convergence to equilibrium of gradient flows defined on planar curves we consider the evolution of open planar curves by the steepest descent flow of a geometric functional with different boundary conditions we prove that if any set of stationary solutions with fixed energy is finite then a solution of the flow converges to a stationary solution as time goes to infinity we also present a few applications of this result

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

isogeometric analysis of the cahn hilliard equation a convergence study herein we present a numerical convergence study of the cahn hilliard phase field model within an isogeometric finite element analysis framework using a manufactured solution a mixed formulation of the cahn hilliard equation and the direct discretisation of the weak form which requires a c 1 continuous approximation are compared in terms of convergence rates for approximations that are higher than second order in space the direct discretisation is found to be superior suboptimal convergence rates occur when splines of order p 2 are used this is validated with a priori error estimates for linear problems the convergence analysis is completed with an investigation of the temporal discretisation second order accuracy is found for the generalised method this ensures the functionality of an adaptive time stepping scheme which is required for the efficient numerical solution of the cahn hilliard equation the isogeometric finite element framework is eventually validated by two numerical examples of spinodal decomposition

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

rotation free isogeometric thin shell analysis using pht splines this paper presents a novel approach for isogeometric analysis of thin shells using polynomial splines over hierarchical t meshes pht splines the method exploits the flexibility of t meshes for local refinement the main advantage of the pht splines in the context of thin shell theory is that it achieves c1 continuity so the kirchhoff love theory can be used in pristine form no rotational degrees of freedom are needed numerical results show the excellent performance of the present method

a hierarchical approach to adaptive local refinement in isogeometric analysis abstract adaptive local refinement is one of the key issues in isogeometric analysis in this article we present an adaptive local refinement technique for isogeometric analysis based on extensions of hierarchical b splines we investigate the theoretical properties of the spline space to ensure fundamental properties like linear independence and partition of unity furthermore we use concepts well established in finite element analysis to fully integrate hierarchical spline spaces into the isogeometric setting this also allows us to access a posteriori error estimation techniques numerical results for several different examples are given and they turn out to be very promising

a reproducing kernel method with nodal interpolation property a general formulation for developing reproducing kernel rk interpolation is presented this is based on the coupling of a primitive function and an enrichment function the primitive function introduces discrete kronecker delta properties while the enrichment function constitutes reproducing conditions a necessary condition for obtaining a rk interpolation function is an orthogonality condition between the vector of enrichment functions and the vector of shifted monomial functions at the discrete points a normalized kernel function with relative small support is employed as the primitive function this approach does not employ a finite element shape function and therefore the interpolation function can be arbitrarily smooth to maintain the convergence properties of the original rk approximation a mixed interpolation is introduced a rigorous error analysis is provided for the proposed method optimal order error estimates are shown for the meshfree interpolation in any sobolev norms optimal order convergence is maintained when the proposed method is employed to solve one dimensional boundary value problems numerical experiments are done demonstrating the theoretical error estimates the performance of the method is illustrated in several sample problems copyright 2003 john wiley sons ltd

isogeometric analysis using polynomial splines over hierarchical t meshes for two dimensional elastic solids isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries one of the major drawbacks of nurbs based isogeometric finite elements is the inefficiency of local refinement in this study we present an alternative to nurbs based isogeometric analysis that allows for local refinement the idea is based on polynomial splines and exploits the flexibility of t meshes for local refinement the shape functions satisfy important properties such as non negativity local support and partition of unity several numerical examples are used to demonstrate the reliability of the present method

a consistently coupled isogeometric meshfree method abstract a consistently coupled isogeometric meshfree method is presented this method takes advantage of the geometry exactness of isogeometric analysis and the refinement flexibility of meshfree method the coupling of isogeometric approximation and meshfree approximation is based upon the reproducing or consistency conditions which are crucial for the coupled method to achieve the expected optimal convergence rates it is shown that unlike the reproducing kernel meshfree shape functions which satisfy the reproducing conditions with the nodal points as the reproducing locations the monomial reproducing points for different orders of b spline basis functions in isogeometric analysis are different and consequently a rational method is proposed to compute these reproducing points both theoretical proof and computational justification of the reproducing conditions for b spline basis functions are given subsequently within the framework of reproducing conditions a mixed reproducing point vector is proposed to ensure arbitrary order monomial reproducibility for both b spline basis functions and reproducing kernel meshfree shape functions which leads to a consistently coupled approximation with smoothing transition between b spline basis functions and reproducing kernel meshfree shape functions consequently a coupled isogeometric meshfree method is established with the galerkin formulation the effectiveness of the proposed coupled isogeometric meshfree method is demonstrated through a series of benchmark numerical examples

how robust is the n cube the n cube network is called faulty if it contains any faulty processor or any faulty link for any number k we want to compute the minimum number f n k of faults which is necessary for an adversary to make every n k dimensional subcube faulty reversely formulated the existence of an n k dimensional non faulty subcube can be guaranteed if there are less than f n k faults in the n cube in this paper several lower and upper bounds for f n k are derived such that the resulting gaps are small for instance if k 2 is constant then f n k q logn especially for k 2 and large n f n 2 a email protected a n 2 where a n logn 1 2 log log n 1 2 or if k w log log n then 2 k f n k 2 1 k with chosen arbitrarily small the aforementioned upper bounds are obtained by analysing the behaviour of an adversary who makes worst case distributions of a given number of faulty processors for k 2 the worst case distribution is obtained constructively in the general case the constructive methods presented in this paper lead to a rather bad upper bound which can be significantly improved by probabilistic arguments the bounds mentioned above change if the notions are relativized with respect to some given parallel fault checking procedure p in this case only subcubes which are possible outputs of p must be made faulty by the adversary the notion of directed chromatic index is defined in order to analyse the case k 2 relations between the directed chromatic index and the chromatic number are derived which are of interest in their own right

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

a gradient flow for the p elastic energy defined on closed planar curves we study the evolution of closed inextensible planar curves under a second order flow that decreases the p elastic energy a short time existence result for p in 1 infty is obtained via a minimizing movements method for p 2 that is in the case of the classic elastic energy long time existence is retrieved

duality and unified analysis of discrete approximations in structural dynamics and wave propagation comparison of p method finite elements with k method nurbs we study the discretization behavior of classical finite element and nurbs approximations on problems of structural vibrations and wave propagation we find that on the basis of equal numbers of degrees of freedom and bandwidth nurbs have superior approximation properties in fact we observe that the high mode behavior of classical finite elements is divergent with the order of approximation a surprisingly negative result on the other hand nurbs offer almost spectral approximation properties and all modes converge with increasing order of approximation

blending isogeometric analysis and local maximum entropy meshfree approximants abstract we present a method to blend local maximum entropy lme meshfree approximants and isogeometric analysis the coupling strategy exploits the optimization program behind lme approximation treats isogeometric and lme basis functions on an equal footing in the reproducibility constraints but views the former as data in the constrained minimization the resulting scheme exploits the best features and overcomes the main drawbacks of each of these approximants indeed it preserves the high fidelity boundary representation exact cad geometry of isogeometric analysis out of reach for bare meshfree methods and easily handles volume discretization and unstructured grids with possibly local refinement while maintaining the smoothness and non negativity of the basis functions we implement the method with b splines in two dimensions but the procedure carries over to higher spatial dimensions or to other non negative approximants such as nurbs or subdivision schemes the performance of the method is illustrated with the heat equation and linear and nonlinear elasticity the ability of the proposed method to impose directly essential boundary conditions in non convex domains and to deal with unstructured grids and local refinement in domains of complex geometry and topology is highlighted by the numerical examples

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

adaptivity for structured meshfree particle methods in 2d and 3d the implementation of h adaptivity for meshfree particle methods within a structured framework is described in this framework the initial particle arrangement is structured along with a background mesh and outside boundaries and interior interfaces are described by implicit functions the advantage of meshfree approximations in this framework lies in the ease of implementing h adaptivity and the simplicity of the data structures particles can easily be added and removed without complications in the data structure although there are some issues in the quadrature an a posteriori error estimation is used for the adaptive refinement an adaptive refinement strategy is applied to several linear elastic problems with high stress and strain gradients and singularities several non linear examples are also given copyright 2005 john wiley sons ltd

on greedy algorithms in coding theory we study a wide class of problems in coding theory for which we consider two different formulations in terms of incidence matrices and in terms of hypergraphs these problems are dealt with using a greedy algorithm due to stein 1974 and lovasz 1975 some examples including constructing covering codes codes for conflict resolution separating systems source encoding with distortion etc are given a unified treatment under certain conditions derandomization can be performed leading to an essential reduction in the complexity of the constructions

enhancement of planar shape through optimization of functionals for curves we show how optimization of the nordstrom and mumford shah functionals can be used to develop a type of curve evolution that is able to preserve salient features of closed curves while simultaneously suppressing noise and irrelevant details the idea is to characterize a curve by means of its angle function and apply the appropriate dynamics to this representation upon convergence the resulting form of the contour is reconstructed from the representation

nodally integrated implicit gradient reproducing kernel particle method for convection dominated problems convective transport terms in eulerian conservation laws lead to numerical instability in the solution of bubnov galerkin methods for these non self adjoint pdes stabilized petrov galerkin methods overcome this difficulty however gradient terms are required to construct the test functions which are typically expensive for meshfree methods in this work the implicit gradient reproducing kernel particle method is introduced which avoids explicit differentiation of test functions stabilization is accomplished by including gradient terms in the reproducing condition of the reproducing kernel approximation the proposed method is computationally efficient and simplifies stabilization procedures it is also shown that the implicit gradient resembles the diffuse derivative originally introduced in the diffuse element method in nayroles et al 1992 and maintains the desirable properties of the full derivative since careful attention must be paid to efficiency of domain integration in meshfree methods nodal integration is examined for this class of problems and a nodal integration method with enhanced accuracy and stability is introduced numerical examples are provided to show the effectiveness of the proposed method for both steady and transient problems

an improved nurbs based isogeometric analysis with enhanced treatment of essential boundary conditions the nurbs based isogeometric analysis offers a seamless integration between the cad and subsequent finite element analysis and has been shown to be very effective for wide classes of problems due to its accurate geometric description however similar to the moving least square or reproducing kernel meshfree shape functions the nurbs basis functions generally are not interpolatory functions in this work it is shown that the direct imposition of the inhomogeneous essential boundary conditions to the nurbs control points may lead to significant errors with deteriorated rates of convergence consequently an improved formulation for nurbs based isogeometric analysis is proposed this is fulfilled by employing a transformation method that relates the control variables to the collocated nodal values at the essential boundary by using open knot vectors the resulting nurbs basis functions associated with the interior control points vanish at the boundary thus unlike the meshfree approximation the nurbs control points can be clearly partitioned into boundary and interior groups therefore the transformation method can be only applied to the boundary control points via invoking collocation of physical values at a set of boundary points the nurbs approximation enhanced with transformed physical boundary variables is kinematically admissible and the essential boundary conditions can be enforced straightforwardly like the finite element method several potential and elasticity problems evince that much higher solution accuracy with optimal convergence rates can be achieved by the present improved formulation compared with the method with direct imposition of essential boundary conditions to control variables

reproducing kernel formulation of b spline and nurbs basis functions a meshfree local refinement strategy for isogeometric analysis abstract a reproducing kernel meshfree formulation is presented for the b spline and non uniform rational b spline nurbs basis functions used in isogeometric analysis it is shown that after properly introducing meshfree nodes support size and consistency conditions the reproducing kernel meshfree shape functions are capable of exactly representing the isogeometric b spline and nurbs basis functions consequently the proposed formulation successfully establishes a correspondence or close link between the meshfree methods and the isogeometric analysis more importantly the proposed reproducing kernel meshfree representation of isogeometric basis functions provides a reliable meshfree strategy to the local model refinement in isogeometric analysis this strategy inherits the strength of meshfree methods and gives considerable easiness for the local refinement i e the shape functions in the refined regions can be naturally constructed in a straightforward meshfree manner meanwhile the consistency and independence of the shape functions required by the subsequent computational analysis are ensured by the consistency conditions of reproducing kernel meshfree formulation a detailed illustration of the proposed approach for isogeometric local model refinement is presented the effectiveness of the proposed meshfree local refinement strategy for isogeometric analysis is demonstrated through numerical examples

global analysis of the generalised helfrich flow of closed curves immersed in r n in this paper we consider the evolution of regular closed elastic curves immersed in r n equipping the ambient euclidean space with a vector eld

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

a coupled iga meshfree discretization of arbitrary order of accuracy and without global geometry parameterization abstract this article presents a novel approach for coupling of isogeometric analysis iga and meshfree discretizations taking advantage of the strengths of both techniques we make iga responsible for the representation of the exact geometry of the problem domain boundary while the reproducing kernel particle method rkpm discretization is employed in the interior of the domain the coupling procedure relies on the higher order consistency or reproducing conditions that are directly imposed in the physical domain the resulting iga rkpm coupling technique preserves the geometric exactness of iga while circumventing the need for global volumetric parameterization of the problem domain and achieves arbitrary order approximation accuracy while maintaining higher order smoothness of the discretization numerical examples demonstrate the optimal convergence properties of the coupled iga rkpm formulation and show its effectiveness in constructing volumetric discretizations for complex geometry objects

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

analysis suitable t splines are dual compatible abstract in this paper we define dual compatible dc t splines and we prove that analysis suitable as t splines are dual compatible we show that the classical construction of a dual basis for tensor product t splines easily generalizes to dc t spline spaces and we discuss in the last section of the paper how it paves the way to a mathematical theory of as t splines

hamming codes hypercube embeddings and fault tolerance in this paper we devise a special 1 error correcting code that enables us to embed the graph product of an n log n node hypercube and a log n node complete graph into in an n node hypercube with constant load dilation and congestion we apply the result to construct improved embeddings of trees and other structures in a hypercube and to design more efficient and robust algorithms for reconfiguring a hypercube around random or worst case faults the result has also been used subsequently by others to show that the n node hypercube can emulate all n node planar graphs with constant slowdown

a phase field description of dynamic brittle fracture abstract in contrast to discrete descriptions of fracture phase field descriptions do not require numerical tracking of discontinuities in the displacement field this greatly reduces implementation complexity in this work we extend a phase field model for quasi static brittle fracture to the dynamic case we introduce a phase field approximation to the lagrangian for discrete fracture problems and derive the coupled system of equations that govern the motion of the body and evolution of the phase field we study the behavior of the model in one dimension and show how it influences material properties for the temporal discretization of the equations of motion we present both a monolithic and staggered time integration scheme we study the behavior of the dynamic model by performing a number of two and three dimensional numerical experiments we also introduce a local adaptive refinement strategy and study its performance in the context of locally refined t splines we show that the combination of the phase field model and local adaptive refinement provides an effective method for simulating fracture in three dimensions

the influence of elasticity on analysis the classic heritage etude des domaines suivants le catenaire solutions doubles et le calcul variationnel l elastique fonctions elliptiques analyse qualitative solutions multiples geometrie differentielle des courbes gauches systemes en petites vibrations nombres propres et modes simples equations differentielles lineaires fonctions de bessel polynomes de laguerre transformees integrales oscillations resonantes equations aux derives partielles concept de solution discontinuites la definition moderne d une fonction base fonctionnelle singularites solutions generalisees plaques la courbure gaussienne theorie tridimensionnelle deformation des regions deformation et rotation locale tenseurs nombres et vecteurs propres decomposition polaire resolution spectrale isotropie et hemitropie groupes torsion d un cylindre solution principale d un systeme d equations differentielles et son etat d approximation d autres solutions

the heat equation shrinks embedded plane curves to round points soit c 0 s 1 r 2 une courbe lisse plongee dans le plan alors c s 1 0 t r 2 existe en satisfaisant c t k n ou k est la courbure de c et n est son vecteur unite normal entrant c t est lisse pour tout t il converge vers un point quand t t et sa forme limite quand t t est un cercle rond avec convergence dans norme c

novel higher order mass matrices for isogeometric structural vibration analysis abstract a set of novel higher order mass matrices are presented for isogeometric analysis of structural vibrations using nurbs the proposed method for the construction of higher order mass matrices contains two essential steps firstly based upon the standard consistent mass matrix a special reduced bandwidth mass matrix is designed this reduced bandwidth mass matrix meets the requirement of mass conservation while simultaneously preserves the same order of frequency accuracy as the corresponding consistent mass matrix subsequently a mixed mass matrix is formulated through a linear combination of the reduced bandwidth mass matrix and the consistent mass matrix the desired higher order mass matrix is then deduced from the mixed mass matrix by optimizing the linear combination parameter to achieve the most favorable order of accuracy both quadratic and cubic formulations are discussed in detail and it is shown that with regard to the vibration frequency the proposed higher order mass matrices have 6th and 8th orders of accuracy in contrast to the 4th and 6th orders of accuracy associated with the quadratic and cubic consistent mass matrices a generalization to two dimensional higher order mass matrix is further realized by the tensor product operation on the one dimensional reduced bandwidth and consistent mass matrices a series of benchmark examples congruously demonstrate that the proposed higher order mass matrices are capable of achieving the theoretically derived optimal accuracy orders for structural vibration analysis

randomization derandomization and antirandomization three games abstract three games are given between two players paul and carole with a common theme in each round paul does a split and carole chooses random play by carole allows a bound for the game value through derandomization this becomes a deterministic strategy for carole minimizing a weight function paul can use that same weight function to give a bound for the game value in the other direction

solid t spline construction from boundary representations for genus zero geometry abstract this paper describes a novel method to construct solid rational t splines for complex genus zero geometry from boundary surface triangulations we first build a parametric mapping between the triangulation and the boundary of the parametric domain a unit cube after that we adaptively subdivide the cube using an octree subdivision project the boundary nodes onto the input triangle mesh and at the same time relocate the interior nodes via mesh smoothing this process continues until the surface approximation error is less than a pre defined threshold t mesh is then obtained by pillowing the subdivision result one layer on the boundary and its quality is improved templates are implemented to handle extraordinary nodes and partial extraordinary nodes in order to get a gap free t mesh the obtained solid t spline is c 2 continuous except for the local region around each extraordinary node and partial extraordinary node the boundary surface of the solid t spline is c 2 continuous everywhere except for the local region around the eight nodes corresponding to the eight corners of the parametric cube finally a bezier extraction technique is used to facilitate t spline based isogeometric analysis the obtained bezier mesh is analysis suitable with no negative jacobians several examples are presented in this paper to show the robustness of the algorithm

measuring teachability using variants of the teaching dimension in a typical algorithmic learning model a learner has to identify a target object from partial information conversely in a teaching model a teacher has to give information that allows the learners to identify a target object we devise two variants of the classical teaching model for boolean concept classes based on the teaching dimension and describe them by teaching dimension like combinatorial parameters in the first model the learners choose consistent hypotheses with least complexity we show that 1 decision lists are the harder to teach the longer they are and that 2 term dnfs are the harder to teach the more terms they have this contrasts with the teachability results for these classes in the teaching dimension model in our second model the learners choose consistent hypotheses based on the assumption that the teacher is optimal we show that monomials can be taught with a linear number of examples whereas some 1 decision lists need exponentially many

truncated hierarchical catmull clark subdivision with local refinement in this paper we present a new method termed truncated hierarchical catmull clark subdivision thccs which generalizes truncated hierarchical b splines to control grids of arbitrary topology thccs basis functions satisfy partition of unity are linearly independent and are locally refinable thccs also preserves geometry during adaptive hh refinement and thus inherits the surface continuity of catmull clark subdivision namely c2c2 continuous everywhere except at the local region surrounding extraordinary nodes where the surface continuity is c1c1 adaptive isogeometric analysis is performed with thccs basis functions on a benchmark problem with extraordinary nodes local refinement on complex surfaces is also studied to show potential wide application of the proposed method

finite element and nurbs approximations of eigenvalue boundary value and initial value problems abstract we study the spectral approximation properties of finite element and nurbs spaces from a global perspective we focus on eigenfunction approximations and discover that the l 2 norm errors for finite element eigenfunctions exhibit pronounced spikes about the transition points between branches of the eigenvalue spectrum this pathology is absent in nurbs approximations by way of the pythagorean eigenvalue error theorem we determine that the squares of the energy norm errors of the eigenfunctions are the sums of the eigenvalue errors and the squares of the l 2 norm eigenfunction errors the spurious behavior of the higher eigenvalues for standard finite elements is well known and therefore inherited by the energy norm errors along with the spikes in the l 2 norm of the eigenfunction errors the eigenvalue pathology is absent for nurbs the implications of these results to the corresponding elliptic boundary value problem and parabolic and hyperbolic initial value problems are discussed

the zero set of a solution of a parabolic equation on etudie l ensemble nul d une solution u t x de l equation u t a x t u xx b x t u x c x t u sous des hypotheses tres generales sur les coefficients a b et c

the heat equation shrinking convex plane curves soient m et m des varietes de riemann et f m m une application reguliere si m est une courbe convexe plongee dans le plan r 2 l equation de la chaleur contracte m a un point

large eddy simulation of turbulent taylor couette flow using isogeometric analysis and the residual based variational multiscale method we present an application of the residual based variational multiscale turbulence modeling rbvms methodology to the computation of turbulent taylor couette flow at high reynolds number we show that the rbvms formulation globally conserves angular momentum a feature that is felt to be important for flows dominated by rotation and that is not shared by standard stabilized formulations of fluid flow weak imposition of dirichlet boundary conditions is employed to enhance the accuracy of the rbvms framework in the presence of thin turbulent boundary layers near solid walls calculation of conservative boundary forces and torques is also presented for the case of weakly enforced boundary conditions nurbs based isogeometric analysis is employed for the spatial discretization and mesh refinement is performed to assess the convergence characteristics of the proposed methodology numerical tests show that very accurate results are obtained on relatively coarse grids to the best of the authors knowledge this paper is the first to report large eddy simulation computations of this challenging test case

moving least square reproducing kernel methods i methodology and convergence this paper formulates the moving least square interpolation scheme in a framework of the so called moving least square reproducing kernel mlsrk representation in this study the procedure of constructing moving least square interpolation function is facilitated by using the notion of reproducing kernel formulation which as a generalization of the early discrete approach establishes a continuous basis for a partition of unity this new formulation possesses the quality of simplicity and it is easy to implement moreover the reproducing kernel formula proposed is not only able to reproduce any mth order polynomial exactly on an irregular particle distribution but also serves as a projection operator that can approximate any smooth function globally with an optimal accuracy in this contribution a generic m consistency relation has been found which is the essential property of the mlsrk approximation an interpolation error estimate is given to assess the convergence rate of the approximation it is shown that for sufficiently smooth function the interpolant expansion in terms of sampled values will converge to the original function in the sobolev norms as a meshless method the convergence rate is measured by a new control variable dilation parameter of the window function instead of the mesh size h as usually done in the finite element analysis to illustrate the procedure convergence has been shown for the numerical solution of the second order elliptic differential equations in a galerkin procedure invoked with this interpolant in the numerical example a two point boundary problem is solved by using the method and an optimal convergence rate is observed with respect to various norms

truncated t splines fundamentals and methods in this paper we present truncated t splines as a new type of t splines suitable for both geometric design and analysis supporting highly localized refinement truncated t spline basis functions are piece wise polynomials that are linearly independent and form a partition of unity refinement of truncated t splines produces nested spline spaces furthermore we study truncated t splines and local refinement on the general domain 2 manifold with extraordinary points in the t mesh g1g1 continuity is attained around extraordinary points by properly capping quartic bezier patches where a constrained optimization problem is solved in the end we study benchmark problems using truncated t splines in the context of isogeometric analysis we also apply truncated t splines to complex geometries to show the smooth surfaces and simulation results under local refinement

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

superconvergent isogeometric free vibration analysis of euler bernoulli beams and kirchhoff plates with new higher order mass matrices abstract a superconvergent isogeometric free vibration analysis is presented for euler bernoulli beams and kirchhoff plates this method is featured by new higher order mass matrices for the 1d euler bernoulli beam problem it is shown that a new higher order mass matrix can be directly established by optimizing a reduced bandwidth mass matrix the reduced bandwidth mass matrix is designed based upon the consistent mass matrix and it contains adjustable parameters to be determined via maximizing the order of accuracy of the vibration frequency as a result 4th and 6th orders of accuracy are observed for the proposed quadratic and cubic higher order mass matrices while their corresponding consistent mass matrices are 2nd and 4th order accurate respectively thus the higher order beam mass matrices have more superior frequency accuracy simultaneously with smaller bandwidth compared with their corresponding consistent mass matrices while for the 2d kirchhoff plate problem in order to compute arbitrary frequency in a superconvergent fashion a mixed mass matrix is formulated through a linear combination of the consistent mass matrix and the reduced bandwidth mass matrix then by introducing the wave propagation angle the higher order plate mass matrix can be rationally derived from the mixed mass matrix it is proved that the optimal combination parameter for higher order mass matrix depends on the wave propagation angle consequently a particular higher order mass matrix can always be set up for a superconvergent computation of arbitrary vibration frequency it is shown that the quadratic and cubic higher order mass matrices possess 4th and 6th orders of accuracy which are two orders higher than those of the consistent plate mass matrices the construction of higher order mass matrices and the analytical results for vibration frequencies are systematically demonstrated by a set of numerical examples

a hybrid variational collocation immersed method for fluid structure interaction using unstructured t splines summary we present a hybrid variational collocation immersed and fully implicit formulation for fluid structure interaction fsi using unstructured t splines in our immersed methodology we define an eulerian mesh on the whole computational domain and a lagrangian mesh on the solid domain which moves arbitrarily on top of the eulerian mesh mathematically the problem reduces to solving three equations namely the linear momentum balance mass conservation and a condition of kinematic compatibility between the lagrangian displacement and the eulerian velocity we use a weighted residual approach for the linear momentum and mass conservation equations but we discretize directly the strong form of the kinematic relation deriving a hybrid variational collocation method we use t splines for both the spatial discretization and the information transfer between the eulerian mesh and the lagrangian mesh t splines offer us two main advantages against non uniform rational b splines they can be locally refined and they are unstructured the generalized method is used for the time discretization we validate our formulation with a common fsi benchmark problem achieving excellent agreement with the theoretical solution an example involving a partially immersed solid is also solved the numerical examples show how the use of t junctions and extraordinary nodes results in an accurate efficient and flexible method copyright 2015 john wiley sons ltd

intersecting codes and independent families a binary intersecting code is a linear code with the property that any two nonzero codewords have intersecting supports these codes appear in a wide variety of contexts and applications e g multiple access cryptography and information theory this paper is devoted partly to the study of intersecting codes and partly to their use in constructing large t independent families of binary vectors the latter subject has by now been extensively studied and has application in vlsi testing defect correction e biased probability spaces and derandomization by concatenation methods we construct codes with the highest known fate asymptotically we then generalize the concept to t wise intersecting codes we give bounds on the achievable rate of such codes both existential and constructive we show how t wise intersecting codes can be used to obtain t 1 independent families with this method we obtain improved asymptotical constructions of t independent families complexity issues are discussed

curve shortening straightening flow for non closed planar curves with infinite length abstract we consider a motion of non closed planar curves with infinite length the motion is governed by a steepest descent flow for the geometric functional which consists of the sum of the length functional and the total squared curvature we call the flow shortening straightening flow in this paper first we prove a long time existence result for the shortening straightening flow for non closed planar curves with infinite length then we show that the solution converges to a stationary solution as time goes to infinity moreover we give a classification of the stationary solution