generalized multiple scale reproducing kernel particle methods abstract an approach to unify reproducing kernel methods under one large umbrella and an extension to include time and spatial shifting are proposed the study is divided into three major topics the groundwork is set by revisiting the fourier analysis of discrete systems the multiresolution concept and its significance in devising the reproducing kernel methods and its discrete counterpart reproducing kernel particle methods are explained an edge detection technique based on multiresolution analysis is developed this wavelet approach together with particle methods gives rise to a straightforward h adaptivity algorithm by using this framework a hermite reproducing kernel method is also proposed and its relation to wavelet methods is presented it is also shown that the new approach generalizes existing kernel methods and it can easily be degenerated into other widely used methods such as partition of unity moving least square interpolants smooth particle hydrodynamics scaling functions and wavelets and multiple scale analysis furthermore the hermite reproducing kernel particle method a particle based discrete version of the hermite reproducing kernel method is developed finally multiple scale methods based on frequency and wave number shifting techniques are presented a stability analysis is also presented for newmark time integration schemes for the low frequency equation numerical examples are presented throughout the paper to illustrate the flexibility and accuracy of this class of multiple scale methods

new estimates for ritz vectors the following estimate for the rayleigh ritz method is proved u u au u sin u u u 1 here a is a bounded self adjoint operator in a real hilbert euclidian space u one of its eigenpairs u a trial subspace for the rayleigh ritz method and u a ritz pair this inequality makes it possible to analyze the fine structure of the error of the rayleigh ritz method in particular it shows that u u c 2 if an eigenvector u is close to the trial subspace with accuracy and a ritz vector u is an approximation to another eigenvector with a different eigenvalue generalizations of the estimate to the cases of eigenspaces and invariant subspaces are suggested and estimates of approximation of eigenspaces and invariant subspaces are proved

transition system specifications with negative premises abstract in this article the general approach to plotkin style operational semantics of groote and vaandrager 1989 is extended to transition system specifications tsss with rules that may contain negative premises two problems arise firstly the rules may be inconsistent and secondly it is not obvious how a tss determines a transition relation we present a general method based on the stratification technique in logic programming to prove consistency of a set of rules and we show how a specific transition relation can be associated with a tss in a natural way then a special format for the rules the ntyft ntyxt format is defined it is shown that for this format three important theorems hold the first theorem says that bisimulation is a congruence if all operators are defined using this format the second theorem states that under certain restrictions a tss in ntyft format can be added conservatively to a tss in pure ntyft ntyxt format finally it is shown that the trace congruence for image finite processes induced by the pure ntyft ntyxt format is precisely bisimulation equivalence

convergence analysis for gmsfem approximation of elliptic eigenvalue problems abstract in this paper we analyze the approximation of elliptic eigenvalue problems using generalized multiscale finite element method gmsfem and get error estimates for eigenfunctions and eigenvalues for the case of simple eigenvalues the approximation errors for eigenfunctions are considered in both energy error and l 2 error the derived error estimates clearly give the relation between the errors and the coarse mesh size local multiscale enrichment and the corresponding eigenvalues the convergence analysis shows that the approximation of eigenvalue problems using gmsfem does not depend on the contrastness of the coefficient when the diffusion coefficient is highly heterogeneous a few numerical examples are presented to illustrate the performance of the gmsfem approximation and the theoretic analysis for the eigenvalue problems

shape optimization using reproducing kernel particle method and an enriched genetic algorithm combining reproducing kernel particle method rkpm with the proposed multi family genetic algorithm mfga a novel approach to continuum based shape optimization problems is brought forward in this paper taking full advantage of the features of meshfree method and the merits of mfga the new method solves shape optimization problems in such a unique way that remeshing is avoided and particularly the computation burden and errors caused by sensitivity analysis are eliminated completely the effectiveness versatility and performance of the proposed approach are demonstrated via three 2 d numerical examples

cylindrical smoothed particle hydrodynamics abstract smoothed particle hydrodynamics sph is formulated in two dimensional axisymmetric coordinates starting with a three dimensional cartesian representation of sph we integrate out the angular component and find a two dimensional cylindrical description a smoothed particle in this formulation becomes a smoothed torus the hoop stress resulting from interactions within the toroidal ring is a natural consequence of the derivation no pathological behavior is observed at the symmetry axis the formulation has been extended to include the entire stress tensor not just the pressure and is therefore applicable to a wide range of materials and flow speeds three calculations are presented and compared to known results

the algebra of timed processes atp the algebra of timed processes atp uses a notion of discrete global time and suggests a conceptual framework for introducing time by extending untimed languages the action vocabularly of atp contains a special element representing the progress of time the algebra has apart from standard operators of process algebras such as prefixing by an action alternative choice and parallel composition a primitive unit delay operator for two arguments processes p and q this operator gives a process which behaves as p before the execution of a time event and behaves as q afterwards it is shown that several d unit delay constructs such as timeouts and watchdogs can be expressed in terms of the unit delay operator and standard process algebra operators a sound and complete axiomatization for bisimulation semantics is studied and two examples illustrating the adequacy of the language for the description of timed systems are given finally we provide a comparison with existing timed process algebras

certified error bounds for uncertain elliptic equations in many applications partial differential equations depend on parameters which are only approximately known using tools from functional analysis and global optimization methods are presented for obtaining certificates for rigorous and realistic error bounds on the solution of linear elliptic partial differential equations in arbitrary domains either in an energy norm or of key functionals of the solutions given an approximate solution uncertainty in the parameters specifying the partial differential equations can be taken into account either in a worst case setting or given limited probabilistic information in terms of clouds

an improved complex variable element free galerkin method for two dimensional large deformation elastoplasticity problems abstract this paper presents the formulation and numerical implementation of the improved complex variable element free galerkin icvefg method for two dimensional large deformation problems of elastoplasticity in total lagrangian description the icvefg method is a novel element free galerkin efg method based on the improved complex variable moving least squares icvmls approximation the icvmls approximation has all the advantages inherited from the complex variable moving least squares cvmls approximation the function j in the icvmls approximation has an explicit physical meaning compared with the former the galerkin weak form is employed to obtain the equations system and the penalty method is used to apply essential boundary conditions several numerical examples presented show that the icvefg method has greater precision and efficiency compared to the efg and cvefg methods

new a priori fem error estimates for eigenvalues we analyze the ritz galerkin method for symmetric eigenvalue problems and prove a priori eigenvalue error estimates for a simple eigenvalue we prove an error estimate that depends mainly on the approximability of the corresponding eigenfunction and provide explicit values for all constants for a multiple eigenvalue we prove in addition what is apparently the first truly a priori error estimates that show the levels of the eigenvalue errors depending on approximability of eigenfunctions in the corresponding eigenspace these estimates reflect a known phenomenon that different eigenfunctions in the corresponding eigenspace may have different approximabilities thus resulting in different levels of errors for the approximate eigenvalues for clustered eigenvalues we derive eigenvalue error bounds that do not depend on the width of the cluster our results are readily applicable to the classical ritz method for compact symmetric integral operators and to finite element method eigenvalue approximation for symmetric positive definite differential operators

compositionality of hennessy milner logic by structural operational semantics this paper presents a method for the decomposition of hml formulas it can be used to decide whether a process algebra term satisfies a hml formula by checking whether subterms satisfy certain formulas obtained by decomposing the original formula the method uses the structural operational semantics of the process algebra the main contribution of this paper is the extension of an earlier decomposition method for the de simone format from the ph d thesis of larsen in 1986 to more general formats

a meshless method for axi symmetric poroelastic simulations numerical study a meshless model based on the meshless local petrov galerkin mlpg approach is developed and implemented for the solution of axi symmetric poroelastic problems the solution accuracy and the code performance are investigated on a realistic application concerning the prediction of land subsidence above a deep compacting reservoir the analysis addresses several numerical issues including the parametric selection of the optimal size of the local sub domains for the weak form and the nodal supports the appropriate integration rule and the linear system solver the results show that mlpg can be more accurate than the standard finite element fe method on coarse discretizations with its superiority decreasing as the nodal resolution increases this is due to both a slower convergence rate and a progressively higher computational cost compared to fe these drawbacks can be partially mitigated by improving the efficiency of the numerical integration and the system solver with the aid of projection techniques based on krylov subspace methods the outcome of the present analysis supports the development of coupled methods where a limited number of mlpg nodes are used to locally improve a fe solution copyright 2006 john wiley sons ltd

parallel computation of meshless methods for explicit dynamic analysis a parallel computational implementation of modern meshless methods is presented for explicit dynamic analysis the procedures are demonstrated by application of the reproducing kernel particle method rkpm aspects of a coarse grain parallel paradigm are detailed for a lagrangian formulation using model partitioning integration points are uniquely defined on separate processors and particle definitions are duplicated as necessary so that all support particles for each point are defined locally on the corresponding processor several partitioning schemes are considered and a reduced graph based procedure is presented partitioning issues are discussed and procedures to accommodate essential boundary conditions in parallel are presented explicit mpi message passing statements are used for all communications among partitions on different processors the effectiveness of the procedure is demonstrated by highly deformable inelastic example problems

numerical simulations of strain localization in inelastic solids using mesh free methods in this paper a comprehensive account on using mesh free methods to simulate strain localization in inelastic solids is presented using an explicit displacement based formulation in mesh free computations high resolution shear band formations are obtained in both two dimensional 2 d and three dimensional 3 d simulations without recourse to any mixed formulation discontinuous incompatible element or special mesh design the numerical solutions obtained here are insensitive to the orientation of the particle distributions if the local particle distribution is quasi uniform which to a large extent relieves the mesh alignment sensitivity that finite element methods suffer moreover a simple h adaptivity procedure is implemented in the explicit calculation and by utilizing a mesh free hierarchical partition of unity a spectral wavelet adaptivity procedure is developed to seek high resolution shear band formations moreover the phenomenon of multiple shear band and mode switching are observed in numerical computations with a relatively coarse particle distribution in contrast to the costly fine scale finite element simulations copyright 2000 john wiley sons ltd

principal angles between subspaces in an a based scalar product algorithms and perturbation estimates computation of principal angles between subspaces is important in many applications e g in statistics and information retrieval in statistics the angles are closely related to measures of dependency and covariance of random variables when applied to column spaces of matrices the principal angles describe canonical correlations of a matrix pair we highlight that all popular software codes for canonical correlations compute only cosine of principal angles thus making impossible because of round off errors finding small angles accurately we review a combination of sine and cosine based algorithms that provide accurate results for all angles we generalize the method to the computation of principal angles in an a based scalar product for a symmetric and positive definite matrix a we provide a comprehensive overview of interesting properties of principal angles we prove basic perturbation theorems for absolute errors for sine and cosine of principal angles with improved constants numerical examples and a detailed description of our code are given

a partial ordering semantics for ccs a new operational semantics for pure ccs is proposed that considers the parallel operator as a first class one and permits a description of the calculus in terms of partial orderings the new semantics also for unguarded agents is given in the sos style via the partial ordering derivation relation ccs agents are decomposed into sets of sequential subagents the new derivations relate sets of subagents and describe their actions and the casual dependencies among them the computations obtained by composing partial ordering derivations are observed either as interleaving or partial orderings of events interleavings coincide with milner s many step derivations and linearizations of partial orderings are all and only interleavings abstract semantics are obtained by introducing two relations of observational equivalence and congruence that preserve concurrency these relations are finer than milner s in that they distinguish interleaving of sequential nondeterministic agents from their concurrent execution

a stabilized least squares radial point collocation method ls rpcm for adaptive analysis abstract in this paper a stabilized radial point collocation method rpcm that uses locally supported nodes is proposed using least squares stabilization technique the focus of this work is to stabilize the solution of the rpcm in order to perform adaptive analysis good stiffness matrix properties such as symmetric and positive definite spd are gained via a least squares procedure and yet the formulation procedure of the stabilized ls rpcm is still kept simple and straightforward adaptive analysis study has then been successfully carried out using the stabilized ls rpcm error indicator based on interpolation error is adopted in the adaptive scheme for nodal refinement thanks for the meshfree features of the rpcm refinement process can be easily done by inserting additional nodes based on the voronoi diagram without worrying about nodal connectivity in the formulation of system equations good numerical performance has been shown in the numerical examples presented in this paper

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

finite element galerkin approximation of the eigenvalues and eigenvectors of selfadjoint problems abstract this paper establishes some refined estimates for the approximation of the eigenvalues and eigenvectors of selfadjoint eigenvalue problems by finite element or more generally galerkin methods suppose lambda is an eigenvalue of multiplicity q of a selfajoint problem and let m lambda denote the space of eigenvectors corresponding to lambda keywords hilbert space

asynchronous mappings and asynchronous cellular automata the aim of this paper is the study of asynchronous automata a special kind of automata which encode the independency relation between actions and which enable their concurrent execution these automata introduced by zielonka rairo inform theor appl 21 99 135 1987 constitute a natural extension of finite automata to the case of asynchronous parallelism their behaviour is described by trace languages subsets of partially commutative monoids the main result concerning this class of automata states that they accept exactly all recognizable trace languages in this paper we give new improved constructions of asynchronous automata in the final part of the paper we present a distributed system of messages with bounded time stamps based on asynchronous automata

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

regularity and numerical solution of eigenvalue problems with piecewise analytic data this paper discusses the regularity of the eigenfunctions of eigenvalue problems with piecewise analytic data and the approximation of the eigenvalues and eigenfunctions of such problems a detailed and systematic numerical study of these approximations is presented together with an analysis of the numerical results in light of the theoretical results the specific aim is to assess the reliability of the theoretical results which are of an asymptotic nature as a guide to practical computations which may take place in the pre asymptotic phase and to look for characteristic features of the numerical results that are not completely explained by known theoretical results

additive models of probabilistic processes we propose a new model of probabilistic processes in this model a probability is assigned to the action of a prefix and a probability distribution is assigned to the components of a parallel composition in addition the probability of a transition of a probabilistic summation is evaluated as the sum of the probabilities of the same transition of summands multiplied by the probabilities associated to them in the summation the concepts of strong bisimulation degree and weak bisimulation degree are introduced these notions provide us with continuous spectra of strong bisimilarities weak bisimilarities and observation congruences which equate probabilistic processes with different degrees of belief various equational laws of probabilistic processes with respect to these equivalence relations are presented and substitutivities of these equivalence relations under various combinators are established

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

two decentralized algorithms for strong interaction fairness for systems with unbounded speed variability abstract we present two randomized algorithms one for message passing and the other for shared memory that with probability 1 schedule multiparty interactions in a strongly fair manner both algorithms improve upon a previous result by joung and smolka proposed in a shared memory model along with a straightforward conversion to the message passing paradigm in the following aspects first processes speeds as well as communication delays need not be bounded by any predetermined constant secondly our algorithms are completely decentralized and the shared memory solution makes use of only single writer variables finally both algorithms are symmetric in the sense that all processes execute the same code and no unique identifier is used to distinguish processes

rational eigenvalue problems and applications to photonic crystals we establish new analytic results for a general class of rational spectral problems they arise e g in modelling photonic crystals whose capability to control the flow of light depends on specific

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 generalized smoothed particle hydrodynamics method for nonlinear dynamic problems abstract a generalized smoothed particle hydrodynamics sph method was developed for the numerical simulation of nonlinear dynamic problems the performance of the proposed method was demonstrated by solving burgers equations over a wide range of the viscosity parameters in one and two space dimensions it was shown that the present results agree very well with other existing solutions as compared to other meshless methods this algorithm is quite straightforward and simple and can be coded easily

discretization errors associated with reproducing kernel methods one dimensional domains abstract the reproducing kernel particle method rkpm is a discretization technique for partial differential equations that uses the method of weighted residuals classical reproducing kernel theory and modified kernels to produce either mesh free or mesh full methods although rkpm has many appealing attributes the method is new and its numerical performance is just beginning to be quantified in order to address the numerical performance of rkpm von neumann analysis is performed for semi discretizations of three model one dimensional pdes the von neumann analyses results are used to examine the global and asymptotic behavior of the semi discretizations the model pdes considered for this analysis include the parabolic and hyperbolic first and second order wave equations numerical diffusivity for the former and phase speed for the latter are presented over the range of discrete wavenumbers and in an asymptotic sense as the particle spacing tends to zero group speed is also presented for the hyperbolic problems excellent diffusive and dispersive characteristics are observed when a consistent mass matrix formulation is used with the proper choice of refinement parameter in contrast the row sum lumped mass matrix formulation severely degraded performance the asymptotic analysis indicates that very good rates of convergence o x 6 o x 8 are possible when the consistent mass matrix formulation is used with an appropriate choice of refinement parameter and quadrature rule

block locally optimal preconditioned eigenvalue xolvers blopex in hypre and petsc we describe our software package block locally optimal preconditioned eigenvalue xolvers blopex recently publicly released blopex is available as a stand alone serial library as an external package to petsc portable extensible toolkit for scientific computation a general purpose suite of tools developed by argonne national laboratory for the scalable solution of partial differential equations and related problems and is also built into hypre high performance preconditioners a scalable linear solvers package developed by lawrence livermore national laboratory the present blopex release includes only one solver the locally optimal block preconditioned conjugate gradient lobpcg method for symmetric eigenvalue problems hypre provides users with advanced high quality parallel multigrid preconditioners for linear systems with blopex the same preconditioners can now be efficiently used for symmetric eigenvalue problems petsc facilitates the integration of independently developed application modules with strict attention to component interoperability and makes blopex extremely easy to compile and use with preconditioners that are available via petsc we present the lobpcg algorithm in blopex for hypre and petsc we demonstrate numerically the scalability of blopex by testing it on a number of distributed and shared memory parallel systems including a beowulf system sun fire 880 an amd dual core opteron workstation and ibm bluegene l supercomputer using petsc domain decomposition and hypre multigrid preconditioning we test blopex on a model problem the standard 7 point finite difference approximation of the 3 d laplacian with the problem size in the range of 10 5 10 8

stable families of behavioural equivalences abstract many of the behavioural equivalences studied in the literature see 1 2 3 4 are defined generically on any transition system in particular on their own quotient system it would seem reasonable to expect such an equivalence to be idempotent in this respect in other words to yield the identity the second time we capture this idea in the notion of a stable family of preorders on transition systems and investigate the stability of the equivalences in 1 2 3 4 in addition our approach involves general schemes of definition of equivalences on transition systems which lead to extensions of the hierarchy results of 1

a fully abstract denotational semantics for the calculus of higher order communicating systems abstract in this paper we study the calculus of higher order communicating systems chocs thomsen proc of popl 89 acm 1989 pp 143 154 inform comput 116 1 1995 38 57 in a denotational setting we present a construction of a denotational semantics for chocs which resides in a domain constructed using the standard constructions of separated sum cartesian product the plotkin power domain constructor and recursively defined domains we show under mild restrictions that the denotational semantics and the operational semantics of chocs are fully abstract we have previously proved using bisimulation arguments that processes as first class objects are powerful enough to simulate recursion however the proof is very long and tedious to demonstrate the power of the denotational approach we use it to obtain a very simple proof of the simulation of recursion result

on accuracy of approximate boundary and distributed h1 shape gradient flows for eigenvalue optimization abstract the boundary and distributed shape gradients of elliptic eigenvalues in shape optimization are approximated by the finite element method we show a priori error estimates for the two approximate shape gradients in h 1 shape gradient flows the convergence analysis shows that the volume integral formula converges faster and offers higher accuracy when the finite element method is used for discretization numerical results verify the theory for the dirichlet case shape optimization examples solved by algorithms illustrate the more effectiveness of distributed shape gradients for the dirichlet case for optimizing a neumann eigenvalue the boundary and volume h 1 flows have the same efficiency moreover we observe that the distributed h 1 shape gradient flow is more efficient than the boundary l 2 shape gradient flow in literature

parametric study for an efficient meshless method in vibration analysis based on the moving least squares mls approach an efficient meshless method is employed to generate the displacement functions for vibration analysis of elastic bodies the equation of motion is established by following the standard procedure and the boundary conditions are imposed by applying penalty functions as the displacement functions are expressed in terms of weight functions the accuracy will depend on the parameters of the weight functions therefore a parametric study is carried out to determine the best values for these parameters to demonstrate the accuracy modal analyses of the beams and plates with different boundaries have been carried out in addition the responses of these structures under dynamic excitation have been analyzed the examples include simply supported beams subjected to sudden excitations and simply supported plates subjected to initial displacements

generalized om bisimulation history preserving bisimilarity and maximality preserving bisimilarity take full account of the interplay between causality and branching and they are congruences w r t action refinement for suitable classes of petri nets but even for finite safe petri nets they are based on possibly infinite transition systems and it is not obvious how to decide them om bisimulation gives a characterization of history preserving bisimulation for safe nets without internal moves and it allows a decidability result in this paper we generalize om bisimulation and this decidability result to safe nets with internal moves and also treat the case of maximality preserving bisimulation

element free galerkin methods for static and dynamic fracture abstract element free galerkin efg methods are presented and applied to static and dynamic fracture problems efg methods which are based on moving least square mls interpolants require only nodal data no element connectivity is needed the description of the geometry and numerical model of the problem consists only of a set of nodes and a description of exterior boundaries and interior boundaries from any cracks this makes the method particularly attractive for growing crack problems since only minimal remeshing is needed to follow crack growth in moving least square interpolants the dependent variable at any point is obtained by minimizing a function in terms of the nodal values of the dependent variable in the domain of influence of the point numerical examples involving fatigue crack growth and dynamic crack propagation are presented to illustrate the performance and potential of this method

a weighted least squares particle in cell method for solid mechanics a novel meshfree method is proposed that incorporates features of the material point mpm and generalized interpolation material point gimp methods and can be used within an existing mpm gimp implementation weighted least squares kernel functions are centered at stationary grid nodes and used to approximate field values and gradients integration is performed over cells of the background grid and material boundaries are approximated with an implicit surface the proposed method avoids nearest neighbor searches while significantly improving accuracy over mpm and gimp implementation is discussed in detail and several example problems are solved including one manufactured solution which allows measurement of dynamic non linear large deformation performance advantages and disadvantages of the method are discussed copyright 2010 john wiley sons ltd

dynamic fracture using element free galerkin methods the element free galerkin method for dynamic crack propagation is described and applied to several problems this method is a gridless method which facilitates the modelling of growing crack problems because it does not require remeshing the growth of the crack is modelled by extending its surfaces the essential feature of the method is the use of moving least squares interpolants for the trial and test functions in these interpolants the dependent variable is obtained at any point by minimizing a weighted quadratic form involving the nodal variables within a small domain surrounding the point the discrete equations are obtained by a galerkin method the procedures for modelling dynamic crack propagation based on dynamic stress intensity factors are also described

an iterative method for elliptic problems on regions partitioned into substructures some new preconditioners for discretizations of elliptic boundary problems are studied with these preconditioners the domain under consideration is broken into subdomains and preconditioners are defined which only require the solution of matrix problems on the subdomains analytic estimates are given which guarantee that under appropriate hypotheses the preconditioned iterative procedure converges to the solution of the discrete equations with a rate per iteration that is independent of the number of unknowns numerical examples are presented which illustrate the theoretically predicted iterative convergence rates

cpo models for compact gsos languages in this paper we present a general way of giving denotational semantics to a class of languages equipped with an operational semantics that fits the gsos format of bloom istrail and meyer the canonical model used for this purpose will be abramsky s domain of synchronization trees and the denotational semantics automatically generated by our methods will be guaranteed to be fully abstract with respect to the finitely observable part of the bisimulation preorder in the process of establishing the full abstraction result we also obtain several general results on the bisimulation preorder including a complete axiomatization for it and give a novel operational interpretation of gsos languages

a stabilized iterative scheme for coupled hydro mechanical systems using reproducing kernel particle method summary in this paper a novel iterative coupling scheme is developed for solving coupled hydro mechanical problems using reproducing kernel particle method the numerical scheme calls the fluid and the solid solvers sequentially and iteratively until convergent solutions are obtained to overcome the numerical instability problem a simple stabilization technique is developed and proved to be unconditionally stable through stability analysis the accuracy and convergence of the proposed numerical scheme are demonstrated through extensive parametric studies of one dimensional and two dimensional consolidation simulations using fully saturated elastic medium as well as biaxial test using a fully nonlinear soil model copyright 2014 john wiley sons ltd

a corrective smoothed particle method for boundary value problems in heat conduction combining the kernel estimate with the taylor series expansion is proposed to develop a corrective smoothed particle method cspm this algorithm resolves the general problem of particle deficiency at boundaries which is a shortcoming in standard smoothed particle hydrodynamics ssph in addition the method s ability to model derivatives of any order could make it applicable for any time dependent boundary value problems an example of the applications studied in this paper is unsteady heat conduction which is governed by second order derivatives numerical results demonstrate that besides the capability of directly imposing boundary conditions the present method enhances the solution accuracy not only near or on the boundary but also inside the domain published in 1999 by john wiley sons ltd this article is a u s government work and is in the public domain in the united states

a numerical method for suspension flow abstract peskin s j comput phys 25 220 1977 immersed boundary technique is modified to give a new numerical method for studying a fluid with suspended elastic particles as before the presence of the suspended particles is transmitted to the fluid through a force density term in the fluid equations as a result one set of equations holds in the entire computational domain eliminating the need to apply boundary conditions on the surface of suspended objects the new method computes the force density by discretizing the stress strain constitutive equations for an elastic solid on a grid using data provided by clusters of lagrangian points this approach clearly specifies the material properties of the suspended objects a simple data structure for the lagrangian points makes it easy to model suspended solids with arbitrary shape and size the method is validated by comparing numerical results for elastic vibrations and particle settling in viscous fluids with theory and analysis the capability of the method to do a wide range of problems is illustrated by qualitative results for lubrication and cavity flow problems

a complete axiomatization of finite state acsr processes a real time process algebra called acsr has been developed to facilitate the specification and analysis of real time systems acsr supports synchronous timed actions and asynchronous instantaneous events timed actions are used to represent the usage of resources and to model the passage of time events are used to capture synchronization between processes to be able to specify real time systems accurately acsr supports a notion of priority that can be used to arbitrate among timed actions competing for the use of resources and among events that are ready for synchronization in addition to operators common to process algebra acsr includes the scope operator which can be used to model timeouts and interrupts equivalence between acsr terms is based on the notion of strong bisimulation this paper briefly describes the syntax and semantics of acsr and then presents a set of algebraic laws that can be used to prove equivalence of acsr processes the contribution of this paper is the soundness and completeness proofs of this set of laws the completeness proof is for finite state acsr processes which are defined to be processes without free variables under parallel operator or scope operator

space time finite element computation of compressible flows involving moving boundaries and interfaces abstract the deformable spatial domain stabilized space time dsd sst formulation introduced by tezduyar et al is applied to computation of viscous compressible flows involving moving boundaries and interfaces the stabilization technique employed is a streamline upwind petrov galerkin supg method with a modified supg stabilization matrix the stabilized finite element formulation of the governing equations is written over the space time domain of the problem and therefore the deformation of the spatial domain with respect to time is taken into account automatically the frequency of remeshing is minimized to minimize the projection errors involved in remeshing and also to increase the parallelization potential of the computations the implicit equation systems arising from the space time finite element discretizations are solved iteratively it is demonstrated that the combination of the supg stabilization and the space time approach gives the capability of handling complicated compressible flow problems including those with moving surfaces and shock boundary layer interactions

multiple scale finite element methods new temporal and spatial discretization methods are developed for multiple scale structural dynamic problems the concept of fast and slow time scales is introduced for the temporal discretization the required time step is shown to be dependent only on the slow time scale and therefore large time steps can be used for high frequency problems to satisfy the spatial counterpart of the requirement on time step constraint finite spectral elements and finite wave elements are developed finite spectral element methods combine the usual finite elements with the fast convergent spectral functions to obtain a faster convergence rate whereas finite wave elements are developed in parallel to the temporal shifting technique therefore the spatial resolution is increased substantially these methods are especially applicable to structural acoustics and linear space structures numerical examples are presented to illustrate the effectiveness of these methods

elasto plasticity revisited numerical analysis via reproducing kernel particle method and parametric quadratic programming aiming to simplify the solution process of elasto plastic problems this paper proposes a reproducing kernel particle algorithm based on principles of parametric quadratic programming for elasto plasticity the parametric quadratic programming theory is useful and effective for the assessment of certain features of structural elasto plastic behaviour and can also be exploited for numerical iteration examples are presented to illustrate the essential aspects of the behaviour of the model proposed and the flexibility of the coupled parametric quadratic programming formulations with the reproducing kernel particle method copyright 2002 john wiley sons ltd

petri nets event structures and domains part i abstract the general aim of this paper is to find a theory of concurrency combining the approaches of petri and scott and others in part i we introduce our formalisms to connect the abstract ideas of events and domains of information we show how casual nets induce certain kinds of domains where the information points are certain sets of events this allows translations between the languages of net theory and domain theory following the idea that events of causal nets are occurrences we generalise causal nets to occurrence nets by adding forwards conflict just as infinite flow charts unfold finite ones so transition nets can be unfolded into occurrence nets next we extend the above connections between nets and domains to these new nets event structures which are intermediate between nets and domains play an important part in all our work finally as an example of how concepts translate from one formalism to the other we show how petri s notion of confusion ties up with kahn and plotkin s concrete domains in part ii we shall continue the job of connecting up notions within net theory and the theory of domains in particular we shall examine the idea of states of computations

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

hp finite elements for elliptic eigenvalue problems error estimates which are explicit with respect to lambda h and p convergence rates for finite element discretizations of elliptic eigenvalue problems in the literature usually are of the following form if the mesh width h is fine enough then the eigenvalues resp eigenfunctions converge at some well defined rate in this paper we will determine the maximal mesh width h 0 more precisely the minimal dimension of a finite element space so that the asymptotic convergence estimates hold for h leq h 0 this mesh width will depend on the size and spacing of the exact eigenvalues the spatial dimension and the local polynomial degree of the finite element space for example in the one dimensional case the condition lambda 3 4 h 0 lesssim1 is sufficient for piecewise linear finite elements to compute an eigenvalue lambda with optimal convergence rates as h 0 geq h rightarrow0 it will turn out that the condition for eigenfunctions is slightly more restrictive furthermore we will analyze the dependence of the ratio of the errors of the galerkin approximation and of the best approximation of an eigenfunction on lambda and h in this paper the error estimates for the eigenvalue function are limited to the selfadjoint case however the regularity theory and approximation property cover also the nonselfadjoint case and hence pave the way towards the error analysis of nonselfadjoint eigenvalue function problems

an adaptive homotopy approach for non selfadjoint eigenvalue problems this paper presents adaptive algorithms for eigenvalue problems associated with non selfadjoint partial differential operators the basis for the developed algorithms is a homotopy method which departs from a well understood selfadjoint problem apart from the adaptive grid refinement the progress of the homotopy as well as the solution of the iterative method are adapted to balance the contributions of the different error sources the first algorithm balances the homotopy discretization and approximation errors with respect to a fixed stepsize in the homotopy the second algorithm combines the adaptive stepsize control for the homotopy with an adaptation in space that ensures an error below a fixed tolerance e the outcome of the analysis leads to the third algorithm which allows the complete adaptivity in space homotopy stepsize as well as the iterative algebraic eigenvalue solver all three algorithms are compared in numerical examples

on the semantics of markov automata markov automata describe systems in terms of events which may be nondeterministic may occur probabilistically or may be subject to time delays we define a novel notion of weak bisimulation for such systems and prove that this provides both a sound and complete proof methodology for a natural extensional behavioural equivalence between such systems a generalisation of reduction barbed congruence the well known touchstone equivalence for a large variety of process description languages

angles between infinite dimensional subspaces with applications to the rayleigh ritz and alternating projectors methods we define angles for infinite dimensional subspaces of hilbert spaces inspired by the work of e j hannan 1961 1962 the angles of dixmier and friedrichs and the gaps are characterized we establish connections between the angles corresponding to orthogonal complements the sensitivity of angles with respect to subspaces is estimated we show that the squared cosines of the angles from one subspace to another can be interpreted as ritz values in the rayleigh ritz method the hausdorff distance between the ritz values corresponding to different trial subspaces is shown to be bounded by a constant times the gap between the subspaces we prove a similar eigenvalue perturbation bound that involves the gap squared an ultimate acceleration of the classical alternating projectors method is proposed its convergence rate is estimated in terms of the angles we illustrate the acceleration for a domain decomposition method with a small overlap for the 1d diffusion equation

determinancy observation equivalence trace equivalence abstract if an experiment s is conducted on a parallel process p then in general different processes may result from the experiment due to the nondeterministic behaviour of p in the notation of milner 1980 p p for different p process p is called determinate if the resulting processes are all equivalent i e if p p and p p then p and p are equivalent this means that although p behaves nondeterministically this cannot be detected by an observer of p let denote observation equivalence used in ccs milner 1980 let f denote the much weaker failure equivalence used for csp hoare et al 1981 brookes 1983 and let t denote the still weaker trace equivalence we show that the three corresponding notions of determinancy are the same and that for determinate processes f and t are the same determinacy is preserved under and f but not under t

non well founded sets modeled as ideal fixed points abstract motivated by ideas from the study of abstract data types we show how to interpret non well founded sets as fixed points of continuous transformations of an initial continuous algebra we conisder a preordered structure closely related to the set hf of well founded hereditarily finite sets by taking its ideal completion we obtain an initial continuous algebra in which we are able to solve all of the usual systems of equations that characterize hereditarily finite non well founded sets in this way we are able to obtain a structure which is isomorphic to hf 1 the non well founded analog of hf

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

on solving large strain hyperelastic problems with the natural element method in this paper an extension of the natural element method nem is presented to solve finite deformation problems since nem is a meshless method its implementation does not require an explicit connectivity definition consequently it is quite adequate to simulate large strain problems with important mesh distortions reducing the need for remeshing and projection of results extremely important in three dimensional problems nem has important advantages over other meshless methods such as the interpolant character of its shape functions and the ability of exactly reproducing essential boundary conditions along convex boundaries the nem extension generalizes this behaviour to non convex boundaries a total lagrangian formulation has been employed to solve different problems with large strains considering hyperelastic behaviour several examples are presented in two and three dimensions comparing the results with the ones of the finite element method nem performs better showing its important capabilities in this kind of applications copyright 2004 john wiley sons ltd

application of reproducing kernel particle methods in electromagnetics abstract motivated by the success of the reproducing kernal particle methods rkpm for solving the helmholtz equation rkpm is used as the interpolating basis functions for solving three dimensional electromagnetics problems the electromagnetics problem is the vector form of the wave equation treatment of the divergenceless condition is discussed as well as accurate treatment of the boundary conditions a simple shorted cylindrical waveguide is solved under te 11 excitation the accuracy of the rkpm is demonstrated for the three dimensional problem

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

an unified numerical approach of steady convection between two parallel plates this paper considers the problem of laminar forced convection between two parallel plates we present an unified numerical approach for some problems related to this case the problem of viscous dissipation with dirichlet and neumann boundary conditions and the graetz problem the solutions of these problems are obtained by a series expansion of the complete eigenfunctions system of some sturm liouville problems the eigenfunctions and eigenvalues of this sturm liouville problem are obtained by using galerkin s method numerical examples are given for viscous fluids with various brinkman numbers

semantics for finite delay abstract we produce a fully abstract model for a notion of process equivalence taking into account issues of fairness called by milner fair bisimilarity the model uses aczel s anti foundation axiom and it is constructed along the lines of the anti founded model for sccs given by aczel we revisit aczel s semantics for sccs where we prove a unique fixpoint theorem under the assumption of guarded recursion then we consider milner s extension of sccs to include a finite delay operator e working with fair bisimilarity we construct a fully abstract model which is also fully abstract for fortification we discuss the solution of recursive equations in the model the paper is concluded with an investigation of the algebraic theory of fair bisimilarity

on meije and sccs infinite sum operators vs non guarded definitions une des principales differences actuellement entre meije et sccs se trouve dans les limites que le calcul precedent etablit a l interieur de sa syntaxe sur la creation de choix de comportement inifini a chaque point du processus

a novel complex variable element free galerkin method for two dimensional large deformation problems abstract based on complex variable theory and moving least squares mls approximation the improved complex variable moving least squares icvmls approximation is discussed in this paper compared with complex variable moving least squares cvmls approximation the function in the icvmls approximation has an explicit physics meaning by using a new basis function the icvmls approximation can obtain greater precision and computational efficiency based on the icvmls approximation an improved complex variable element free galerkin icvefg method which belongs to a novel element free galerkin efg method is presented for two dimensional large deformation problems the galerkin weak form is employed to obtain the equations while the penalty method is used to apply the essential boundary conditions then the corresponding formulae of the icvefg method for two dimensional large deformation problems are obtained compared with the efg method the icvefg method has greater precision and efficiency

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

towards categorical models for fairness fully abstract presheaf semantics of sccs with finite delay we present a presheaf model for the observation of infinite as well as finite computations we give a concrete representation of the presheaf model as a category of generalised synchronisation trees and show that it is coreflective in a category of generalised transition systems which are a special case of the general transition systems of hennessy and stirling this can be viewed as a first step towards representing fairness in categorical models for concurrency the open map bisimulation is shown to coincide with extended bisimulation of hennessy and stirling which is essentially fair ctl bisimulation we give a denotational semantics of milner s sccs with finite delay in the presheaf model which differs from previous semantics by giving the meanings of recursion by final coalgebras and meanings of finite delay by initial algebras of the process equations for delay finally we formulate milner s operational semantics of sccs with finite delay in terms of generalised transition systems and prove that the presheaf semantics is fully abstract with respect to extended bisimulation

calculi for synchrony and asynchrony abstract a calculus for distributed computation is studied based upon four combinators a central idea is an abelian group of actions which models the interfaces between components of a distributed computing agent using a notion of bisimulation congruence relations are defined over computing agents and thence an algebraic theory is derived the calculus models both synchronous and asynchronous computation in particular it is shown that the author s calculus of communicating systems 1980 which is an asynchronous model is derivable from the calculus presented here

branching time and abstraction in bisimulation semantics in comparative concurrency semantics one usually distinguishes between linear time and branching time semantic equivalences milner s notion of observatin equivalence is often mentioned as the standard example of a branching time equivalence in this paper we investigate whether observation equivalence really does respect the branching structure of processes and find that in the presence of the unobservable action of ccs this is not the case therefore the notion of branching bisimulation equivalence is introduced which strongly preserves the branching structure of processes in the sense that it preserves computations together with the potentials in all intermediate states that are passed through even if silent moves are involved on closed ccs terms branching bisimulation congruence can be completely axiomatized by the single axion scheme a y z y a y z where a ranges over all actions and the usual loaws for strong congruence we also establish that for sequential processes observation equivalence is not preserved under refinement of actions whereas branching bisimulation is for a large class of processes it turns out that branching bisimulation and observation equivalence are the same as far as we know all protocols that have been verified in the setting of observation equivalence happen to fit in this class and hence are also valid in the stronger setting of branching bisimulation equivalence

algebraic calculi of processes and net expressions abstract it is shown that the meije algebra of processes can be expressed in a flow algebra the algebra of net expressions we then use this fact to derive a normal form for the calculus

an optimal adaptive fem for eigenvalue clusters the analysis of adaptive finite element methods in practice immediately leads to eigenvalue clusters which requires the simultaneous marking in adaptive finite element methods a first analysis for multiple eigenvalues of the recent work dai et al arxiv preprint 1210 1846v2 2013 introduces an adaptive method whose marking strategy is based on the element wise sum of local error estimator contributions for multiple eigenvalues this paper proves the optimality of a practical adaptive algorithm based on a lowest order conforming finite element method for eigenvalue clusters for the eigenvalues of the laplace operator in terms of nonlinear approximation classes all estimates are explicit in the initial mesh size the eigenvalues and the cluster width to clarify the dependence of the involved constants

multi scale methods in this paper four multiple scale methods are proposed the meshless hierarchical partition of unity is used as a multiple scale basis the multiple scale analysis with the introduction of a dilation parameter to perform multiresolution analysis is discussed the multiple field based on a 1 d gradient plasticity theory with material length scale is also proposed to remove the mesh dependency difficulty in softening localization problems a non local smoothing particle integration procedure with its multiple scale analysis are then developed these techniques are described in the context of the reproducing kernel particle method results are presented for elastic plastic one dimensional problems and 2 d large deformation strain localization problems to illustrate the effectiveness of these methods copyright 2000 john wiley sons ltd

cluster robust accuracy bounds for ritz subspaces abstract given an approximating subspace for a hermitian matrix a the rayleigh ritz procedure is commonly used to compute a few approximate eigenvalues called ritz values and corresponding approximate eigenvectors called ritz vectors in this paper new bounds on the canonical angles between the invariant subspace of a associated with its few extreme smallest or largest eigenvalues and its approximating ritz subspace in terms of the differences between ritz values and the targeted eigenvalues are obtained from this result various bounds are readily available to estimate how accurate the ritz vectors computed from the approximating subspace may be based on information on approximation accuracies in the ritz values the result is helpful in understanding how ritz vectors move towards eigenvectors while ritz values are made to move towards eigenvalues

estimates for the errors in eigenvalue and eigenvector approximation by galerkinmethods with particular attention to the case of multiple eigenvalues refined estimates for the errors in eigenvalue and eigenvector approximation by finite element or more generally galerkin methods as they apply to selfadjoint problems are presented particular attention is given to the case of multiple eigenvalues the results are new in this case the proof is based on a novel approach which yields the known results for simple eigenvalues in a simple way numerical computations are presented and analyzed in light of the theoretical results

an oscillation free adaptive fem for symmetric eigenvalue problems a refined a posteriori error analysis for symmetric eigenvalue problems and the convergence of the first order adaptive finite element method afem is presented the h 1 stability of the l 2 projection provides reliability and efficiency of the edge contribution of standard residual based error estimators for p 1 finite element methods in fact the volume contributions and even oscillations can be omitted for courant finite element methods this allows for a refined averaging scheme and so improves mao et al in adv comput math 25 1 3 135 160 2006 the proposed afem monitors the edge contributions in a bulk criterion and so enables a contraction property up to higher order terms and global convergence numerical experiments exploit the remaining l 2 error contributions and confirm our theoretical findings the averaging schemes show a high accuracy and the afem leads to optimal empirical convergence rates

cluster robust error estimates for the rayleigh ritz approximation ii estimates for eigenvalues this is the second part of a paper that deals with error estimates for the rayleigh ritz approximations of the spectrum and invariant subspaces of a bounded hermitian operator in a hilbert or euclidean space this part addresses the approximation of eigenvalues two kinds of estimates are considered i estimates for the eigenvalue errors via the best approximation errors for the corresponding invariant subspaces and ii estimates for the same via the corresponding residuals estimates of these two kinds are needed for respectively the a priori and a posteriory error analysis of numerical methods for computing eigenvalues the paper s major concern is to ensure that the estimates in question are accurate and cluster robust i e are not adversely affected by the presence of clustered i e closely situated eigenvalues among those of interest the paper s main new results introduce estimates for clustered eigenvalues whereby not only the distances between eigenvalues in the cluster are not present but also the distances between the cluster and the rest of the spectrum appear in asymptotically insignificant terms only

bisimulation and action refinement abstract for event structures with silent moves we consider several types of bisimulation that incorporate true concurrency to a varying degree and show how each can be lifted in a uniform way to a congruence with respect to action refinement we prove that we have constructed the coarsest congruences that respect interleaving pomset and history preserving bisimulation