a stabilized conforming nodal integration for galerkin mesh free methods domain integration by gauss quadrature in the galerkin mesh free methods adds considerable complexity to solution procedures direct nodal integration on the other hand leads to a numerical instability due to under integration and vanishing derivatives of shape functions at the nodes a strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integration for convergence an integration constraint ic is introduced as a necessary condition for a linear exactness in the mesh free galerkin approximation the gradient matrix of strain smoothing is shown to satisfy ic using a divergence theorem no numerical control parameter is involved in the proposed strain smoothing stabilization the numerical results show that the accuracy and convergent rates in the mesh free method with a direct nodal integration are improved considerably by the proposed stabilized conforming nodal integration method it is also demonstrated that the gauss integration method fails to meet ic in mesh free discretization for this reason the proposed method provides even better accuracy than gauss integration for galerkin mesh free method as presented in several numerical examples copyright 2001 john wiley sons ltd

computing nonnegative rank factorizations abstract the existence of nonnegative generalized inverses in terms of nonnegative rank factorizations is considered an algorithm is presented which computes a nonnegative rank factorization of a nonnegative matrix when a nonnegative 1 inverse exists

methods of infinite dimensional morse theory for geodesics on finsler manifolds abstract we prove the shifting theorems of the critical groups of critical points and critical orbits for the energy functionals of finsler metrics on hilbert manifolds of h 1 curves and two splitting lemmas for the functionals on banach manifolds of c 1 curves two results on critical groups of iterated closed geodesics are also proved their corresponding versions on riemannian manifolds are based on the usual splitting lemma by gromoll and meyer 1969 our approach consists in deforming the square of the finsler metric in a lagrangian which is smooth also on the zero section and then in using the splitting lemma for nonsmooth functionals that the author recently developed in lu 2011 0000 2013 the argument does not involve finite dimensional approximations and any palais result in palais 1966 as an application we extend to finsler manifolds a result by v bangert and w klingenberg 1983 about the existence of infinitely many geometrically distinct closed geodesics on a compact riemannian manifold

isometry invariant geodesics and the fundamental group we prove that on closed riemannian manifolds with infinite abelian but not cyclic fundamental group any isometry that is homotopic to the identity possesses infinitely many invariant geodesics we conjecture that the result remains true if the fundamental group is infinite cyclic we also formulate a generalization of the isometry invariant geodesics problem and a generalization of the celebrated weinstein conjecture on a closed contact manifold with a selected contact form any strict contactomorphism that is contact isotopic to the identity possesses an invariant reeb orbit

the natural element method in solid mechanics the application of the natural element method nem 1 2 to boundary value problems in two dimensional small displacement elastostatics is presented the discrete model of the domain consists of a set of distinct nodes n and a polygonal description of the boundary in the natural element method the trial and test functions are constructed using natural neighbour interpolants these interpolants are based on the voronoi tessellation of the set of nodes n the interpolants are smooth c 1 everywhere except at the nodes where they are c 0 in one dimension nem is identical to linear nite elements the nem interpolant is strictly linear between adjacent nodes on the boundary of the convex hull which facilitates imposition of essential boundary conditions a methodology to model material discontinuities and non convex bodies cracks using nem is also described a standard displacement based galerkin procedure is used to obtain the discrete system of linear equations application of nem to various problems in solid mechanics which include the patch test gradient problems bimaterial interface and a static crack problem are presented excellent agreement with exact analytical solutions is obtained which exemplies the accuracy and robustness of nem and suggests its potential application in the context of other classes of problems crack growth plates and large deformations to name a few 1998 john wiley sons ltd

on the geometric interpretation of the nonnegative rank the nonnegative rank of a nonnegative matrix is the minimum number of nonnegative rank one factors needed to reconstruct it exactly the problem of determining this rank and computing the corresponding nonnegative factors is difficult however it has many potential applications e g in data mining graph theory and computational geometry in particular it can be used to characterize the minimal size of any extended reformulation of a given combinatorial optimization program in this paper we introduce and study a related quantity called the restricted nonnegative rank we show that computing this quantity is equivalent to a problem in polyhedral combinatorics and fully characterize its computational complexity this in turn sheds new light on the nonnegative rank problem and in particular allows us to provide new improved lower bounds based on its geometric interpretation we apply these results to slack matrices and linear euclidean distance matrices and obtain counter examples to two conjectures of beasly and laffey namely we show that the nonnegative rank of linear euclidean distance matrices is not necessarily equal to their dimension and that the rank of a matrix is not always greater than the nonnegative rank of its square

looking for nonnegative solutions of a leontief dynamic model let a be an n n nonnegative real matrix we know that a is monotone if it has a nonnegative inverse moreover if a has an appropriate generalized inverse then we can obtain nonnegative solutions for the linear system ax b where b 0 in this paper using properties about nonnegatives matrices we present sufficient conditions in order that the leontief price model i f p k 1 1 r k fp k gp0 k 1 a0 where f i at 1bt and g i at 1 have nonnegative solutions

a stable nodal integration method for static and quasi static electromagnetic field computation a stable nodal integration method snim is presented to solve static and quasi static electromagnetic problems in this paper the analysis domain is firstly discretized into a set of triangular or tetrahedral elements and linear interpolation is adopted within each element a weakened weak formulation based on the nodes is further considered framing the so called node based smoothing domains equivalent smoothing domains are then acquired as circular or spherical regions where the gradient of shape function is expanded as the first order taylor form subsequently four or six temporary integration points on the region are picked to obtain items of the stiffness matrix and the external load vector by simplifying the equations the stiffness matrix can be received in quite concise form with one point integration and stabilization terms which are calculated on original node based smoothing domains the implementation of snim on electromagnetic problems is thus realized the proposed formulation is validated against both analytical solutions and traditional methods and its effectiveness and potentialities can be well represented and clarified by numerical examples

strongly absolute stability of lur e type differential algebraic systems in this paper we consider lur e type differential algebraic systems lds and introduce the concept of strongly absolute stability such a notion is a generalization of absolute stability for lur e type standard state space systems lss by a lur e type lyapunov function we derive an lmi based stability criterion for lds to be strongly absolutely stable using extended strictly positive realness espr we present the frequency domain interpretation of the obtained criterion by which we simplify the criterion and show that the criterion is a generalization of the well known popov criterion finally we illustrate the effectiveness of the main results by a numerical example

a geometric treatment of generalized inverses and semigroups of nonnegative matrices abstract the purpose of this paper is to provide a unified treatment from the geometric viewpoint of the following closely related aspects of nonnegative matrices nonnegative matrices with nonnegative generalized inverses of various kinds nonnegative rank factorization regular elements green s relations and maximal subgroups of the semigroups of nonnegative matrices stochastic matrices column stochastic matrices and doubly stochastic matrices

structure of a nonnegative regular matrix and its generalized inverses abstract a nonnegative matrix is called regular if it admits a nonnegative generalized inverse the structure of such matrices has been studied by several authors if a is a nonnegative regular matrix then we obtain a complete description of all nonnegative generalized inverses of a in particular it is shown that if a is a nonnegative regular matrix with no zero row or column then the zero nonzero pattern of any nonnegative generalized inverse of a is dominated by that of a t the transpose of a we also obtain the structure of nonnegative matrices which admit nonnegative least squares and minimum norm generalized inverses

new boundary condition treatments in meshfree computation of contact problems due to the loss of kronecker delta properties in the meshfree shape functions the imposition of essential boundary conditions consumes significant cpu time in meshfree computation in this work two boundary condition treatments are proposed to enhance the computational efficiency of meshfree methods for contact problems the mixed transformation method is modified from the previous full transformation method by introducing a node partitioning and a mixed coordinate so that the matrix inversion and multiplication of coordinate transformation involves operations only on the sub degrees of freedom associated with the boundary group the boundary singular kernel method introduces singularities to the kernel functions of the essential and contact boundary nodes so that the corresponding coefficients of the singular kernel shape functions recover nodal values and consequently kinematic constraints can be imposed directly the effectiveness of the proposed methods is demonstrated in several numerical examples

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 node based smoothed finite element method ns fem for upper bound solution to visco elastoplastic analyses of solids using triangular and tetrahedral meshes abstract a node based smoothed finite element method ns fem was recently proposed for the solid mechanics problems in the ns fem the system stiffness matrix is computed using the smoothed strains over the smoothing domains associated with nodes of element mesh in this paper the ns fem is further extended to more complicated visco elastoplastic analyses of 2d and 3d solids using triangular and tetrahedral meshes respectively the material behavior includes perfect visco elastoplasticity and visco elastoplasticity with isotropic hardening and linear kinematic hardening a dual formulation for the ns fem with displacements and stresses as the main variables is performed the von mises yield function and the prandtl reuss flow rule are used in the numerical procedure however the stress variables are eliminated and the problem becomes only displacement dependent the numerical results show that the ns fem has higher computational cost than the fem however the ns fem is much more accurate than the fem and hence the ns fem is more efficient than the fem it is also observed from the numerical results that the ns fem possesses the upper bound property which is very meaningful for the visco elastoplastic analyses which almost have not got the analytical solutions this suggests that we can use two models ns fem and fem to bound the solution and can even estimate the global relative error of numerical solutions

numerical integration in natural neighbour galerkin methods in this paper issues regarding numerical integration of the discrete system of equations arising from natural neighbour natural element galerkin methods are addressed the sources of error in the traditional delaunay triangle based numerical integration are investigated two alternative numerical integration schemes are analysed first a local approach in which nodal shape function supports are exactly decomposed into triangles and circle segments is shown not to give accurate enough results second a stabilized nodal quadrature scheme is shown to render high levels of accuracy while resulting specially appropriate in a natural neighbour galerkin approximation method the paper is completed with several examples showing the performance of the proposed techniques copyright 2004 john wiley sons ltd

positive n periodic descriptor control systems this paper establishes the relationship between the positive n periodic descriptor system in discrete time and its associated invariant systems reachability and controllability properties of these kinds of systems are analyzed transmission of structural properties from the n periodic system to their associated invariant systems is studied finally some comments on the stability property are made

arbitrarily smooth generalized finite element approximations this paper presents a procedure to build ck k arbitrarily large generalized finite element fe shape functions defined on non structured finite element meshes the functions have the same support as corresponding global fe lagrangian shape functions meshes with both convex and non convex clouds set of elements sharing a vertex node can be used the so called r functions are used to build ck fe based partition of unity functions with non convex support a technique to combine c0 lagrangian fe shape functions with the proposed ck partition of unity is presented the technique allows the use of ck generalized fe shape functions in parts of the computational domain where their high smoothness is required as in the case of problems with distributional boundary conditions and the less computationally demanding c0 generalized fe shape functions elsewhere in the domain a linear elasticity problem with a concentrated moment is solved using the proposed ck generalized fe method higher order distributional boundary conditions can also be handled by the method a detailed convergence analysis is presented for this class of problems as well as for problems in energy space the integrability of the functions using standard gauss legendre rules is also investigated

enforcement of essential boundary conditions in meshless approximations using finite elements abstract a technique for easily treating essential boundary conditions for approximations which are not interpolants such as moving least square approximations in the element free galerkin method is presented the technique employs a string of elements along the essential boundaries and combines the finite element shape functions with the approximation in the resulting approximation essential boundary conditions can be treated exactly as in finite elements it is shown that the resulting approximation can exactly reproduce linear polynomials so that it satisfies the patch test numerical studies show that the method retains the high rate of convergence associated with moving least square approximations

completely positive factorizations associated with euclidean distance matrices corresponding to an arithmetic progression abstract euclidean distance matrices corresponding to an arithmetic progression have rich spectral and structural properties we exploit those properties to develop completely positive factorizations of translations of those matrices we show that the minimal translation that makes such a matrix positive semidefinite results in a completely positive matrix we also discuss completely positive factorizations of such matrices over the integers methods developed in the paper can be used to find completely positive factorizations of other matrices with similar properties

free surface fluid dynamics on moving domains this paper presents a lagrangian approach for the simulation of two dimensional free surface flows along with a systematic validation fluid flow is traditionally modeled using an eulerian description in association with finite differences and more recently finite elements free surface flow introduces new difficulties in connection with the time dependence of the domain the proposed approach sets a framework for meshfree and finite element formulations it is extended to two phase media in preisig and zimmermann m preisig th zimmermann two phase free surface fluid dynamics on moving domains j comput phys 229 7 2010 2740 2758 in this paper triangular finite elements and a remeshing procedure to avoid excessive element distortion are chosen for their robustness convergence of the lagrangian description is analyzed and compared to results obtained with an eulerian description the equivalence of the two formulations for confined flows is demonstrated numerically illustrations include stratified flow flow over a backward facing step propagation of a solitary wave and dam break meshfree formulations will be addressed in separate papers c 2010 elsevier b v all rights reserved

on the complexity of nonnegative matrix factorization nonnegative matrix factorization nmf has become a prominent technique for the analysis of image databases text databases and other information retrieval and clustering applications the problem is most naturally posed as continuous optimization in this report we define an exact version of nmf then we establish several results about exact nmf i that it is equivalent to a problem in polyhedral combinatorics ii that it is np hard and iii that a polynomial time local search heuristic exists

a particle method for history dependent materials abstract a broad class of engineering problems including penetration impact and large rotations of solid bodies causes severe numerical problems for these problems the constitutive equations are history dependent so material points must be followed this is difficult to implement in a eulerian scheme on the other hand purely lagrangian methods typically result in severe mesh distortion and the consequence is ill conditioning of the element stiffness matrix leading to mesh lockup or entanglement remeshing prevents the lockup and tangling but then interpolation must be performed for history dependent variables a process which can introduce errors proposed here is an extension of the particle in cell method in which particles are interpreted to be material points that are followed through the complete loading process a fixed eulerian grid provides the means for determining a spatial gradient because the grid can also be interpreted as an updated lagrangian frame the usual convection term in the acceleration associated with eulerian formulations does not appear with the use of maps between material points and the grid the advantages of both eulerian and lagrangian schemes are utilized so that mesh tangling is avoided while material variables are tracked through the complete deformation history example solutions in two dimensions are given to illustrate the robustness of the proposed convection algorithm and to show that typical elastic behavior can be reproduced also it is shown that impact with no slip is handled without any special algorithm for bodies governed by elasticity and strain hardening plasticity

a meshfree enriched finite element method for compressible and near incompressible elasticity summary in this paper a two dimensional displacement based meshfree enriched fem me fem is presented for the linear analysis of compressible and near incompressible planar elasticity the me fem element is established by injecting a first order convex meshfree approximation into a low order finite element with an additional node the convex meshfree approximation is constructed using the generalized meshfree approximation method and it possesses the kronecker delta property on the element boundaries the gradient matrix of me fem element satisfies the integration constraint for nodal integration and the resultant me fem formulation is shown to pass the constant stress test for the compressible media the me fem interpolation is an element wise meshfree interpolation and is proven to be discrete divergence free in the incompressible limit to prevent possible pressure oscillation in the near incompressible problems an area weighted strain smoothing scheme incorporated with the divergence free me fem interpolation is introduced to provide the smoothing on strains and pressure with this smoothed strain field the discrete equations are derived based on a modified hu washizu variational principle several numerical examples are presented to demonstrate the effectiveness of the proposed method for the compressible and near incompressible problems copyright 2012 john wiley sons ltd

limit analysis of plates and slabs using a meshless equilibrium formulation a meshless element free galerkin efg equilibrium formulation is proposed to compute the limit loads which can be sustained by plates and slabs in the formulation pure moment fields are approximated using a moving least squares technique which means that the resulting fields are smooth over the entire problem domain there is therefore no need to enforce continuity conditions at interfaces within the problem domain which would be a key part of a comparable finite element formulation the collocation method is used to enforce the strong form of the equilibrium equations and a stabilized conforming nodal integration scheme is introduced to eliminate numerical instability problems the combination of the collocation method and the smoothing technique means that equilibrium only needs to be enforced at the nodes and stable and accurate solutions can be obtained with minimal computational effort the von mises and nielsen yield criteria which are used in the analysis of plates and slabs respectively are enforced by introducing second order cone constraints ensuring that the resulting optimization problem can be solved using efficient interior point solvers finally the efficacy of the procedure is demonstrated by applying it to various benchmark plate and slab problems

characterization and stability of autonomous positive descriptor systems this note addresses two problems the characterization of positivity of autonomous descriptor systems and the problem of finding conditions for their stability for these fundamental issues we provide necessary and sufficient conditions complemented with a numerically reliable computational approach the given conditions can be checked by means of linear programming lp also we derive a necessary and sufficient condition for stability that is connected to the underlying eigenstructure of the system

reachability conditions for switched linear singular systems the reachability problem of switched linear singular systems is investigated in this note by using the geometric approach and the admissible control set introduced a necessary condition and a sufficient condition on complete reachability are presented the conditions are the same as those of the conventional nonsingular switched linear systems and normal nonswitching singular systems given in previous papers when the systems degenerate to normal singular systems and conventional switched systems respectively

the nonnegative rank factorizations of nonnegative matrices abstract let a p m n r the set of all m n nonnegative matrices having the same rank r for matrices a in p m n n we introduce the concepts of a has only trivial nonnegative rank factorizations and a can have nontrivial nonnegative rank factorizations correspondingly the set p m n n is divided into two disjoint subsets p 1 and p 2 such that p 1 p 2 p m n n it happens that the concept of a has only trivial nonnegative rank factorizations is a generalization of a is prime in p n n n we characterize the sets p 1 and p 2 some of our results generalize some theorems in the paper of daniel j richman and hans schneider 9

consistent pseudo derivatives in meshless methods a meshless petrov galerkin formulation is developed in which derivatives of the trial functions are obtained as a linear combination of derivatives of shepard functions a key contribution is the development of conditions on test functions and trial functions for nonintegrable pseudo derivatives for petrov galerkin method which pass the patch test numerical results show that the resulting method is substantially more accurate than the galerkin method with shepard approximants and exceeds the rate of convergence of linear finite elements

linear smoothed polygonal and polyhedral finite elements the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method in this work we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes the main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain this new strain is then used in the computation of the stiffness matrix the convergence properties and accuracy of the proposed scheme are discussed by solving a few benchmark problems numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes able to deliver the same optimal convergence rate as traditional quadrilateral and hexahedral approximations the accuracy is also improved and all the methods tested pass the patch test to machine precision

consistent and stable meshfree galerkin methods using the virtual element decomposition summary over the past two decades meshfree methods have undergone significant development as a numerical tool to solve partial differential equations pdes in contrast to finite elements the basis functions in meshfree methods are smooth nonpolynomial functions and they do not rely on an underlying mesh structure for their construction these features render meshfree methods to be particularly appealing for higher order pdes and for large deformation simulations of solid continua however a deficiency that still persists in meshfree galerkin methods is the inaccuracies in numerical integration which affects the consistency and stability of the method several previous contributions have tackled the issue of integration errors with an eye on consistency but without explicitly ensuring stability in this paper we draw on the recently proposed virtual element method to present a formulation that guarantees both the consistency and stability of the approximate bilinear form we adopt maximum entropy meshfree basis functions but other meshfree basis functions can also be used within this framework numerical results for several two dimensional and three dimensional elliptic poisson and linear elastostatic boundary value problems that demonstrate the effectiveness of the proposed formulation are presented copyright 2017 john wiley sons ltd

non negative matrix factorization revisited uniqueness and algorithm for symmetric decomposition non negative matrix factorization nmf has found numerous applications due to its ability to provide interpretable decompositions perhaps surprisingly existing results regarding its uniqueness properties are rather limited and there is much room for improvement in terms of algorithms as well uniqueness aspects of nmf are revisited here from a geometrical point of view both symmetric and asymmetric nmf are considered the former being tantamount to element wise non negative square root factorization of positive semidefinite matrices new uniqueness results are derived e g it is shown that a sufficient condition for uniqueness is that the conic hull of the latent factors is a superset of a particular second order cone checking this condition is shown to be np complete yet this and other results offer insights on the role of latent sparsity in this context on the computational side a new algorithm for symmetric nmf is proposed which is very different from existing ones it alternates between procrustes rotation and projection onto the non negative orthant to find a non negative matrix close to the span of the dominant subspace simulation results show promising performance with respect to the state of art finally the new algorithm is applied to a clustering problem for co authorship data yielding meaningful and interpretable results

nonnegative ranks decompositions and factorizations of nonnegative matrices the nonnegative rank of a nonnegative matrix is the smallest number of nonnegative rank one matrices into which the matrix can be decomposed additively such decompositions are useful in diverse scientific disciplines we obtain characterizations and bounds and show that the nonnegative rank can be computed exactly over the reals by a finite algorithm

matrices with a transitive graph and inverse m matrices abstract the relationship between inverse m matrices and matrices whose graph is transitive is studied the results are applied to obtain a new proof of the characterization due to m lewin and m neumann of 0 1 inverse m matrices

a novel reduced basis method with upper and lower bounds for real time computation of linear elasticity problems abstract this paper presents a novel reduced basis method for analyzing problems of linear elasticity in a systematical rapid and reliable fashion for solutions with both upper and lower bounds to the exact solution in the form of energy norm or compliance output the lower bound of the solution output is obtained form the well known reduced basis method based on the galerkin projection used in the finite element method which is termed as gp rbm for the upper bound a new reduced basis approach is developed by the combination of the reduced basis method and a smoothed galerkin projection used in the linearly conforming point interpolation method and it is thus termed as sgp rbm to examine the present sgp rbm we first conduct a theoretical study on the very important upper bound property reduced basis models for both gp rbm and sgp rbm are constructed with the aid of an asymptotic error estimation and greedy adaptive procedure the gp rbm and the newly proposed sgp rbm are applied to analyze a cantilever beam with an oblique crack to verify the proposed rbm technique in terms of accuracy convergence bound properties and computational savings both theoretical analysis and numerical results have demonstrated that the present method is a very efficient method for real time solutions providing exact output bounds

second order accurate derivatives and integration schemes for meshfree methods summary the consistency condition for the nodal derivatives in traditional meshfree galerkin methods is only the differentiation of the approximation consistency dac one missing part is the consistency between a nodal shape function and its derivatives in terms of the divergence theorem in numerical forms in this paper a consistency framework for the meshfree nodal derivatives including the dac and the discrete divergence consistency ddc is proposed the summation of the linear ddc over the whole computational domain leads to the so called integration constraint in the literature a three point integration scheme using background triangle elements is developed in which the corrected derivatives are computed by the satisfaction of the quadratic ddc we prove that such smoothed derivatives also meet the quadratic dac and therefore the proposed scheme possesses the quadratic consistency that leads to its name qc3 numerical results show that qc3 is the only method that can pass both the linear and the quadratic patch tests and achieves the best performances for all the four examples in terms of stability convergence accuracy and efficiency among all the tested methods particularly it shows a huge improvement for the existing linearly consistent one point integration method in some examples copyright 2012 john wiley sons ltd

a note on nonnegative rank factorizations abstract a nonnegative weakly monotone matrix of rank r has a nonnegative rank factorization if and only if it possesses an r x r monomial submatrix

meshless method for shallow water equations with free surface flow solving problems with free surface often encounters numerical difficulties related to excessive mesh distortion as is the case of dambreak or breaking waves in this paper the natural element method nem is used to simulate a 2d shallow water flows in the presence of theses strong gradients this particle based method used a fully lagrangian formulation based on the notion of natural neighbors in the present study we consider the full non linear set of shallow water equations with a transient flow under the coriolis effect for the numerical treatment of the nonlinear terms we used a lagrangian technique based on the method of characteristics this will allow avoiding divergence of newton raphson scheme when dealing with the convective terms we also define a thin area close to the boundaries and a computational domain dedicated for nodal enrichment at each time step two numerical test cases were performed to verify the well founded hopes for the future of this method in real applications

low dimensional polytope approximation and its applications to nonnegative matrix factorization in this study nonnegative matrix factorization is recast as the problem of approximating a polytope on the probability simplex by another polytope with fewer facets working on the probability simplex has the advantage that data are limited to a compact set with a known boundary making it easier to trace the approximation procedure in particular the supporting hyperplane that separates a point from a disjoint polytope a fact asserted by the hahn banach theorem can be calculated in finitely many steps this approach leads to a convenient way of computing the proximity map which in contrast to most existing algorithms where only an approximate map is used finds the unique and global minimum per iteration this paper sets up a theoretical framework outlines a numerical algorithm and suggests an effective implementation testing results strongly evidence that this approach obtains a better low rank nonnegative matrix approximation in fewer steps than conventional methods

a sub domain smoothed galerkin method for solid mechanics problems summary a sub domain smoothed galerkin method is proposed to integrate the advantages of mesh free galerkin method and fem arbitrarily shaped sub domains are predefined in problems domain with mesh free nodes in each sub domain based on mesh free galerkin weak formulation the local discrete equation can be obtained by using the moving kriging interpolation which is similar to the discretization of the high order finite elements strain smoothing technique is subsequently applied to the nodal integration of sub domain by dividing the sub domain into several smoothing cells moreover condensation of dof can also be introduced into the local discrete equations to improve the computational efficiency the global governing equations of present method are obtained on the basis of the scheme of fem by assembling all local discrete equations of the sub domains the mesh free properties of galerkin method are retained in each sub domain several 2d elastic problems have been solved on the basis of this newly proposed method to validate its computational performance these numerical examples proved that the newly proposed sub domain smoothed galerkin method is a robust technique to solve solid mechanics problems based on its characteristics of high computational efficiency good accuracy and convergence copyright 2014 john wiley sons ltd

nodal integration of the element free galerkin method abstract spatial integration of the element free galerkin efg method is achieved by evaluating the integrals of the weak form only at the nodes in previous efg formulations a grid of cells was used to perform gaussian quadrature over the domain the absence of a cell structure for nodal integration results in a completely meshless method similar in simplicity to particle methods such as smooth particle hydrodynamics sph it is shown that nodal integration like sph suffers from spurious singular modes this spatial instability results from underintegration of the weak form and it is treated by the addition to the potential energy functional of a stabilization term which contains the square of the residual of the equilibrium equation example problems illustrate the effect of the stabilization and provide the basis for convergence studies

inverse m matrices abstract this is an attempt at a comprehensive expository study of those nonnegative matrices which happen to be inverses of m matrices and is aimed at an audience conversant with basic ideas of matrix theory a theme is the parallels anddifferences between the class of m matrices and the class of inverse m matrices among the primary tools used are diagonal multiplications the neumann expansion and the form of the inverse of a partitioned matrix some of the results seem not to have appeared before and several unsolved problems are mentioned

mls moving least square based finite elements for three dimensional nonmatching meshes and adaptive mesh refinement abstract with the aid of moving least square mls approximation a new class of three dimensional finite elements are proposed for treating nonmatching meshes and adaptive mesh refinement for which the existing finite elements are hardly efficient with a special choice of the weight function supports and the base functions the method results in useful elements with the polynomial shape function for which the c 1 continuity breaks down on the boundaries between the neighboring subdomains comprising one element the effectiveness of the new elements in handling the discontinuities due to nonmatching interfaces and automatic mesh refinement is demonstrated via three dimensional examples

voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids voronoi cells and the notion of natural neighbours are used to develop a finite difference method for the diffusion operator on arbitrary unstructured grids natural neighbours are based on the voronoi diagram which partitions space into closest point regions the sibson and the laplace non sibsonian interpolants which are based on natural neighbours have shown promise within a galerkin framework for the solution of partial differential equations in this paper we focus on the laplace interpolant with a two fold objective first to unify the previous developments related to the laplace interpolant and to indicate its ties to some well known numerical methods and secondly to propose a voronoi cell finite difference scheme for the diffusion operator on arbitrary unstructured grids a conservation law in integral form is discretized on voronoi cells to derive a finite difference scheme for the diffusion operator on irregular grids the proposed scheme can also be viewed as a point collocation technique a detailed study on consistency is conducted and the satisfaction of the discrete maximum principle stability is established owing to symmetry of the laplace weight a symmetric positive definite stiffness matrix is realized which permits the use of efficient linear solvers on a regular rectangular or hexagonal grid the difference scheme reduces to the classical finite difference method numerical examples for the poisson equation with dirichlet boundary conditions are presented to demonstrate the accuracy and convergence of the finite difference scheme copyright 2003 john wiley sons ltd

natural neighbour galerkin methods summary natural neighbour co ordinates sibson co ordinates is a well known interpolation scheme for multivariate data tting and smoothing the numerical implementation of natural neighbour co ordinates in a galerkin method is known as the natural element method nem in the natural element method natural neighbour co ordinates are used to construct the trial and test functions recent studies on nem have shown that natural neighbour co ordinates which are based on the voronoi tessellation of a set of nodes are an appealing choice to construct meshless interpolants for the solution of partial dierential equations in belikov et al computational mathematics and mathematical physics 1997 37 1 9 15 a new interpolation scheme non sibsonian interpolation based on natural neighbours was proposed in the present paper the nonsibsonian interpolation scheme is reviewed and its performance in a galerkin method for the solution of elliptic partial dierential equations that arise in linear elasticity is studied a methodology to couple nite elements to nem is also described two signicant advantages of the non sibson interpolant over the sibson interpolant are revealed and numerically veried the computational eciency of the non sibson algorithm in 2 dimensions which is expected to carry over to 3 dimensions and the ability to exactly impose essential boundary conditions on the boundaries of convex and non convex domains copyright 2001 john wiley sons ltd

computation of limit and shakedown loads using a node based smoothed finite element method summary this paper presents a novel numerical procedure for computing limit and shakedown loads of structures using a node based smoothed fem in combination with a primal dual algorithm an associated primal dual form based on the von mises yield criterion is adopted the primal dual algorithm together with a newton like iteration are then used to solve this associated primal dual form to determine simultaneously both approximate upper and quasi lower bounds of the plastic collapse limit and the shakedown limit the present formulation uses only linear approximations and its implementation into finite element programs is quite simple several numerical examples are given to show the reliability accuracy and generality of the present formulation compared with other available methods copyright 2011 john wiley sons ltd

normalized smoothing functions for sph impact computations this paper presents a normalized smoothing function nsf algorithm that can improve the accuracy of smooth particle hydrodynamics sph impact computations it is presented specifically for axisymmetric geometry but the principles also apply to plane strain and three dimensional geometry the approach consists of adjusting the standard smoothing functions for every node and every cycle such that the normal strain rates are computed exactly for conditions of constant strain rates linear velocity distributions this in turn generally improves accuracy for non uniform strain rates this can significantly improve the accuracy for free boundaries for non uniform arrangements of sph nodes and for small smoothing distances a new smoothing function is also introduced the nsf algorithm is shown to provide improved accuracy for a series of cylinder impact examples that includes two different smoothing functions and two different smoothing distances

rational homotopy of the homotopy fixed point sets of circle actions in this paper when g is the circle s 1 and m is a g space we study the rational homotopy type of the fixed point set m g the homotopy fixed point set m hg and the natural injection m g m hg c 2009 elsevier inc all rights reserved

on the condition number anomaly of gaussian correlation matrices abstract spatial correlation matrices appear in a large variety of applications for example they are an essential component of spatial gaussian processes also known as spatial linear models or kriging estimators which are powerful and well established tools for a multitude of engineering applications such as the design and analysis of computer experiments geostatistical problems and meteorological tasks in radial basis function interpolation gaussian correlation matrices arise frequently as interpolation matrices from the gaussian radial kernel function in the field of data assimilation in numerical weather prediction such matrices arise as background error covariances over the past thirty years it was observed by several authors from several fields that the gaussian correlation model is exceptionally prone to suffer from ill conditioning but a quantitative theoretical explanation for this anomaly was lacking in this paper a proof for the special position of the gaussian correlation matrix is given the theoretical findings are illustrated by numerical experiment

smoothing and accelerated computations in the element free galerkin method two topics in the formulation and implementation of meshless methods are considered the smoothing of the approximating functions at concave boundaries and the speedup of the calculation of the approximating functions and their derivatives these techniques are described in the context of the element free galerkin method but they are applicable to other meshless methods results are presented for some elastostatic problems which show a moderate improvement in the accuracy of the smoothed interpolant the speedup in calculating the shape functions is about a factor of two

some applications of spectral theory of nonnegative matrices to input output models abstract we show the necessary and sufficient condition that a nonnegative matrix has a unique positive eigenvector where the analytic expression displaying the linear relations between each remnant component and a basic characteristic subvector of the unique eigenvector is discovered when the nonnegative matrix is reducible as a result we infer the exact necessary and sufficient condition that the iteration matrix m 1 n as a special nonnegative matrix has a unique positive eigenvector when m n is an m splitting which is applied to the condition for the existence and uniqueness of a balanced growth solution for the leontief dynamic input output model previous work in the field did not clearly involve the uniqueness of the balanced growth solution in this paper we develop the prior results that is we find the necessary and sufficient condition that the leontief dynamic input output model has a unique bal anced growth solution finally we obtain the necessary and sufficient condition for theexistence and uniqueness of both the balanced growth solution and the production prices system

upper and lower bounds for natural frequencies a property of the smoothed finite element methods node based smoothed finite element method ns fem using triangular type of elements has been found capable to produce upper bound solutions to the exact solutions for force driving static solid mechanics problems due to its monotonic soft behavior this paper aims to formulate an ns fem for lower bounds of the natural frequencies for free vibration problems to make the ns fem temporally stable an fem is devised by combining the compatible and smoothed strain fields in a partition of unity fashion controlled by 0 1 so that both the properties of stiff fem and the monotonically soft ns fem models can be properly combined for a desired purpose for temporally stabilizing ns fem is chosen small so that it acts like a regularization parameter making the ns fem stable but still with sufficient softness ensuring lower bounds for natural frequency solution our numerical studies demonstrate that 1 using a proper the spurious non zero energy modes can be removed and the ns fem becomes temporally stable 2 the stabilized ns fem becomes a general approach for solids to obtain lower bounds to the exact natural frequencies over the whole spectrum 3 fem can even be tuned for obtaining nearly exact natural frequencies

controllability and reachability criteria for discrete time positive systems discrete time positive systems have been the object of widespread interest in the literature in the last decade particular attention has been devoted to the analysis and characterization of the different notions of reachability and controllability which in this context make their appearance in this paper the properties of ordinary and essential controllability and reachability are analysed based on a graph theoretic approach we provide practical criteria to verify whether a given positive system f g is endowed with these properties together with canonical forms for describing reachable controllable pairs

positivity of discrete singular systems and their stability in this paper we present an efficient approach to the analysis of discrete positive singular systems one of our main objectives is to investigate the problem of characterizing positivity of such systems previously this issue was not completely addressed we provide easily checkable necessary and sufficient conditions for such problem to be solved on the other hand we study the stability of discrete positive singular systems note that this is not a trivial problem since the set of admissible initial conditions is not the whole space but it is represented by a special cone all the conditions we provide are necessary and sufficient and are based on a reliable computational approach via linear programming

quaternions further contributions to a matrix oriented approach abstract by representing quaternions as four dimensional vectors and the multiplication of quaternions as matrix by vector product we employ a matrix oriented approach to the topic we investigate properties of the fundamental real matrix associated with a quaternion and examine a frequently considered quaternion equation from which the n th power of a quaternion can be determined

real rank versus nonnegative rank abstract we consider the set of m n nonnegative real matrices and define the nonnegative rank of a matrix a to be the minimum k such that a bc where b is m k and c is k n given that the real rank of a is j for some j we give bounds on the nonnegative rank of a and a 2

on the existence of infinitely many invariant reeb orbits in this article we extend results of grove and tanaka bull am math soc 82 497 498 1976 acta math 140 33 48 1978 and tanaka j differ geom 17 171 184 1982 on the existence of isometry invariant geodesics to the setting of reeb flows and strict contactomorphisms specifically we prove that if m is a closed connected manifold with the property that the betti numbers of the free loop space lambda m are asymptotically unbounded then for every fibrewise star shaped hypersurface sigma subset t m and every strict contactomorphism varphi sigma rightarrow sigma which is contact isotopic to the identity there are infinitely many invariant reeb orbits

on the nonnegative rank of euclidean distance matrices abstract the euclidean distance matrix for n distinct points in r r is generically of rank r 2 it is shown in this paper via a geometric argument that its nonnegative rank for the case r 1 is generically n