evaluation of the integral terms in reproducing kernel methods reproducing kernel method rkm has its origins in wavelets and it is based on convolution theory being their continuous version rkm is often referred as the general framework for meshless methods in fact since in real computation discretization is inevitable these integrals need to be evaluated numerically leading to the creation of reproducing kernel particle method rkpm and moving least squares mls approximation nevertheless in this paper the integrals in rkm are explicitly evaluated for polynomials basis function and simple geometries in one two and three dimensions even with conforming holes moreover a general formula is provided for complicated shapes also for multiple connected domains this is possible through a boundary formulation where domain integrals involved in rkm are transformed by gauss theorem in circular or flux integrals parallelization is readily enabled since no preliminary arrangements of nodes is needed for the moments matrix furthermore using symbolic inversion computation of shape functions in rkm is considerably speeded up

recent trends in ale formulation and its applications in solid mechanics this paper presents a complete derivation and implementation of the arbitrary lagrangian eulerian ale formulation for the simulation of nonlinear static and dynamic problems in solid mechanics the ale equations are presented using a fully coupled implicit approach full expression for the ale virtual work equations and finite element matrices are given the matrix equations are presented in a level of details that facilitates straightforward implementation time integration relations for the dynamic equations are also derived special techniques are presented to adapt the formulation for simulating crack propagation problems several applications in the areas of metal forming metal cutting and crack propagation are solved and presented

kalman filtering in triplet markov chains let x xn nisinin be a hidden process y yn nisinin an observed process and r rn nisinin some additional process we assume that t x r y is a so called triplet vector markov chain tmc we first show that the linear tmc model encompasses and generalizes among other models the classical state space systems with colored process and or measurement noise s we next propose restoration kalman like filters for arbitrary linear gaussian lg tmc

bifurcation and multiple solutions for perturbations of linear elliptic problems abstract combining a bifurcation theorem with a local leray schauder degree theorem of krasnoselskii and zabreiko in the case of a simple singular point we obtain an existence result on the number of small solutions for a class of functional bifurcation equations since this result contains the information of local leray schauder degree we obtain new multiplicity results for the perturbations of second order linear elliptic problems by unbounded nonlinearities as applications here by a priori bounds essentially due to gupta and by a leray schauder degree computation

fracture mechanics analysis using the wavelet galerkin method and extended finite element method summary this paper presents fracture mechanics analysis using the wavelet galerkin method and extended finite element method the wavelet galerkin method is a new methodology to solve partial differential equations where scaling wavelet functions are used as basis functions in solid structural analyses the analysis domain is divided into equally spaced structured cells and scaling functions are periodically placed throughout the domain to improve accuracy wavelet functions are superposed on the scaling functions within a region having a high stress concentration such as near a hole or notch thus the method can be considered a refinement technique in fixed grid approaches however because the basis functions are assumed to be continuous in applications of the wavelet galerkin method there are difficulties in treating displacement discontinuities across the crack surface in the present research we introduce enrichment functions in the wavelet galerkin formulation to take into account the discontinuous displacements and high stress concentration around the crack tip by applying the concept of the extended finite element method this paper presents the mathematical formulation and numerical implementation of the proposed technique as numerical examples stress intensity factor evaluations and crack propagation analyses for two dimensional cracks are presented copyright 2012 john wiley sons ltd

a constrained two dimensional triangulation and the solution of closest node problems in the presence of barriers a delaunay triangulation of a set of nodes is a collection of triangles whose vertices are at the nodes and whose union fills the convex hull of the set of nodes it also has several geometrical properties making it useful for solving closest point problems the generalization presented here allows the triangulation to cover nonconvex regions including those with holes although a variety of such generalizations are possible the one presented here is shown to retain important closest point characteristics thus it is useful for determining shortest paths within planar regions with polygonal boundaries

a unified approach to the mathematical analysis of generalized rkpm gradient rkpm and gmls abstract it is well known that the conventional reproducing kernel particle method rkpm is unfavorable when dealing with the derivative type essential boundary conditions 1 2 3 to remedy this issue a group of meshless methods in which the derivatives of a function can be incorporated in the formulation of the corresponding interpolation operator will be discussed formulation of generalized moving least squares gmls on a domain and gmls on a finite set of points will be presented the generalized rkpm will be introduced as the discretized form of gmls on a domain another method that helps to deal with derivative type essential boundary conditions is the gradient rkpm which incorporates the first gradients of the function in the reproducing equation in present work the formulation of gradient rkpm will be derived in a more general framework some important properties of the shape functions for the group of methods under consideration are discussed moreover error estimates for the corresponding interpolants are derived by generalizing the concept of corrected collocation method it will be seen that in the case of employing each of the proposed methods to a bvp not only the essential boundary conditions involving the function but also the essential boundary conditions which involve the derivatives could be satisfied exactly at particles which are located on the boundary

high order central difference scheme for caputo fractional derivative abstract in this paper we propose a class of central difference schemes for resolving the caputo fractional derivative the accuracy may reach any selected integer order more precisely the caputo fractional derivative operator is decomposed into symmetric and antisymmetric components starting from difference schemes of lower order accuracy for each component we enhance the accuracy by a weighted average of shifted differences the weights are calculated by matching the symbols of the scheme and the operators we further illustrate the application of the proposed schemes to a fractional advection diffusion equation together with the crank nicolson algorithm it reaches designed accuracy order and is unconditionally stable numerical tests are presented to demonstrate the nice features

on a new notion of linking and application to elliptic problems at resonance abstract in this paper we introduce a new notion of linking which includes in particular the notions of homotopical linking and local linking critical point theorems for continuous functionals on metric spaces are presented finally an application to nonlinear elliptic problems at resonance is given

a viterbi smoother for discrete state space model in this paper we introduce a method for estimating the parameters of a hidden markov model in a discrete time framework based on new extensions of the viterbi algorithm we consider a model in which both the hidden states and observations take values in a finite state space recursive estimates are obtained using measure change methods

control of discrete time hmm partially observed under fractional gaussian noises a discrete time control problem of a finite state hidden markov chain partially observed in a fractional gaussian process is discussed using filtering the control problem is then recast as a separated problem with information variables given by the unnormalized conditional probabilities of the whole path of the hidden markov chain a dynamic programming result and a minimum principle are obtained

moving least square reproducing kernel method part ii fourier analysis in part i of this work the moving least square reproducing kernel mlsrk method is formulated and implemented based on its generic construction an m consistency structure is discovered and the convergence theorems are established in this part of the work a systematic fourier analysis is employed to evaluate and further establish the method the preliminary fourier analysis reveals that the mlsrk method is stable for sufficiently dense non degenerated particle distribution in the sense that the kernel function family satisfies the riesz bound one of the novelties of the current approach is to treat the mlsrk method as a variant of the standard finite element method and depart from there to make a connection with the multiresolution approximation in the spirits of multiresolution analysis we propose the following mlsrk transformation fm k hu i 1npu k ik h x xi x w1 the highlight of this paper is to embrace the mlsrk formulation with the notion of the controlled fp approximation based on its characterization the strang fix condition for example a systematic procedure is proposed to design new window functions so they can enhance the computational performance of the mlsrk algorithm the main effort here is to obtain a constant correction function in the interior region of a general domain i e c h 1 this can create a leap in the approximation order of the mlsrk algorithm significantly if a highly smooth window function is embedded within the kernel one consequence of this development is the synchronized convergence phenomenon a unique convergence mechanism for the mlsrk method i e by properly tuning the dilation parameter the convergence rate of higher order error norms will approach the same order convergence rate of the l2 error norm they are synchronized

nonselfadjoint resonance problems with unbounded perturbations soit un domaine borne de r n n 1 a frontiere de classe c 2 pour 0 1 soit lu i 1 n j 1 n a idj x 2 u x i x j i 1 n b i x u x i a 0 x u ou a ij x a ji x 1 i j n a 0 x 0 sur et i 1 n j 1 n a ij x i j 0 pour x et r n 0 on considere le probleme lu 1 u g u h u 0 ou 1 est la valeur propre principale de l h c et g est localement lipschitzien sur

reproducing kernel element method part iv globally compatible cn n 1 triangular hierarchy in this part of the work a globally compatible c n x triangular element hierarchy is constructed in the framework of reproducing kernel element method rkem for arbitrary two dimensional domains in principle the smoothness of the globally conforming element can be made arbitrarily high np 1 the triangle interpolation field can interpolate the derivatives of an unknown function up to arbitrary mth order i m and it can reproduce complete kth order polynomials with k p m this is the first interpolation hierarchical structure that has ever been constructed with both minimal degrees of freedom and higher order smoothness and continuity over discretizations of a multiple dimensional domain the performance of the newly constructed compatible element is evaluated in solving several kirchhoff plate problems

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

constrained boundary recovery for three dimensional delaunay triangulations summary a new constrained boundary recovery method for three dimensional delaunay triangulations is presented it successfully resolves the difficulties related to the minimal addition of steiner points and their good placement applications to full mesh generation are discussed and numerical examples are provided to illustrate the effectiveness of guaranteed recovery procedure copyright 2004 john wiley sons ltd

element free galerkin approach based on the reproducing kernel particle method for solving 2d fractional tricomi type equation with robin boundary condition the traditional element free galerkin efg approach is constructed on variational weak form that the test and trial functions are shape functions of moving least squares mls approximation in the current paper we propose a new version of the efg method based on the shape functions of reproducing kernel particle method rkpm in other words based on the developed approach in han and meng 2001 the fractional tricomi type equation will be solved using the new technique the fractional derivative has been introduced in the caputos sense and is approximated by a finite difference plan of order o 3 1 2 we use the efg rkpm to discrete the spatial direction we illustrate some numerical results on non rectangular domains the unconditional stability and convergence of the new technique have been proved numerical examples display the theoretical results and the efficiency of the proposed approach also the numerical results are compared with the finite element method fem and efg mls procedure

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

kalman type filter under stationary noises abstract in this paper we are interested in finding an explicit solution to the filtering problem for a d dimensional autoregressive signal observed through a linear channel when the noises are stationary gaussian with the same covariance we represent the signal observation pair in terms of a 2 d dimensional autoregressive process driven by a white gaussian noise simulations are given for fractional gaussian noises fgn autoregressive noises ar 1 and moving average noises ma in order to analyze the performance of the filtering algorithm compared to other approaches in the literature

an iterative kalman like algorithm ignoring noise and initial conditions we address a p shift finite impulse response fir unbiased estimator ue for linear discrete time varying filtering p 0 p step prediction p 0 and p lag smoothing p 0 in state space with no requirements for initial conditions and zero mean noise a solution is found in a batch form and represented in a computationally efficient iterative kalman like one it is shown that the kalman like fir ue is able to outperform the kalman filter if the noise covariances and initial conditions are not known exactly noise is not white and both the system and measurement noise components need to be filtered out otherwise the errors are similar extensive numerical studies of the fir ue are provided in gaussian and non gaussian environments with outliers and temporary uncertainties

asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic navier equation abstract in this work we study reproducing kernel rk collocation method for peridynamic navier equation in the first part we apply a linear rk approximation to both displacement and dilatation and then back substitute dilatation and solve the peridynamic navier equation in a pure displacement form the rk collocation scheme converges to the nonlocal limit for a fixed nonlocal interaction length and also to the local limit as nonlocal interactions vanish the stability is shown by comparing the collocation scheme with the standard galerkin scheme using fourier analysis in the second part we apply the rk collocation to the quasi discrete peridynamic navier equation and show its convergence to the correct local limit when the ratio between the nonlocal length scale and the discretization parameter is fixed the analysis is carried out on a special family of rectilinear cartesian grids for the rk collocation method with a designated kernel with finite support we assume the lame parameters satisfy to avoid extra assumptions on the nonlocal kernel finally numerical experiments are conducted to validate the theoretical results

fast kalman like filtering for large dimensional linear and gaussian state space models this article considers the filtering problem for linear and gaussian state space models with large dimensions a setup in which the optimal kalman filter kf might not be applicable owing to the excessive cost of manipulating huge covariance matrices among the most popular alternatives that enable cheaper and reasonable computation is the ensemble kf enkf a monte carlo based approximation in this article we consider a class of a posteriori distributions with diagonal covariance matrices and propose fast approximate deterministic based algorithms based on the variational bayesian vb approach more specifically we derive two iterative kf like algorithms that differ in the way they operate between two successive filtering estimates one involves a smoothing estimate and the other involves a prediction estimate despite its iterative nature the prediction based algorithm provides a computational cost that is on the one hand independent of the number of iterations in the limit of very large state dimensions and on the other hand always much smaller than the cost of the enkf the cost of the smoothing based algorithm depends on the number of iterations that may in some situations make this algorithm slower than the enkf the performances of the proposed filters are studied and compared to those of the kf and enkf through a numerical example

maximum principle and convergence analysis for the meshfree point collocation method the discrete laplacian operator is considered in the sense of the meshfree point collocation method which will be called the strong meshfree laplacian operator to define the strong meshfree laplacian operator we use the fast version of the generalized moving least square approximation which can calculate the approximated derivatives of shape functions some types of the locally layered node distribution are defined in this paper and two specific domains are constructed onto which we can distribute locally layered nodes at such nodes the discrete maximum principle can be shown to hold through the representation formula for the strong meshfree laplacian operator the discrete maximum principle together with the reproducing property of the meshfree approximations results in an a priori estimate for the strong meshfree laplacian operator in the nodal solution space furthermore the a priori estimate we have obtained guarantees the existence and the uniqueness of the numerical solution and plays a central role in achieving converged results for the poisson problem with dirichlet boundary conditions in the nodal solution space the order of convergence of the nodal solutions can be raised up to o h2 at the proposed type of nodes in specific domains for generally shaped domains immersed in the previously mentioned domains we can obtain the first order convergence result of o h

on the numerical implementation of variational arbitrary lagrangian eulerian vale formulations this paper is concerned with the implementation of variational arbitrary lagrangian eulerian formulations also known as variational r adaption methods these methods seek to minimize the energy function with respect to the finite element mesh over the reference configuration of the body we propose a solution strategy based on a viscous regularization of the configurational forces this procedure eliminates the ill posedness of the problem without changing its solutions i e the minimizers of the regularized problems are also minimizers of the original functional we also develop strategies for optimizing the triangulation or mesh connectivity and for allowing nodes to migrate in and out of the boundary of the domain selected numerical examples demonstrate the robustness of the solution procedures and their ability to produce highly anisotropic mesh refinement in regions of high energy density

reproducing kernel triangular b spline based fem for solving pdes abstract we propose a reproducing kernel triangular b spline based finite element method fem as an improvement to the conventional triangular b spline element for solving partial differential equations pdes in the latter unexpected errors can occur throughout the analysis domain mainly due to the excessive flexibilities in defining the b spline the performance therefore becomes unstable and cannot be controlled in a desirable way to address this issue the proposed improvement adopts the reproducing kernel approximation in the calculation of b spline kernel function three types of pde problems are tested to validate the present element and compare against the conventional triangular b spline it has been shown that the improved triangular b spline satisfies the partition of unity condition even for extreme conditions including corners and holes

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

on solvability for a class of quasilinear resonance elliptic equations abstract in this paper we obtain an existence result for a class of high order quasilinear elliptic equations with higher eigenvalues the proofs rely on galerkin type techniques brouwer s fixed points theorem in this case the nonlinearity is unbounded and satisfies sublinear growth the equation is one of the most useful sets of navier stokes equations which describe the motion of viscous fluid substances such as liquids gases and so on

signal and image segmentation using pairwise markov chains the aim of this paper is to apply the recent pairwise markov chain model which generalizes the hidden markov chain one to the unsupervised restoration of hidden data the main novelty is an original parameter estimation method that is valid in a general setting where the form of the possibly correlated noise is not known several experimental results are presented in both gaussian and generalized mixture contexts they show the advantages of the pairwise markov chain model with respect to the classical hidden markov chain one for supervised and unsupervised restorations

reproducing kernel element method part i theoretical formulation in this paper and its sequels we introduce and analyze a new class of methods collectively called the reproducing kernel element method rkem the central idea in the development of the new method is to combine the strengths of both finite element methods fem and meshfree methods two distinguished features of rkem are the arbitrarily high order smoothness and the interpolation property of the shape functions these properties are desirable especially in solving galerkin weak forms of higher order partial differential equations and in treating dirichlet boundary conditions so unlike the fem there is no need for special treatment with the rkem in solving high order equations compared to meshfree methods dirichlet boundary conditions do not present any difficulty in using the rkem a rigorous error analysis and convergence study of the method are presented the performance of the method is illustrated and assessed through some numerical examples

a high order finite volume method with improved isotherms reconstruction for the computation of multiphase flows using the navier stokes korteweg equations abstract in this work we solve the navier stokes korteweg nsk equations to simulate a two phase fluid with phase change we use these equations on a diffuse interface approach where the properties of the fluid vary continuously across the interface that separates the different phases the model is able to describe the behavior of both phases with the same set of equations and it is also able to handle problems with great changes in the topology of the problem however high order derivatives are present in nsk equations which is a difficulty for the design of a numerical method to solve the problem here we propose the use of a high order finite volume method with moving least squares approximations to handle high order derivatives and solve the nsk equations moreover a new methodology to obtain accurate equations of state is presented in this method we use any accurate equation of state for the pure phases under the saturation curve a b spline reconstruction fulfilling a given set of thermodynamic criteria is performed the new eos can be used for computations using diffuse interface modeling several numerical examples to show the accuracy of the new approach are presented

translates of multivarlate splines abstract we study spaces generated by translations of a fixed function over lattice points we provide some new algebraic and approximation properties for these spaces which show their applicability for finite element analysis

dealing with extremely large deformation by nearest nodes fem with algorithm for updating element connectivity in the recently developed nearest nodes finite element method nn fem elements are mainly used for numerical integration while shape functions are constructed in a similar way as in meshless methods based on this strategy nn fem inherits major merits from both the classical finite element method and meshless methods one of them is that nn fem is nearly not affected by element distortion so nn fem is more efficient than the classical fem on dealing with large deformation problems nevertheless nn fem still has a requirement on finite element meshes that is elements in a mesh are required not to overlap or penetrate to each other to avoid difficulty in numerical integration to eliminate overlapped elements nn fem is supplemented with an algorithm for updating element connectivity with this supplement nn fem is able to deal with extremely large deformation in updating element connectivity element nodes are kept not changed and all information associated with nodes are not touched therefore there is no need to transfer solution data and error introduced by solution transfer is avoided

approximation of parametric curves by moving least squares method in this work we propose a method to approximate a parametric curve in r d some distinct points in r d are given we assume that these points belong to a parametric curve and our aim is to approximate these data by moving least squares method we mention several applications of the proposed method to emphasize the importance of the work also root mean squares errors and hausdorff distances between the exact curve and its approximation are presented to demonstrate the efficiency and reliability of the method

a generalized moving least square reproducing kernel method a generalization of moving least square reproducing kernel method is presented in this work the moving least square reproducing kernel method is obtained by using a moving least square scheme but not in the discrete version the resulted scheme provides a continuous basis which is able to reproduce any m th order polynomial and prepares a scheme that can approximate smooth functions with an optimal accuracy on the other hand considering the power of moving least square scheme in meshless approximation for the numerical solution of partial differential equations the generalized moving least square approximation is able to approximate l u just in terms of node values where l is an arbitrary linear operator in this paper a generalization of moving least square reproducing kernel method is presented which employs the generalized version of moving least square method the method approximates a test functional based on the values of nodes the convergence rate of the method is measured in terms of dilation parameter of window function the method is simpler and faster to implement than the classical ones where it does not use the shape function numerical tests are presented to confirm the theoretical results the numerical results establish the efficiency of the proposed method

a filter for a hidden markov chain observed in fractional gaussian noise abstract estimates of parameters and hidden states in a hidden markov model where the noise in the observations is fractional gaussian noise are obtained

super convergence of reproducing kernel approximation abstract the reproducing kernel particle methods rkpm are meshfree methods arising in mechanics especially in dealing with problems involving large deformation and singularities we provide a theoretical analysis of super convergence in sobolev norms for reproducing kernel rk approximations when the interpolation order p is even super convergence phenomenon means the convergence rate is higher than the order that is generally expected we distinguish the continuous rk approximation and the discrete rkp approximation while the continuous rk approximations are proven to be super convergent when p is even its discrete counterpart has super convergence only with uniform particle distribution and special choices of rk kernel functions and support sizes moreover super convergence does not exist for the discrete rkp approximation with general rk support sizes the concept of pseudo super convergence is then introduced to explain why in practice the super convergence phenomenon is sometimes observed for general cases although in theory it is not true our analysis is general for multi dimensional rk approximations

moving particle finite element method with global smoothness we describe a new version of the moving particle finite element method mpfem that provides solutions within a c 0 finite element framework the finite elements determine the weighting for the moving partition of unity a concept of general shape function is proposed which extends regular finite element shape functions to a larger domain these are combined with shepard functions to obtain a smooth approximation the moving particle finite element method combines desirable features of finite element and meshfree methods the proposed approach in fact can be interpreted as a moving partition of unity finite element method or moving kernel finite element method this method possesses the robustness and efficiency of the c 0 finite element method while providing at least c 1 continuity

error analysis of the reproducing kernel particle method interest in meshfree or meshless methods has grown rapidly in recent years in solving boundary value problems bvps arising in mechanics especially in dealing with difficult problems involving large deformation moving discontinuities etc in this paper we provide a theoretical analysis of the reproducing kernel particle method rkpm which belongs to the family of meshfree methods one goal of the paper is to set up a framework for error estimates of rkpm we introduce the concept of a regular family of particle distributions and derive optimal order error estimates for rkp interpolants on a regular family of particle distributions the interpolation error estimates can be used to yield error estimates for rkp solutions of bvps

results of von neumann analyses for reproducing kernel semi discretizations the reproducing kernel particle method rkpm has many attractive properties that make it ideal for treating a broad class of physical problems rkpm may be implemented in a mesh full or a mesh free manner and provides the ability to tune the method via the selection of a window function and its associated dilation parameter in order to achieve the requisite numerical performance rkpm also provides a framework for performing hierarchical computations making it an ideal candidate for simulating multi scale problems although the method has many appealing attributes it is quite new and its numerical performance is still being quantified with respect to more traditional discretization techniques in order to assess the numerical performance of rkpm detailed studies of the method on a series of model partial differential equations has been undertaken the results of von neumann analyses for rkpm semi discretizations of one and two dimensional first and second order wave equations are presented in the form of phase and group errors excellent dispersion characteristics are found for the consistent mass matrix with the proper choice of dilation parameter in contrast row sum lumping the mass matrix is demonstrated to introduce severe lagging phase errors a higher order mass matrix improves the dispersion characteristics relative to the lumped mass matrix but also yields significant lagging phase errors relative to the fully integrated consistent mass matrix published in 2000 by john wiley sons ltd

a new implementation of the element free galerkin method abstract element free galerkin methods efg are methods for solving partial differential equations with moving least squares interpolants efg methods require only nodal data no element connectivity is needed in a previous implementation of the efg method lagrange multipliers were used to enforce the essential boundary condition however the use of lagrange multipliers increases the cost of solving the linear algebraic equations a new implementation is developed based on a modified variational principle in which the lagrange multipliers are replaced at the outset by their physical meaning so that the discrete equations are banded in addition weighted orthogonal basis functions are constructed so the need for solving equations at each quadrature point is eliminated numerical examples show that the present implementation effectively computes stress concentrations and stress intensity factors at cracks with very irregular arrangements of nodes the latter makes it very advantageous for modelling progressive cracking

convergence estimates for the wavelet galerkin method this paper presents an analysis of the galerkin approximation of a time dependent initial value problem correctly posed in the petrovskii sense the approximating spaces mathcal v h are spanned by translations and dilations of a single function phi and fourier techniques are used to analyze the accuracy of the method this kind of procedure has already been applied in the literature for spline approximations our purpose here is to point out that the same methodology can be used for wavelet based methods since the hypotheses required are automatically satisfied in the context of wavelet analysis for instance the basic function phi is supposed to be regular which means that phi and all its derivatives up to a certain order should have fast decay at infinity phi also must satisfy the so called strang and fix condition which guarantees that smooth functions can be approximated from mathcal v h with good accuracy this class of functions includes not only the b splines but al

arbitrary lagrangian eulerian finite element analysis of large deformation in contacting bodies the primary aim of this research is to implement the arbitrary lagrangian eulerian finite element description to model large deformation of interacting bodies a pure lagrangian description is often incapable of representing their contact with sufficient precision in this work the arbitrary lagrangian eulerian ale description has been extended to the surface nodes of interacting bodies to overcome these limitations a penalty formulation has been implemented to account for the impenetrability constraint the materials have been characterized as elastic viscoplastic implicit integration schemes have been used at the global and constitutive levels for improved stability

robust blind pairwise kalman algorithms using qr decompositions the pairwise kalman filter pkf w pieczynski and f desbouvries kalman filtering using pairwise gaussian models in proc int conf acoust speech signal process icassp hong kong apr 2003 is an extension of the classical kalman filter that keeps propagation equations explicit i e it does not require time consuming simulations the contribution of this note is twofold first new robust equations for filtering smoothing and unsupervised off lined parameters estimation based on qr decompositions are presented second since the model is over parametrized we give a simple condition to uniquely characterize a filter of interest when the dimension of observations is equal to the dimension of states unsupervised experiments based on simulated data confirm the nice behavior of the robust pkf even for a limited number of observations

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

arbitrary lagrangian eulerian formulation for element free galerkin method abstract arbitrary lagrangian eulerian ale formulation of the element free galerkin efg method is presented efg is a meshless method for solving partial differentia equations in which the trial and test functions employed in the discretization process result from moving least square interpolants the most significant advantage of the method is that it requires only nodes and a description of internal and external boundaries and interfaces such as cracks of the model no element connectivity is needed however as for any discretization method acceptable solutions can only be obtained for a sufficiently refined discretization in dynamic fracture problems where the crack path can be arbitrary and is thus a priori unknown this necessitates a refined discretization in large parts of the computational domain which can lead to prohibitive computation costs ale formulation allows to continuously relocate nodes on the computational domain by combining efg with ale it is thus possible in a crack propagation problem to refine locally the spatial discretization in the neighborhood of a propagating crack tip results are presented for a wave propagation problem as well as for 2 d dynamic crack propagation problems

a galerkin boundary node method and its convergence analysis the boundary node method bnm exploits the dimensionality of the boundary integral equation bie and the meshless attribute of the moving least square mls approximations however since mls shape functions lack the property of a delta function it is difficult to exactly satisfy boundary conditions in bnm besides the system matrices of bnm are non symmetric a galerkin boundary node method gbnm is proposed in this paper for solving boundary value problems in this approach an equivalent variational form of a bie is used for representing the governing equation and the trial and test functions of the variational formulation are generated by the mls approximation as a result boundary conditions can be implemented accurately and the system matrices are symmetric total details of numerical implementation and error analysis are given for a general bie taking the dirichlet problem of laplace equation as an example we set up a framework for error estimates of gbnm some numerical examples are also given to demonstrate the efficacity of the method

resonance and nonresonance in terms of average values abstract we prove existence results for nonlinear two point boundary value problems what sets our results apart is that we impose sufficient conditions for solvability in terms of the asymptotic average values of the nonlinearities our solvability conditions allow the nonlinear term to have significant oscillations outside the given spectral gap as long as it remains within the interval on the average in some sense

exact adaptive filters for markov chains observed in gaussian noise abstract a discrete time finite state markov chain is observed through a real or vector valued function whose values are corrupted by gaussian noise by introducing a new measure exact unnormalized recursive estimates and smoothers are obtained for the state of the markov chain for the number of jumps from one state to another for the occupation time in any state and for processes related to the observation parameters using the em algorithm these allow estimates of all the parameters of the model to be revised including the variance of the gaussian noise in the observations the filters are therefore adaptive or self tuning

implementation of boundary conditions for meshless methods abstract boundaries and boundary conditions are an aspect of the numerical solution of partial differential equations where meshless methods have had to surmount many initial difficulties due to the lack of a finite element like kronecker delta condition furthermore it is frequently desirable especially in fluid mechanics to impose general nonlinear boundary and interface constraints this paper describes a computationally efficient algorithm based on d alembert s principle that can be used for general constraints both in meshless methods and finite elements first a method of partitioning meshless shape functions suitable for imposing linear boundary conditions is developed subsequently an analogous method is developed for nonlinear constraints special attention is given to imposing general boundary and fluid structure interface conditions on the navier stokes equations in terms of conservative variables numerical results using d alembert s principle with the reproducing kernel particle method rkpm including viscous supersonic flow past a naca 7012 airfoil are shown

a meshless local petrov galerkin method for the time dependent maxwell equations abstract in this paper the meshless local petrov galerkin mlpg method is employed to solve the 2 d time dependent maxwell equations the mlpg method is a truly meshless method in which the trial and test functions are chosen from totally different functional spaces in the current work the moving least square reproducing kernel mlsrk scheme is chosen to be the trial function the method is applied for the unsteady maxwell equations in different media in the local weak form by employing the difference operator for evolution in time and simultaneously in time and space the semi discrete and fully discrete schemes are obtained respectively the error estimation is discussed for both the semi discrete and fully discrete numerical schemes for modelling the time dependent maxwell equations we show that provided that the time step size is sufficiently small the proposed scheme yields an error of o 2 m 1 2 in the l 2 norm for the square of error the new scheme is implemented and the numerical results are provided to justify our theoretical analysis

painless nonorthogonal expansions in a hilbert space h discrete families of vectors hj with the property that f j hj f hj for every f in h are considered this expansion formula is obviously true if the family is an orthonormal basis of h but also can hold in situations where the hj are not mutually orthogonal and are overcomplete the two classes of examples studied here are i appropriate sets of weyl heisenberg coherent states based on certain non gaussian fiducial vectors and ii analogous families of affine coherent states it is believed that such quasiorthogonal expansions will be a useful tool in many areas of theoretical physics and applied mathematics