use of t splines 30 in isogeometric analysis 24 has been proposed in 5 as a tool to enhance the flexibility of isogeometric methods if t splines are a very general concept their success in isogeometric analysis relies upon some basic properties that needs to be true as e g i linear independence of blending functions and ii polynomial reproducibility at element level in this paper we study these properties for t splines of a reduced regularity order namely for t splines of degree p and regularity p 1 p 2 our results are both for odd and even degree under mild assumptions on the underlying t mesh t splines are shown to be linearly independent and the space they span is characterized in terms of piecewise polynomials on a topological extension of the t mesh also as p is odd we construct a new topological local refinement algorithm and demonstrate its locality properties through numerical examples

diffusion approximation for a controlled stochastic manufacturing system with average cost minimization we consider the problem of production control in a single machine single product unreliable manufacturing system facing a constant demand d the goal is to minimize the expected average per unit time inventory backlog costs under heavy traffic condition i e when the average production capacity is close to demand the problem is approximated by a singular stochastic control problem the approximate problem can be solved explicitly the solution is then interpreted in terms of the actual manufacturing system and a control policy for this system is derived we prove that the resulting policy is nearly optimal under the heavy traffic condition this policy is characterized by a critical level z0 that is produce at maximal rate r when inventory is less than z0 and at the demand rate d when the inventory is equal to z0 the quality of the approximate control is also discussed by comparing it to known results when they are available

instantaneous control of brownian motion a controller continuously monitors a storage system such as an inventory or bank account whose content z zt t 0 fluctuates as a 2 brownian motion in the absence of control holding costs are incurred continuously at rate h zt at any time the controller may instantaneously increase the content of the system incurring a proportional cost of r times the size of the increase or decrease the content at a cost of l times the size of the decrease we consider the case where h is convex on a finite interval and h outside this interval the objective is to minimize the expected discounted sum of holding costs and control costs over an infinite planning horizon it is shown that there exists an optimal control limit policy characterized by two parameters a and b a b roughly speaking this policy exerts the minimum amounts of control sufficient to keep zt a b for all t 0 put another way the optimal control limit policy imposes on z a lower reflecting barrier at a an

a fully locking free isogeometric approach for plane linear elasticity problems a stream function formulation in this paper we study plane incompressible elastic problems by means of a stream function formulation such that a divergence free displacement field can be computed from a scalar potential the numerical scheme is constructed within the framework of nurbs based isogeometric analysis and we take advantage of the high continuity guaranteed by nurbs basis functions in order to obtain the displacement field from the potential differentiation as a consequence the obtained numerical scheme is automatically locking free in the presence of the incompressibility constraint a discontinuous galerkin approach is proposed to deal with multiple mapped possibly multiply connected domains extensive numerical results are provided to show the method capabilities 2007 elsevier b v all rights reserved

superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis abstract in this article we address adaptive methods for isogeometric analysis based on local refinement guided by recovery based a posteriori error estimates isogeometric analysis was introduced a decade ago and an impressive progress has been made related to many aspects of numerical methods and advanced applications however related to adaptive mesh refinement guided by a posteriori error estimators rather few attempts are pursued besides the use of classical residual based error estimators in this article we explore a feature common for isogeometric analysis iga namely the use of structured tensorial meshes that facilitates superconvergence behavior of the gradient in the galerkin discretization by utilizing the concept of structured mesh refinement using lr b splines our aim is to facilitate superconvergence behavior for locally refined meshes as well superconvergence behavior matches well with the use of recovery based a posteriori estimator in the superconvergent patch recovery spr procedure however to our knowledge so far the spr procedure has not been exploited in the iga community we start out by addressing the existence of derivative superconvergent points in the computed finite element solution based on b splines and lr b splines for an elliptic model problem 1d and 2d poisson then we present some recovery procedures for improving the derivatives or gradient of the isogeometric finite element solution where the spr procedure will be the main focus in particular we show that our spr procedure for the improvement of derivatives fulfills the desired consistency criteria at the end we develop a posteriori error estimator where the improved gradient obtained from the proposed recovery procedures is used numerical results are presented to illustrate the efficiency of using spr procedure for the improvement of derivatives or gradient of computed solution in isogeometric analysis then the proposed a posteriori error estimator based adaptive refinement methodology is tested to solve smooth and non smooth elliptic benchmark problems the focus is put on whether optimal convergence rates are obtained in the computed solution or not as well as the effectivity index of the proposed error estimators

convergence of the single pass and online fuzzy c means algorithms scalable versions of the widely used fuzzy c means clustering algorithm called single pass fuzzy c means and online fuzzy c means have been recently introduced both algorithms facilitate scaling to very large numbers of examples while providing partitions that very closely approximate those one would obtain using fuzzy c means both algorithms have been successfully applied to a number of datasets most notably magnetic resonance image volumes of the human brain in this letter we show that weighting examples in the fuzzy c means algorithm does not cause a violation in its convergence proof and we provide a separate proof of convergence that holds for any dataset

isogeometric analysis using lr b splines abstract the recently proposed locally refined b splines denoted lr b splines by dokken et al 2013 6 may have the potential to be a framework for isogeometric analysis to enable future interoperable computer aided design and finite element analysis in this paper we propose local refinement strategies for adaptive isogeometric analysis using lr b splines and investigate its performance by doing numerical tests on well known benchmark cases the theory behind lr b spline is not presented in full details but the main conceptual ingredients are explained and illustrated by a number of examples

robustness of isogeometric structural discretizations under severe mesh distortion abstract this paper investigates higher order and higher continuity functions in isogeometric structural analysis under distortion of the control and physical meshes first the concepts behind isogeometric analysis are briefly reviewed the effect of perturbing control points upon the geometrical mapping is observed in the one dimensional setting the concept is extended to multiple dimensions with a series of cases where the interior of a cube is distorted in different ways and patch tests are performed to assess accuracy a circular fillet patch is introduced through the appropriate degeneration of a control mesh in order to address the problem of modeling small features in finite element models the fillet patch is tested with two problems of linear elasticity and is shown to be accurate the investigation is further extended to the setting of large deformation nearly incompressible nonlinear elasticity with two examples which make use of the recently proposed f projection method

impulse control of brownian motion consider a storage system such as an inventory or cash fund whose content fluctuates as a 2 brownian motion in the absence of control holding costs are continuously incurred at a rate proportional to the storage level and we may cause the storage level to jump by any desired amount at any time except that the content must be kept nonnegative both positive and negative jumps entail fixed plus proportional costs and our objective is to minimize expected discounted costs over an infinite planning horizon a control band policy is one that enforces an upward jump to q whenever level zero is hit and enforces a downward jump to q whenever level s is hit 0 q q s we prove the existence of an optimal control band policy and calculate explicitly the optimal values of the critical numbers q q s

optimizing domain parameterization in isogeometric analysis based on powell sabin splines we address the problem of constructing a high quality parameterization of a given planar physical domain defined by means of a finite set of boundary curves we look for a geometry map represented in terms of powell sabin b splines powell sabin splines are c 1 quadratic splines defined on a triangulation and thus the parameter domain can be any polygon the geometry map is generated by the following three step procedure first the shape of the parameter domain and a corresponding triangulation are determined in such a way that its number of corners matches the number of corners of the physical domain second the boundary control points related to the powell sabin b spline representation are chosen so that they parameterize the boundary curve of the physical domain third the remaining inner control points are obtained by solving a nimble optimization problem based on the winslow functional the proposed domain parameterization procedure is illustrated numerically in the context of isogeometric galerkin discretizations based on powell sabin splines it turns out that the flexibility rising from the generality of the parameter domain has a beneficial effect on the quality of the parameterization and also on the accuracy of the computed approximate solution

isogeometric analysis of the cahn hilliard phase field model abstract the cahn hilliard equation involves fourth order spatial derivatives finite element solutions are not common because primal variational formulations of fourth order operators are only well defined and integrable if the finite element basis functions are piecewise smooth and globally c 1 continuous there are a very limited number of two dimensional finite elements possessing c 1 continuity applicable to complex geometries but none in three dimensions we propose isogeometric analysis as a technology that possesses a unique combination of attributes for complex problems involving higher order differential operators namely higher order accuracy robustness two and three dimensional geometric flexibility compact support and most importantly the possibility of c 1 and higher order continuity a nurbs based variational formulation for the cahn hilliard equation was tested on two and three dimensional problems we present steady state solutions in two dimensions and for the first time in three dimensions to achieve these results an adaptive time stepping method is introduced we also present a technique for desensitizing calculations to dependence on mesh refinement this enables the calculation of topologically correct solutions on coarse meshes opening the way to practical engineering applications of phase field methodology

heavy traffic convergence of a controlled multiclass queueing system this paper provides a rigorous proof of the connection between the optimal sequencing problem for a two station two customer class queueing network and the problem of control of a multidimensional diffusion process obtained as a heavy traffic limit of the queueing problem in particular the diffusion problem which is one of singular control of a brownian motion is used to develop policies which are shown to be asymptotically nearly optimal as the traffic intensity approaches one in the queueing network the results are proved by a viscosity solution analysis of the related hamilton jacobi bellman equations

linear independence of the t spline blending functions associated with some particular t meshes based on the local refinement algorithm addressed in sederberg et al 2004 17 we analyze the linear independence of the bi cubic t spline blending functions corresponding to particular t meshes

a singularly perturbed model problem for numerical computation abstract in this note we introduce a model problem for the numerical solution of a two dimensional singular perturbation problem to combine a number of typical difficulties in a relatively simple problem we propose to solve the linear convection diffusion problem in the domain exterior of a circle we describe the analytical solution of the problem and we comment on its numerical evaluation for small values of the parameter asymptotic approximations of the solution are given based on expansions by friedlander 1958 and waechter 1968 this information gives insight into the behaviour of the solution and allows the computation of a reference solution for small values of the parameter

optimal control of production rate in a failure prone manufacturing system we address the problem of controlling the production rate of a failure prone manufacturing system so as to minimize the discounted inventory cost where certain cost rates are specified for both positive and negative inventories and there is a constant demand rate for the commodity produced the underlying theoretical problem is the optimal control of a continuous time system with jump markov disturbances with an infinite horizon discounted cost criterion we use two complementary approaches first proceeding informally and using a combination of stochastic coupling linear system arguments stable and unstable eigenspaces renewal theory parametric optimization etc we arrive at a conjecture for the optimal policy then we address the previously ignored mathematical difficulties associated with differential equations with discontinuous right hand sides singularity of the optimal control problem smoothness and validity of the dynamic programming equation etc to give a rigorous proof of optimality of the conjectured policy it is hoped that both approaches will find uses in other such problems also we obtain the complete solution and show that the optimal solution is simply characterized by a certain critical number which we call the optimal inventory level if the current inventory level exceeds the optimal one should not produce at all if less one should produce at the maximum rate while if exactly equal one should produce exactly enough to meet demand we also give a simple explicit formula for the optimal inventory level

impulse control of brownian motion the constrained average cost case when a manufacturer places repeated orders with a supplier to meet changing production requirements he faces the challenge of finding the right balance between holding costs and the operational costs involved in adjusting the shipment sizes we consider an inventory whose content fluctuates as a brownian motion in the absence of control at any moment a controller can adjust the inventory level by any positive or negative quantity but incurs both a fixed cost and a cost proportional to the magnitude of the adjustment the inventory level must be nonnegative at all times and continuously incurs a linear holding cost the objective is to minimize long run average cost we show that control band policies are optimal for the average cost brownian control problem and explicitly calculate the parameters of the optimal control band policy this form of policy is described by three parameters q q s 0 q q s when the inventory falls to zero rises to s the controller expedites curtails shipments to return it to q q employing apparently new techniques based on methods of lagrangian relaxation we show that this type of policy is optimal even with constraints on the size of adjustments and on the maximum inventory level we also extend these results to the discounted cost problem

optimization of clustering criteria by reformulation various hard fuzzy and possibilistic clustering criteria objective functions are useful as bases for a variety of pattern recognition problems at present many of these criteria have customized individual optimization algorithms because of the specialized nature of these algorithms experimentation with new and existing criteria can be very inconvenient and costly in terms of development and implementation time this paper shows how to reformulate some clustering criteria so that specialized algorithms can be replaced by general optimization routines found in commercially available software we prove that the original and reformulated versions of each criterion are fully equivalent finally two numerical examples are given to illustrate reformulation

the importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity mixed fems versus nurbs based approximations in the present paper we investigate the capability of finite element methods to correctly reproduce the stability range of finite strain problems in the incompressible regime to this end we develop a numerical scheme obtained combining a stream function formulation with an isogeometric nurbs approach which is able to sharply estimate the stability limits of the continuous problem using such a method we show a pair of benchmark problems on which various well known finite element methods largely fail in approximating the correct stability range

on the similarities and differences between classical hierarchical truncated hierarchical and lr b splines abstract smooth spline functions such as b splines and nurbs are already an established technology in the field of computer aided design cad and have in recent years been given a lot of attention from the computer aided engineering cae community the advantages of local refinement are obvious for anyone working in either field and as such several approaches have been proposed among others we find the three strategies classical hierarchical b splines truncated hierarchical b splines and locally refined b splines we will in this paper present these three frameworks and highlight similarities and differences between them in particular we will look at the function space they span and the support of the basis functions we will then analyse the corresponding stiffness and mass matrices in terms of sparsity patterns and conditioning numbers we show that the basis functions in general do not span the same space and that conditioning numbers are comparable moreover we show that the weighting needed by the classical hierarchical basis to maintain partition of unity has significant implications on the conditioning numbers

routing and singular control for queueing networks in heavy traffic the problem of routing control in an open queueing network under conditions of heavy traffic and finite scaled buffers is dealt with the operating statistics can be state dependent the sequence of scaled controlled state processes converges to a singularly controlled reflected diffusion with the associated costs under broad conditions due to the nature of the controls a scaling method is introduced to obtain the convergence since the actual sequence of processes does not necessarily converge in the skorokhod topology owing to finite buffers an extension of the reflection mapping needs to be obtained the optimal value functions for the physical processes converge to the optimal value function of the limit process under broad conditions approximations to the optimal control for the limit process are obtained as well as properties of the sequence of physical processes the optimal or controlled but not necessarily optimal limit process can be used to approximate a large variety of functio

optimal and approximately optimal control policies for queues in heavy traffic the approximately optimal control problem for tandem queueing or production networks with local feedback allowed under heavy traffic is treated the buffers scaled with traffic are finite the controls allow various inputs connecting links and the processors to be shut down or opened to manage the system the service and arrival rates as well as the routing probabilities can also be controlled and the system statistics can depend on the system state scaled buffer occupancies the associated costs involve holding costs costs for shutting off turning on the links or processors and the opportunity cost for lost production it is shown that the scaled controlled system converges weakly in an appropriate sense to a controlled limit reflected diffusion in the resealed time the actions of the controllers lead to multiple simultaneous impulses in the limit problem thus a nonstandard limit control problem is obtained and the usual methods of weak convergence for systems under heavy traffi

reflected brownian motion on an orthant we consider a k dimensional diffusion process z whose state space is the nonnegative orthant on the interior of the orthant z behaves like a kdimensional brownian motion with arbitrary covariance matrix and drift vector at each of the k 1 dimensional hyperplanes that form the boundary of the orthant z reflects instantaneously in a direction that is constant over that hyperplane there is no extant theory of multidimensional diffusion that applies to this process because the boundary of its state space is not smooth we adopt an approach that requires a restriction on the directions of reflection but reiman has shown that this restriction is met by all diffusions z arising as heavy traffic limits in open k station queuing networks our process z is defined as a path to path mapping of k dimensional brownian motion from this construction it follows that z is a continuous markov process and a semimartingale using the latter property we obtain a change of variable formula from which one can develop a complete analytical theory for the process z

nearly optimal singular controls for wideband noise driven systems singular stochastic control problems arise in many applications for example in storage inventory finite fuel consumption and investment and limits of impulsive control problems here the increment of the control effort is not of the usual form u t dt but is the differential of a nondecreasing and suitably adapted process the diffusion process models used are only approximations to some physical process which might be a wideband noise driven system or a suitably scaled discrete parameter process since the optimal controls for the physical processes are usually impossible to obtain it is of interest to know whether nearly optimal controls for the diffusion model are nearly optimum when applied to the physical problem it is shown that this is true under broad conditions for discounted and average cost per unit time problems the usual weak convergence analysis via the skorokhod topology on d 0 infty is not appropriate here due to the nature of the singular controls and it is ne

isogeometric analysis in electromagnetics b splines approximation abstract we introduce a new discretization scheme for maxwell equations in two space dimension inspired by the new paradigm of isogeometric analysis introduced in hughes et al 2005 16 we propose an algorithm based on the use of bivariate b splines spaces suitably adapted to electromagnetics we construct b splines spaces of variable interelement regularity on the parametric domain these spaces and their push forwards on the physical domain form a de rham diagram and we use them to solve the maxwell source and eigen problem our scheme has the following features i is adapted to treat complex geometries ii is spectral correct iii provides regular e g globally c 0 discrete solutions of maxwell equations

axiomatic generalization of the membership degree weighting function for fuzzy c means clustering for decades practitioners have been using the center based partitional clustering algorithms like fuzzy c means fcm which rely on minimizing an objective function comprising of an appropriately weighted sum of distances of each data point from the cluster representatives numerous generalizations in terms of choice of the distance function have been introduced for fcm since its inception in a stark contrast to this fact to the best of our knowledge there has not been any significant effort to address the issue of convergence of the algorithm under the structured generalization of the weighting function here by generalization we mean replacing the conventional weighting function uijm where uij indicates the membership of data xi to cluster cj and m is the real valued fuzzifier with 1 m with a more general function g uij which can assume a wide variety of forms under some mild assumptions in this article for the first time we present a novel axiomatic development of the general weighting function based on the membership degrees we formulate the fuzzy clustering problem along with the intuitive justification of the technicalities behind the axiomatic approach we develop an alternative optimization ao procedure to solve the main clustering problem by solving the partial optimization problems in an iterative way the novelty of the article lies in the development of an axiomatic generalization of the weighting function of fcm formulation of an ao algorithm for the fuzzy clustering problem with the extension to this general class of weighting functions and a detailed convergence analysis of the proposed algorithm

adaptive isogeometric analysis by local h refinement with t splines isogeometric analysis based on non uniform rational b splines nurbs as basis functions preserves the exact geometry but suffers from the drawback of a rectangular grid of control points in the parameter space which renders a purely local refinement impossible this paper demonstrates how this difficulty can be overcome by using t splines instead t splines allow the introduction of so called t junctions which are related to hanging nodes in the standard fem obeying a few straightforward rules rectangular patches in the parameter space of the t splines can be subdivided and thus a local refinement becomes feasible while still preserving the exact geometry furthermore it is shown how state of the art a posteriori error estimation techniques can be combined with refinement by t splines numerical examples underline the potential of isogeometric analysis with t splines and give hints for further developments

weighted regularization of maxwell equations in polyhedral domains we present a new method of regularizing time harmonic maxwell equations by a bf grad div term adapted to the geometry of the domain this method applies to polygonal domains in two dimensions as well as to polyhedral domains in three dimensions in the presence of reentrant corners or edges the usual regularization is known to produce wrong solutions due the non density of smooth fields in the variational space we get rid of this undesirable effect by the introduction of special weights inside the divergence integral standard finite elements can then be used for the approximation of the solution this method proves to be numerically efficient

variational multiscale residual based turbulence modeling for large eddy simulation of incompressible flows we present an les type variational multiscale theory of turbulence our approach derives completely from the incompressible navier stokes equations and does not employ any ad hoc devices such as eddy viscosities we tested the formulation on forced homogeneous isotropic turbulence and turbulent channel flows in the calculations we employed linear quadratic and cubic nurbs a dispersion analysis of simple model problems revealed nurbs elements to be superior to classical finite elements in approximating advective and diffusive processes which play a significant role in turbulence computations the numerical results are very good and confirm the viability of the theoretical framework

singular higher order complete vector bases for finite methods this paper presents new singular curl and divergence conforming vector bases that incorporate the edge conditions singular bases complete to arbitrarily high order are described in a unified and consistent manner for curved triangular and quadrilateral elements the higher order basis functions are obtained as the product of lowest order functions and silvester lagrange interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties are discussed and these bases are proved to be fully compatible with the standard high order regular vector bases used in adjacent elements the curl divergence conforming singular bases guarantee tangential normal continuity along the edges of the elements allowing for the discontinuity of normal tangential components adequate modeling of the curl divergence and removal of spurious modes solutions these singular high order bases should provide more accurate and efficient numerical solutions of both surface integral and differential problems sample numerical results confirm the faster convergence of these bases on wedge problems

b and f projection methods for nearly incompressible linear and non linear elasticity and plasticity using higher order nurbs elements abstract this paper presents projection methods to treat the incompressibility constraint in small and large deformation elasticity and plasticity within the framework of isogeometric analysis after reviewing some fundamentals of isogeometric analysis we investigate the use of higher order non uniform rational b splines nurbs within the b projection method the higher continuity property of such functions is explored in nearly incompressible applications and shown to produce accurate and robust results a new non linear f projection method based on a modified minimum potential energy principle and inspired by the b method is proposed for the large deformation case it leads to a symmetric formulation for which the consistent linearized operator for fully non linear elasticity is derived and used in a newton raphson iterative procedure the performance of the methods is assessed on several numerical examples and results obtained are shown to compare favorably with other published techniques

fuzzy consensus clustering with applications on big data consensus clustering aims to find a single partition of data that agrees as much as possible with existing basic partitions given its robustness and generalizability consensus clustering has emerged as a promising solution to find cluster structures inside heterogeneous big data rising from various application domains in the area of fuzzy systems however research along this line is still in its initial stage with some unsystematic algorithmic studies finding a fuzzy consensus partition from multiple fuzzy basic partitions in an efficient flexible and robust way is still an exciting open problem calling for further investigation in light of this this paper provides a systematic study of fuzzy consensus clustering fcc from a utility perspective specifically we first define the objective function of fcc clearly using the novel fuzzified contingency matrix we then derive a family of fcc utility functions termed as fccu that can transform fcc to a weighted piecewise fuzzy c means clustering pifcm problem this helps us to establish an algorithmic framework for fcc with flexible choice of utility functions and speeds fcc significantly with a fcm like iterative process of pifcm to meet the big data challenge we further parallelize fcc on the spark platform with both vertical and horizontal segmentation schemes extensive experiments on various real world datasets demonstrate the excellent performance of fcc even with a majority of poor basic partitions in particular our method exhibits interesting potential for big data clustering in two real life applications concerned with online event detection and overlapping community detection respectively

double band policy for stochastic manufacturing systems in heavy traffic we consider the control of a manufacturing system producing one product the demand for this product is random the manager can produce the product at a fixed rate r or choose to stop the production each time the production is resumed a setup cost must be paid to prevent the backlog which is not allowed the manager can buy the product from outside vendors paying a fixed order cost and a variable cost there is also a linear inventory holding cost the objective is to minimize the total expected discounted cost under heavy traffic conditions i e when the production capacity is close to the average demand this problem is approximated by an impulse control problem for brownian motion which is solved explicitly the solution is then used to derive a control policy for the original system the resulting control is characterized by three parameters 0 q0 q0 s0 and is dubbed double band policy when the inventory reaches s0 the machine is turned off and it is turned on again when inventory decreases to level q0 an amount of q0 units is purchased from the outside vendor if the inventory level drops to zero we prove that this policy is nearly optimal that is the relative difference between the cost under this policy and the optimal cost is small if traffic intensity is close to one

isogeometric analysis with powell sabin splines for advection diffusion reaction problems abstract this paper presents the use of powell sabin splines in the context of isogeometric analysis for the numerical solution of advection diffusion reaction equations powell sabin splines are piecewise quadratic c 1 functions defined on a given triangulation with a particular macro structure we discuss the galerkin discretization based on a normalized powell sabin b spline basis we focus on the accurate detection of internal and boundary layers and on local refinements we apply the approach to several test problems and we illustrate its effectiveness by a comparison with classical finite element and recent isogeometric analysis procedures

simple a posteriori error estimators in adaptive isogeometric analysis in this article we propose two simple a posteriori error estimators for solving second order elliptic problems using adaptive isogeometric analysis the idea is based on a serendipity11according to wikipedia serendipity means a fortunate happenstance or pleasant surprise it was coined by horace walpole in 1754 one aspect of walpole s original definition of serendipity is the need for an individual to be sagacious enough to link together apparently innocuous facts in order to come to a valuable conclusion we feel that this applies for the present discovery but it is of course up to the readers to judge pairing of discrete approximation spaces s h p k m s h p 1 k 1 m where the space s h p 1 k 1 m is considered as an enrichment of the original basis of s h p k m by means of the k refinement a typical unique feature available in isogeometric analysis the space s h p 1 k 1 m is used to obtain a higher order accurate isogeometric finite element approximation and using this approximation we propose two simple a posteriori error estimators the proposed a posteriori error based adaptive h refinement methodology using lr b splines is tested on classical elliptic benchmark problems the numerical tests illustrate the optimal convergence rates obtained for the unknown as well as the effectiveness of the proposed error estimators

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