schur recursions error formulas and convergence of rational estimators for stationary stochastic sequences an exact and approximate realization theory for estimation and model filters of second order stationary stochastic sequences is presented the properties of j lossless matrices as a unifying framework are used necessary and sufficient conditions for the exact realization of an estimation filter and a model filter as a submatrix of a j lossless system are deduced an extension of the so called schur algorithm yields an approximate j lossless realization based on partial past information about the process the geometric properties of such partial realizations and their convergence are studied finally connections with the nevanlinna pick problem are made and how the techniques presented constitute a generalization of many aspects of the levinson szego theory of partial realizations is shown as a consequence generalized recursive formulas for reproducing kernels and christoffel darboux formulas are obtained in this paper the scalar case is considered the matrix case will be considered in a separate publication

exact energy and momentum conserving algorithms for general models in nonlinear elasticity implicit time integration schemes that inherit the conservation laws of total energy linear and angular momentum are considered for initial boundary value problems in finite deformation elastodynamics conserving schemes are constructed for general hyperelastic material models both compressible and incompressible and are formulated in a way that is independent of spatial discretization three numerical examples for ogden type material models implemented using a finite element discretization in space are given to illustrate the performance of the proposed schemes these examples show that relative to the standard implicit mid point rule the conserving schemes exhibit superior numerical stability properties without a compromise in accuracy

enhancement of stability and accuracy of the moving particle semi implicit method as a lagrangian gridless particle method the mps moving particle semi implicit method has been proven useful in a wide range of engineering applications up to now most of mps applications have been limited to problems with compressive stress states this paper investigates the performance and stability of mps method in simulation of more general hydrodynamic problems including those characterized by tensile stresses or by changes in the stress states it is shown that mps based simulations are prone to become destabilized in presence of attractive interparticle forces this instability appears to be similar to the so called tensile instability in sph method two new modifications namely a modified poisson pressure equation and a corrective matrix for pressure gradient model are proposed to resolve this shortcoming these two new modifications together with two previously proposed improvements are shown to stabilize and enhance the performance of mps method

generic formalism and discrete variational derivative method for the two dimensional vorticity equation the vorticity equation for two dimensional incompressible viscous flows is formulated within the generic formalism for non equilibrium thermodynamics the laws of conservation of energy and increasing entropy derived from the generic formulation are properly inherited by the finite difference equations obtained by invoking the discrete variational derivative method the law of increasing entropy corresponds to the dissipation of enstrophy for the vorticity equation some numerical experiments have been done to examine the usefulness of the proposed method

numerical stability properties of a qr based fast least squares algorithm the numerical stability of a recent qr based fast least squares algorithm is established from a backward stability perspective a stability domain approach applicable to any least squares algorithm constructed from the set of reachable states in exact arithmetic is presented the error propagation question is shown to be subordinate to a backward consistency constraint which requires that the set of numerically reachable variables be contained within the stability domain associated to the algorithm this leads to a conceptually lucid approach to the numerical stability question which frees the analysis of stationary assumptions on the filtered sequences and obviates the tedious linearization methods of previous approaches moreover initialization phenomena and considerations related to poorly exciting inputs admit clear interpretations from this perspective the algorithm under study is proved in contrast to many fast algorithms to be minimal

bracket formulations and energy and helicity preserving numerical methods for the three dimensional vorticity equation abstract the vorticity equation for three dimensional viscous incompressible fluid flows is formulated within different bracket formalisms using the poisson or nambu bracket together with a dissipative bracket the budgets of kinetic energy helicity and enstrophy derived from the bracket formulations are properly inherited by the finite difference equations obtained by invoking the discrete variational derivative method combined with the mimetic finite difference method in particular energy and helicity are conserved precisely in inviscid flow computations the energy and enstrophy dissipate properly owing to viscosity in viscous flow computations and the enstrophy is appropriately produced by the vortex stretching effect in both inviscid and viscous flow computations the relationships between the stream function velocity and vorticity as well as the solenoidal conditions on the velocity and vorticity fields are also inherited numerical experiments on a periodic array of rolls that permits analytical solutions have been done to examine the properties and usefulness of the proposed method

lossless inverse scattering digital filters and estimation theory methods to construct rational solutions of the lossless inverse scattering lis problem for one port passive digital systems are described the first method is recursive and can be viewed as a generalization of the celebrated schur algorithm the second method is global and leads to a parametrization of what we call fundamental solutions from which all lis solutions may be constructed quite a few classical problems in estimation theory and network theory may be viewed as special cases of the lis problem with each fundamental solution there is a solution of a corresponding estimation problem leading to a prediction and a modeling filter for a given stochastic process

structured invariant spaces of vector valued rational functions hermitian matrices and a generalization of the lohvidov laws abstract finite dimensional indefinite inner product spaces of vector valued rational functions which are 1 invariant under the generalized backward shift and 2 subject to a structural identity and subspaces and superspaces thereof are studied the theory of these spaces is then applied to deduce a generalization of a pair of rules due to lohvidov for evaluating the inertia of certain subblocks of hermitian toeplitz and hermitian hankel matrices the connecting link rests on the identification of a hermitian matrix as the gram matrix of a space of vector valued functions of the type considered in the first part of the paper corresponding generalizations of another pair of theorems by lohvidov on the rank of certain subblocks of non hermitian teoplitz and non hermitian hankel matrices are also stated but the proofs will be presented elsewhere

local existence of solutions to some degenerate parabolic equation associated with the p laplacian abstract the existence of local in time solutions of the initial boundary value problem for the following degenerate parabolic equation u t x t p u x t u q 2 u x t f x t x t 0 t where 2 p q is a bounded domain in r n f 0 t r is given and p denotes the so called p laplacian defined by p u u p 2 u with initial data u 0 l r is proved under r n q p p without imposing any smallness on u 0 and f to this end the above problem is reduced into the cauchy problem for an evolution equation governed by the difference of two subdifferential operators in a reflexive banach space and the theory of subdifferential operators and potential well method are employed to establish energy estimates particularly l r estimates of solutions play a crucial role to construct a time local solution and reveal the dependence of the time interval 0 t 0 in which the problem admits a solution more precisely t 0 depends only on u 0 l r and f

a blow up result for nonlinear generalized heat equation in this paper we consider a nonlinear heat equation with nonlinearities of variable exponent type we show that any solution with nontrivial initial datum blows up in finite time we also give a two dimension numerical example to illustrate our result

on displacement shallow water wave equation and symplectic solution abstract in this paper the shallow water wave problem is discussed in the lagrangian description by using the hamilton variational principle in analytical mechanics a displacement shallow water wave equation dswwe is developed for the shallow water wave problem with a sloping water bottom and wet dry interface a numerical scheme based on the discretized hamilton principle is constructed for solving the proposed displacement shallow water wave equation the proposed numerical scheme is symplectic and explicit and can preserve the total energy and mass of the shallow water system in the discrete sense the correctness of the dswwe and the effectiveness of the proposed numerical scheme are verified by using four classical numerical examples numerical examples show that the proposed method performs well with respect to the simulation of the shallow water problem with a sloping water bottom and wet dry interface

non extinction and critical exponent for a polytropic filtration equation abstract this paper is concerned with the homogeneous dirichlet boundary value problem of a polytropic filtration equation with reaction sources we will show the non extinction property of non trivial solutions and determine the critical fujita exponent for the problem

an mps based particle method for simulation of multiphase flows characterized by high density ratios by incorporation of space potential particle concept abstract simulation of multiphase flows characterized by high density ratios is targeted by using a refined particle method the proposed method is founded on moving particle semi implicit mps method which is a projection based particle method the proposed method comprises of a decoupled two step computational algorithm through application of a consistent scheme for coupling the light heavy phases by incorporating the concept of space potential particles spp the proposed coupling scheme guarantees the continuity of pressure and space volume conservation at the phase interface without any need for commonly applied density smoothing averaging schemes or application of numerical stabilizing terms verification of the proposed multiphase particle method is conducted through the simulations of four benchmark tests and the method is shown to possess acceptable accuracy and convergence properties

extinction and positivity of solutions of the p laplacian evolution equation on networks abstract in this paper we consider a discrete version of the following p laplacian evolution equation u t p u with p 1 on a network using the discrete p laplacian operator in graphs which means a nonlinear diffusion phenomenon on networks we first introduce the p laplacian evolution equation on networks in fact spatial derivative in p laplacian evolution equation comparing the continuous case is replaced with the discrete p laplacian operator thus the resulting system is semi discrete discrete in space and continuous in time the main concern is to investigate the large time behaviors of nontrivial solutions of this equation whose initial data are nonnegative and the boundary data vanish in order to do so we use the analytic approaches such as vector calculus on networks maximum principle and comparison principle instead of numerical ones after deriving the basic properties of this equation we finally prove that the solution becomes extinct for 1 p 2 and remains strictly positive for p 2

pairs of functions with indefinite pick matrices results of factorization type are proved that characterize pairs of functions whose pick matrices have not more than a prescribed number of negative eigenvalues these results are in turn used to describe functions having caratheodory matrices with bounded number of negative eigenvalues

multisymplectic geometry variational integrators and nonlinear pdes this paper presents a geometric variational approach to continuous and discrete mechanics and field theories using multisymplectic geometry we show that the existence of the fundamental geometric structures as well as their preservation along solutions can be obtained directly from the variational principle in particular we prove that a unique multisymplectic structure is obtained by taking the derivative of an action function and use this structure to prove covariant generalizations of conservation of symplecticity and noether s theorem natural discretization schemes for pdes which have these important preservation properties then follow by choosing a discrete action functional in the case of mechanics we recover the variational symplectic integrators of veselov type while for pdes we obtain covariant spacetime integrators which conserve the corresponding discrete multisymplectic form as well as the discrete momentum mappings corresponding to symmetries we show that the usual notion of symplecticity along an infinite dimensional space of fields can be naturally obtained by making a spacetime split all of the aspects of our method are demonstrated with a nonlinear sine gordon equation including computational results and a comparison with other discretization schemes

extinction in finite time of solutions to degenerate parabolic equations with nonlinear boundary conditions abstract this work concerns a nonlinear diffusion absorption equation with nonlinear boundary flux the main topic of interest is the problem of finite time extinction i e the solutions vanish after a finite time the sufficient and necessary conditions for occurrence of extinction are established it is shown that extinction is caused by either strong absorption in the interior of the domain or fast diffusion combined with strong absorption through the boundary of the domain extinction results are also obtained for the mixed boundary value problem in contrast to the nonlinear neumann problem the absorption on the boundary is no longer important i e the occurrence of extinction in this case is completely determined by the effects of diffusion and interior absorption

exponential basis functions in solution of incompressible fluid problems with moving free surfaces in this paper a new simple meshless method is presented for the solution of incompressible inviscid fluid flow problems with moving boundaries a lagrangian formulation established on pressure as a potential equation is employed in this method the approximate solution is expressed by a linear combination of exponential basis functions ebfs with complex valued exponents satisfying the governing equation constant coefficients of the solution series are evaluated through point collocation on the domain boundaries via a complex discrete transformation technique the numerical solution is performed in a time marching approach using an implicit algorithm in each time step the governing equation is solved at the beginning and the end of the step with the aid of an intermediate geometry the use of ebfs helps to find boundary velocities with high accuracy leading to a precise geometry updating the developed lagrangian meshless algorithm is applied to variety of linear and nonlinear benchmark problems non linear sloshing fluids in rigid rectangular two dimensional basins are particularly addressed

the meshless finite element method a meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n and the condition that the shape functions depend only on the node positions furthermore the method proposed also shares several of the advantages of the finite element method such as a the simplicity of the shape functions in a large part of the domain b c0 continuity between elements which allows the treatment of material discontinuities and c ease of introduction of the boundary conditions copyright 2003 john wiley sons ltd

evolution inclusions governed by the difference of two subdifferentials in reflexive banach spaces abstract the existence of strong solutions of cauchy problem for the following evolution equation du t dt 1 u t 2 u t f t is considered in a real reflexive banach space v where 1 and 2 are subdifferential operators from v into its dual v the study for this type of problems has been done by several authors in the hilbert space setting the scope of our study is extended to the v v setting the main tool employed here is a certain approximation argument in a hilbert space and for this purpose we need to assume that there exists a hilbert space h such that v h h v with densely defined continuous injections the applicability of our abstract framework will be exemplified in discussing the existence of solutions for the nonlinear heat equation u t x t p u x t u q 2 u x t f x t x t 0 u 0 where is a bounded domain in r n in particular the existence of local in time weak solution is shown under the subcritical growth condition q p sobolev s critical exponent for all initial data u 0 w 0 1 p this fact has been conjectured but left as an open problem through many years

fully conservative higher order finite difference schemes for incompressible flow conservation properties of the mass momentum and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out in particular it is found that none of the existing higher order schemes for a staggered mesh system simultaneously conserve mass momentum and kinetic energy this deficiency is corrected through the derivation of a general family of fully conservative higher order accurate finite difference schemes for staggered grid systems finite difference schemes in a collocated grid system are also analyzed and a violation of kinetic energy conservation is revealed the predicted conservation properties are demonstrated numerically in simulations of inviscid white noise performed in a two dimensional periodic domain the proposed fourth order schemes in a staggered grid system are generalized for the case of a non uniform mesh and the resulting scheme is used to perform large eddy simulations of turbulent channel flow

three dimensional simulation of a solid liquid flow by the dem sph method abstract in this paper we describe a new lagrangian lagrangian algorithm which is referred to be the dem sph method for solid liquid flows involving free surfaces the dem solid phase and the sph liquid phase are coupled using the local averaging technique described by lagrangian approaches where both the continuity equation and the interaction force i e drag force are connected with the local mean voidage conservative forms of momentum transformation are derived for the dem sph interaction via a variational approach by introducing a correction to the sph approximation with explicit inclusion of boundary information arbitrary boundaries can be modeled without any extra wall particles where the boundary is used commonly for both dem and sph phases we deploy level set distance functions to efficiently construct and evaluate this boundary model to examine the validity of the present method we perform three dimensional simulations of a dynamic flow in a solid liquid dam break and a quasi steady flow in a rotating cylindrical tank and we conduct validation experiments to justify the simulation results in the dam break problem positions of wave fronts during the collapse are computed and compared with experimental measurements for the circulating tank some macroscopic aspects of the steady flow e g the shape dimension and velocity profile of the solid bed are obtained for validation data in both cases the simulation results are in good agreement with those of the experiment consequently the dem sph method is proved to be adequate in modeling solid liquid flows through this study

a new approach for the numerical simulation of free surface incompressible flows using a meshfree method abstract this paper proposes a novel approach to solve free surface incompressible flows using finite pointset method fpm our approach is based in the chorin uzawa s projection method and it corresponds to an extension of the work of tiwari and kuhnert 2007 to solve general elliptic equations in a meshfree framework the main features behind this approach as well as details of the computational implementation are presented finally the numerical results of the simulation of some test problems using this approach with first and second order accuracy in time projection schemes are reported and compared with published experimental and theoretical results which show that this approach is promising for simulating free surface incompressible flows

extinction and positivity for the evolution p laplacian equation with l1 initial value abstract the aims of this paper are to discuss extinction and positivity for the evolution p laplacian equation u t x u x p 2 u x with initial value u 0 x l 1 and zero boundary value conditions where p 1 in particular the necessary and sufficient condition for extinction is obtained

extinction and positivity for the evolution p laplacian equation in rn abstract the aim of this paper is to discuss extinction and positivity for the solution of the initial boundary value problem of evolution p laplacian equation it is proved that the weak solution will be extincted for 1 p 2 and will be positive for p 2 for large t

suppressing local particle oscillations in the hamiltonian particle method for elasticity the governing equation of elasticity is discretized into motion equations of the particles in a hamiltonian system a weighted least square method is adopted to evaluate the green lagrange strain using a symplectic scheme for the hamiltonian system we obtain the property of energy conservation in the discretized calculations however local particle oscillations occur and they excessively decrease low frequency motion in this study we propose the use of an artificial potential force to suppress the local oscillations the accuracy of the model with and without the inclusion of the artificial force is examined by analyzing a cantilever beam and wave propagation with the inclusion of the artificial force the local oscillations are reduced while energy conservation is maintained

a unified approach to structured covariances fast generalized sliding window rls recursions for arbitrary basis this paper extends the existing fast rls recursions originally intended to exponentially windowed problems for general models to a generalized sliding window formulation gswrls from a matrix algebra perspective we show explicitly how the displacement rank of the underlying inverse covariance matrix associated to any operator is defined as a function of the number of window breakpoints and how the fast gswrls calculates these rank factors in a fast manner the recursions hold regardless of the first order data structure induced and show that fast fixed order and order recursive rls algorithms can still be obtained for unwindowed data matrices exhibiting a fixed arbitrary relation between successive regressors our approach highlights the existence of a certain degree of freedom inherent to structured data matrices induced by general models showing that efficient representations of their inverse covariances are not limited to factor circulants but rather constructed from any arbitrary operator these bezoutians usually expressed via reproducing kernel relations can be represented exactly in matrix form along with a precise correspondence to variables of a gswrls as a fallout we obtain a vector relation stating the so called minimality property for extended models and windows as opposed to analogous generating function arguments normally seen in original approaches these results pave the way to a more general framework of polynomial vandermonde covariance decompositions which arise naturally via a proper choice of recurrence related polynomials this has further impact on several signal processing applications including superfast realization of equalizers in communications scenarios

lattice filter parameterization and modeling of nonstationary processes a general theory of constant parameter modular lattice models for discrete time nonstationary second order processes is presented a complete parametrization of such processes in terms of schur and congruence coefficients is derived by developing a natural connection between the displacement structure of a covariance matrix and schur s test for positive definiteness of matrices schur coeffieients provide a simple solution to problems of covariance extension and rational spectral approximation for nonstationary covariances and they coincide with the well known reflection or parcor coefficients when the covariance is stationary the congruence coefficients provide the time varying gains of a tapped delay line realization of the whitening filter for the process a constant parameter realization of the same filter is derived by combining a lattice filter structure with a tapped delay line both with time invariant gains this configuration also provides a recursive relation for the congruence coefficients namely a generalized levinson szego recursion the tapped delay line part of the realization can be eliminated by introducing the concept of admissibility admissibility also reduces the parametrization of a nonstationary process to schur coefficients alone in analogy to stationary processes which are completely characterized by their parcor coefficients

a complete characterization of nonlinear absorption for the evolution p laplacian equations to have positive or extinctive solutions this paper is concerned with long time behaviors of solutions to the initial boundary value problem of the evolution p laplacian equations with nonlinear absorption a long time behavior of solutions to these equations has been studied so far for particular types of nonlinear absorption term the purpose of this paper is to give a complete characterization of the nonlinear absorption term according to the parameter p in p laplacian operator and the growth of the nonlinear absorption term near the origin in order to determine whether the solution to the equations is extinctive or positive in addition we also give upper bounds for extinction times of solutions

cost reduction of particle simulations by an ellipsoidal particle model abstract we developed an ellipsoidal particle model to reduce the number of particles and the computational costs of the moving particle semi implicit mps method a coordinate transformation was conducted to treat ellipsoidal particles in the same manner as sphere particles the model for the mps method s laplacian operator was extended for use with ellipsoidal particles the developed method is effective in cases where the rate of change of a physical quantity or shape in any given direction is smaller than that in other directions and the authors have applied it to dam breaking problems in both two and three dimensions as a result the developed method s ability to reduce the required number of particles and the computational costs of particle simulations has been confirmed the developed ellipsoidal particle model was also applied to smoothed particle hydrodynamics

symplectic numerical integrators in constrained hamiltonian systems recent work reported in the literature suggests that for the long time integration of hamiltonian dynamical systems one should use methods that preserve the symplectic or canonical structure of the flow here we investigate the symplecticness of numerical integrators for constrained dynamics such as occur in molecular dynamics when bond lengths are made rigid in order to overcome stepsize limitations due to the highest frequencies this leads to a constrained hamiltonian system of smaller dimension previous work has shown that it is possible to have methods which are symplectic on the constraint manifold in phase space here it is shown that the very popular verlet method with shake type constraints is equivalent to the same method with rattle type constraints and that the latter is symplectic and time reversible this assumes that the iteration is carried to convergence we also demonstrate the global convergence of the verlet scheme in the presence of shake type and rattle type constraints we perform numerical experiments to compare these methods with the second order backward differentiation method commonly recommended for ordinary differential equations with constraints

existence of solutions to some degenerate parabolic equation associated with the p laplacian in the critical case abstract this paper is concerned with the initial boundary value problem for the following degenerate parabolic equation u t x t p u x t u q 2 u x t f x t with initial data u 0 l r akagi 2007 1 established the existence of local in time solutions to this problem in the case r n q p p however the critical case r n q p p has been left as an open problem in this paper even in the critical case r n q p p the existence of solutions to the problem is established under a certain restriction on u 0 the key to our proof is tartar s inequality which enables us to derive desired convergences of approximate solutions to the problem from the compactness of the embedding w 0 1 p l 2 incidentally any smoothness is not imposed on at all while a smooth boundary is needed in 1

on the tangential interpolation problem for functions the aim of this paper is to solve a matrix valued version of the nevanlinna pick interpolation problem for hi functions we reduce this prob lem to a nevanlinna pick interpolation problem for schur functions and obtain a linear fractional transformation which describes the set of all solutions

hamiltonian moving particle semi implicit hmps method for incompressible fluid flows particle methods are meshless simulation techniques in which motion of continua is approximated by discrete dynamics of a finite number of particles and thus have a great degree of flexibility for instance in dealing with the complex motion of surfaces or boundaries in this paper a particle method is developed from a direct discretization of the lagrangian for inviscid incompressible fluid flows the discretized lagrangian is transformed into a hamiltonian with holonomic constraints that stem from the incompressibility condition the rattle algorithm that is a symplectic scheme for holonomically constrained hamiltonian systems is adopted so that the resulting particle method inherits structures possessed by the partial differential equations that govern inviscid incompressible flows the algorithm of the particle method is semi implicit so we call it the hamiltonian moving particle semi implicit hmps method some numerical tests indicate the excellence of the hmps method in conservation of mechanical energy as well as linear and angular momenta

past input reconstruction in fast least squares algorithms this paper solves the following problem given the computed variables in a fast least squares prediction algorithm determine all past input sequences that would have given rise to the variables in question this problem is motivated by the backward consistency approach to numerical stability in this algorithm class the set of reachable variables in exact arithmetic is known to furnish a stability domain our problem is equivalent to a first and second order interpolation problem introduced by mullis and roberts 1976 and studied by others our solution differs in two respects first relations to classical interpolation theory are brought out which allows us to parametrize all solutions by products of our formulation are correct necessary and sufficient conditions for the problem to be solvable in contrast to previous works whose claimed sufficient conditions are shown to fall short second our solution obtains any valid past input as the impulse response of an appropriately constrained orthogonal filter whose rotation parameters derive in a direct manner from the computed variables in a fast least squares prediction algorithm formulas showing explicitly the form of all valid past inputs should facilitate the study of what past input perturbation is necessary to account for accumulated arithmetic errors in this algorithm class this in turn is expected to have an impact in studying accuracy aspects in fast least squares algorithms

extinction and positivity of the solutions of the heat equations with absorption on networks in this paper we propose a discrete version of the following semilinear heat equation with absorption ut u uq with q 1 which is said to be the heat equation with absorption on a network using the discrete laplacian operator on a weighted graph we define the heat equations with absorption on networks and give their physical interpretations the main concern is to investigate the large time behaviors of nontrivial solutions of the equations whose initial data are nonnegative and the boundary data vanish it is proved that the asymptotic behaviors of the solutions u x t as t tends to strongly depend on the sign of q 1

on the existence and construction of solutions to the partial lossless inverse scattering problem with applications to estimation theory the partial lossless inverse scattering plis problem which plays a fundamental role in the solution of a alpha stationary estimation problems is considered some open problems connected with this theory are treated necessary and sufficient conditions for a hermitian matrix to be positive say a covariance matrix are derived in terms of its alpha stationary wave representation a generalization of the recursive construction of plis solutions is proposed it is shown that each invariant subspace of the backward shift operator has a corresponding solution of the plis problem provided the operator that generalized the classical pick matrix is positive definite it is also shown that under fairly general conditions all solutions of the h sup infinity type are essentially obtained in this way and a characterization of the residual wave quantities generated by the scatterer is given stochastic models and forward and backward order recursive innovation filters are derived

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

unconditional stability and long term behavior of transient algorithms for the incompressible navier stokes and euler equations abstract this paper examines the long term behavior dissipativity and unconditional nonlinear stability properties of time integration algorithms for the incompressible navier stokes equations including both direct schemes and fractional step projection methods the algorithms are termed nonlinear unconditionally stable if in the absence of a forcing term but for arbitrary initial conditions the computed kinetic energy decreases for arbitrary step sizes i e l 2 stability such an a priori stability estimate is a characteristic feature of the navier stokes system similarly the algorithms are said to exhibit asymptotic t independent long term dissipative behavior if as the continuum flow generated by the navier stokes equations the algorithmic flow also exhibits an absorbing set and a maximal attractor both direct and fractional step methods are described which inherit these fundamental properties of the navier stokes system for any time step size moreover a subclass of algorithms which retain these strong notions of nonlinear stability and long term dissipative behavior is identified which in addition has the remarkable property of being linear within the time step the key implication is that no iterations are required to compute the solution within a time step a specific member of this class is shown to possess the same absorbing set as the continuum navier stokes system a second order accurate unconditionally stable method is also identified which retains the property of linearity within a time step numerical analysis and computational aspects involved in the implementation of these methods are addressed in detail and illustrated in representative numerical simulations

multichannel stable systems that extend the partial impulse response matrices this paper addresses the problem of identifying the class of all multichannel stable system transfer functions that extend the given partial impulse response matrix sequence this is achieved by making use of the left and right schur recursion algorithms for bounded matrix functions and in this context the classical pade approximations that are also stable are shown to be a special case of this general formulation further the theory developed here is utilized to generate multichannel non minimum phase optimal rational approximations to multichannel nonrational systems from their partial impulse response matrix sequence

the finite mass method the finite mass method a new lagrangian method for the numerical simulation of gas flows is presented and analyzed in contrast to the finite volume and the finite element method the finite mass method is founded on a discretization of mass not of space mass is subdivided into small mass packets of finite extension each of which is equipped with finitely many internal degrees of freedom these mass packets move under the influence of internal and external forces and the laws of thermodynamics and can undergo arbitrary linear deformations the method is based on an approach recently developed by yserentant and can attain a very high accuracy

lagrangian finite element analysis of newtonian fluid flows a fully lagrangian nite element method for the analysis of newtonian ows is developed the approach furnishes in eect a lagrangian implementation of the compressible navier stokes equations as the ow proceeds the mesh is maintained undistorted through continuous and adaptive remeshing of the uid mass the principal advantage of the present approach lies in the treatment of boundary conditions at material surfaces such as free boundaries uid uid or uid solid interfaces in contrast to eulerian approaches boundary conditions are enforced at material surfaces ab initio and therefore require no special attention consistent tangents are obtained for lagrangian implicit analysis of a newtonian uid ow which may exhibit compressibility eects the accuracy of the approach is assessed by comparison of the solution for a sloshing problem with existing numerical results and its versatility demonstrated through a simulation of wave breaking the nite element mesh is maintained undistorted throughout the computation by recourse to frequent and adaptive remeshing 1998 john wiley sons ltd

a hamiltonian particle method for non linear elastodynamics particle methods are meshless simulation techniques in which motion of continua is approximated by discrete dynamics of a finite number of particles they have a great degree of flexibility for instance in dealing with complex large deformations or the fragmentation of solids in this paper a particle method for non linear elastodynamics of compressible and incompressible materials is developed based on a discretization of the lagrangian from which the governing equations of elastodynamics are derived using the principle of least action the discretized lagrangian leads to a finite dimensional hamiltonian system via the legendre transformation if the material is incompressible the hamiltonian system is accompanied by holonomic constraints depending on whether the material is compressible or incompressible the symplectic scheme adopted for numerical time integration is either the stormer verlet scheme or the rattle method respectively the resulting particle method inherits the symplectic structure possessed by the governing equations of elastodynamics in the case of incompressible materials incompressibility is strictly enforced at each time step some numerical tests indicate the excellence of the method for conservation of mechanical energy besides that of linear and angular momenta