a preconditioner for the steady state navier stokes equations we present a new method for solving the sparse linear system of equations arising from the discretization of the linearized steady state navier stokes equations also known as the oseen equations the solver is an iterative method of krylov subspace type for which we devise a preconditioner through a heuristic argument based on the fundamental solution tensor for the oseen operator the preconditioner may also be conceived through a weaker heuristic argument involving differential operators computations indicate that convergence for the preconditioned discrete oseen problem is only mildly dependent on the viscosity inverse reynolds number and most importantly that the number of iterations does not grow as the mesh size is reduced indeed since the preconditioner is motivated through analysis of continuous operators the number of iterations decreases for smaller mesh size which accords with better approximation of these operators

galerkin projected residual method applied to diffusion reaction problems a stabilized finite element method is presented for scalar and linear second order boundary value problems the method is obtained by adding to the galerkin formulation multiple projections of the residual of the differential equation at element level these multiple projections allow the generation of appropriate number of free stabilization parameters in the element matrix depending on the local space of approximation and on the differential operator the free parameters can be determined imposing some convergence and or stability criteria or by postulating the element matrix with the desired stability properties the element matrix of most stabilized methods such as gls and ggls methods can be obtained using this new method with appropriate choices of the stabilization parameters we applied this formulation to diffusion reaction problems optimal rates of convergency are numerically observed for regular solutions

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

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

ccs with hennessy s merge has no finite equational axiomatization this paper confirms a conjecture of bergstra and klop s from 1984 by establishing that the process algebra obtained by adding an auxiliary operator proposed by hennessy in 1981 to the recursion free fragment of milner s calculus of communicating systems is not finitely based modulo bisimulation equivalence thus hennessy s merge cannot replace the left merge and communication merge operators proposed by bergstra and klop at least if a finite axiomatization of parallel composition modulo bisimulation equivalence is desired

a multigrid preconditioner for stabilised discretisations of advection diffusion problems abstract this paper is concerned with the iterative solution of linear systems arising from stabilised discretisations of advection diffusion problems on stretched finite element grids using nonuniform grids of this type leads in general to very badly conditioned matrix problems we therefore consider using gmres in conjunction with a multigrid mg preconditioning strategy in particular we show that in order to achieve the grid size independent convergence which is characteristic of mg methods it is essential to use an effective stabilisation strategy at each level of the mg structure

bisimulation can t be traced in the concurrent language ccs two programs are considered the same if they are bisimilar several years and many researchers have demonstrated that the theory of bisimulation is mathematically appealing and useful in practice however bisimulation makes too many distinctions between programs we consider the problem of adding operations to ccs to make bisimulation fully abstract we define the class of gsos operations generalizing the style and technical advantages of ccs operations we characterize gsos congruence in as a bisimulation like relation called ready simulation bisimulation is strictly finer than ready simulation and hence not a congruence for any gsos language

on parameter choice and iterative convergence for stabilised discretisations of advection diffusion problems abstract in this work we consider the design of robust and efficient finite element approximation methods for solving advection diffusion equations specifically we consider the stabilisation of discrete approximations using uniform grids which do not resolve boundary layers as might arise using a multi level or multigrid iteration strategy to solve the discrete problem our analysis shows that when using supg streamline upwind finite element methodology there is a symbiotic relationship between best solution approximation and fast convergence of smoothers based on the standard gmres iteration we also show that stabilisation based on simple artificial diffusion perturbation terms an approach often advocated by multigrid practitioners is less appealing

an augmented lagrangian based approach to the oseen problem we describe an effective solver for the discrete oseen problem based on an augmented lagrangian formulation of the corresponding saddle point system the proposed method is a block triangular preconditioner used with a krylov subspace iteration like bicgstab the crucial ingredient is a novel multigrid approach for the 1 1 block which extends a technique introduced by schoberl for elasticity problems to nonsymmetric problems our analysis indicates that this approach results in fast convergence independent of the mesh size and largely insensitive to the viscosity we present experimental evidence for both isop2 p0 and isop2 p1 finite elements in support of our conclusions we also show results of a comparison with two state of the art preconditioners showing the competitiveness of our approach

classification of joinings for kleinian groups we classify all locally finite joinings of a horospherical subgroup action on g when g psl2 r or psl2 c and is a geometrically finite zariski dense subgroup of g this generalizes ratner s 1983 joining theorem for the case when is a lattice in g

on three grid fourier analysis for multigrid in this paper we present three grid fourier analysis for multigrid methods due to the recursive structure of a multigrid iteration this analysis can be deduced from the well known two grid fourier analysis the coarse grid correction part of multigrid algorithms can be more accurately evaluated with the three grid analysis we apply the analysis to several scalar equations and discretizations with an emphasis on problems with a multigrid coarse grid correction difficulty like upwind discretizations of the convection diffusion equation the main focus lies on possible improvements by carefully chosen galerkin operators and or by an additional acceleration with restarted gmres gmres m numerical test calculations validate the theoretical predictions

ordering effects on relaxation methods applied to the discrete one dimensional convection diffusion equation the authors present an analysis of relaxation methods for the one dimensional discrete convection diffusion equation based on norms of the iteration matrices in contrast to standard analytic techniques that use spectral radii these results show how the performance of iterative solvers is affected by directions of flow associated with the underlying operator and by orderings of the discrete grid points in particular for problems of size n relaxation against the flow incurs a latency of approximately n steps in which convergence is slow and red black relaxation incurs a latency of approximately n 2 steps there is no latency associated with relaxation that follows the flow these results are largely independent of the choice of discretization

efficient preconditioning of the linearized navier stokes equations for incompressible flow we outline a new class of robust and efficient methods for solving subproblems that arise in the linearization and operator splitting of navier stokes equations we describe a very general strategy for preconditioning that has two basic building blocks a multigrid v cycle for the scalar convection diffusion operator and a multigrid v cycle for a pressure poisson operator we present numerical experiments illustrating that a simple implementation of our approach leads to an effective and robust solver strategy in that the convergence rate is independent of the grid robust with respect to the time step and only deteriorates very slowly as the reynolds number is increased

an analysis of smoothing effects of upwinding strategies for the convection diffusion equation using a technique for constructing analytic expressions for discrete solutions to the convection diffusion equation we examine and characterize the effects of upwinding strategies on solution quality in particular for grid aligned flow and discretization based on bilinear finite elements with streamline upwinding we show precisely how the amount of upwinding included in the discrete operator affects solution oscillations and accuracy when different types of boundary layers are present this analysis provides a basis for choosing a streamline upwinding parameter which also gives accurate solutions for problems with non grid aligned and variable speed flows in addition we show that the same analytic techniques provide insight into other discretizations such as a finite difference method that incorporates streamline diffusion and the isotropic artificial diffusion method

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

a comparison of uniformly convergent difference schemes for two dimensional convection diffusion problems galerkin and petrov galerkin finite element methods are used to obtain new finite difference schemes for the solution of linear two dimensional convection diffusion problems numerical estimates are made of the rates of convergence of these schemes uniformly with respect to the perturbation parameter and these uniform rates are shown to compare favourably with those of established methods

gmres convergence analysis for a convection diffusion model problem when gmres y saad and m h schultz siam j sci statist comput 7 1986 pp 856 869 is applied to streamline upwind petrov galerkin supg discretized convection diffusion problems it typically exhibits an initial period of slow convergence followed by a faster decrease of the residual norm several approaches were made to understand this behavior however the existing analyses are solely based on the matrix of the discretized system and they do not take into account any influence of the right hand side determined by the boundary conditions and or source term in the pde therefore they cannot explain the length of the initial period of slow convergence which is right hand side dependent we concentrate on a frequently used model problem with dirichlet boundary conditions and with a constant velocity field parallel to one of the axes instead of the eigendecomposition of the system matrix which is ill conditioned we use its orthogonal transformation into a block diagonal matrix with nonsymmetric tridiagonal toeplitz blocks and offer an explanation of gmres convergence we show how the initial period of slow convergence is related to the boundary conditions and address the question why the convergence in the second stage accelerates

modular vs non modular preconditioners for fluid structure systems with large added mass effect in this article we address the numerical simulation of fluid structure interaction fsi problems featuring large added mass effect we analyze different preconditioners for the coupled system matrix obtained after space time discretization and linearization of the fsi problem the classical dirichlet neumann preconditioner has the advantage of modularity because it allows to reuse existing fluid and structure codes with minimum effort simple interface communication unfortunately its performance is very poor in case of large added mass effects alternatively we consider two non modular approaches the first one consists in preconditioning the coupled system with a suitable diagonal scaling combined with an ilut preconditioner the system is then solved by a krylov method the drawback of this procedure is that the combination of fluid and structure codes to solve the coupled system is not straightforward the second non modular approach we consider is a splitting technique based on an inexact block lu factorization of the linear fsi system the resulting algorithm computes the fluid velocity separately from the coupled pressure structure system at each iteration reducing the computational cost independently of the preconditioner the efficiency of semi implicit algorithms i e those that treat geometric and fluid nonlinearities in an explicit way is highlighted and their performance compared to the one of implicit algorithms all the methods are tested on three dimensional blood vessel systems the algorithm combining the non modular ilut preconditioner with krylov methods proved to be the fastest

analysis and comparison of geometric and algebraic multigrid for convection diffusion equations the discrete convection diffusion equations obtained from streamline diffusion finite element discretization are solved on both uniform meshes and adaptive meshes estimates of error reduction rates for both geometric multigrid gmg and algebraic multigrid amg are established on uniform rectangular meshes for a model problem our analysis shows that gmg with line gauss seidel smoothing and bilinear interpolation converges if h gg epsilon 2 3 and amg with the same smoother converges more rapidly than gmg if the interpolation constant beta in the approximation assumption of amg satisfies beta ll frac h sqrt epsilon alpha hs 1mm mbox where alpha big begin smallmatrix 1 h sqrt varepsilon 2 h ge sqrt varepsilon end smallmatrix on unstructured triangular meshes the performance of gmg and amg both as solvers and as preconditioners for gmres are evaluated numerical results show that gmres with amg preconditioning is a robust and reliable solver on both type of meshes

a low order galerkin finite element method for the navier stokes equations of steady incompressible flow a stabilization issue and iterative methods a galerkin finite element method is considered to approximate the incompressible navier stokes equations together with iterative methods to solve a resulting system of algebraic equations this system couples velocity and pressure unknowns thus requiring a special technique for handling we consider the navier stokes equations in velocity kinematic pressure variables as well as in velocity bernoulli pressure variables the latter leads to the rotation form of nonlinear terms this form of the equations plays an important role in our studies a consistent stabilization method is considered from a new view point theory and numerical results in the paper address both the accuracy of the discrete solutions and the effectiveness of solvers and a mutual interplay between these issues when particular stabilization techniques are applied 2002 published by elsevier science b v

on spurious oscillations at layers diminishing sold methods for convection diffusion equations part i a review abstract an unwelcome feature of the popular streamline upwind petrov galerkin supg stabilization of convection dominated convection diffusion equations is the presence of spurious oscillations at layers since the mid of the 1980s a number of methods have been proposed to remove or at least to diminish these oscillations without leading to excessive smearing of the layers the paper gives a review and state of the art of these methods discusses their derivation proposes some alternative choices of parameters in the methods and categorizes them some numerical studies which supplement this review provide a first insight into the advantages and drawbacks of the methods

a new stabilized finite element formulation for scalar convection diffusion problems the streamline and approximate upwind petrov galerkin method abstract a new stabilized and accurate finite element formulation for convection dominated problems is herein developed the basis of the new formulation is the choice of a new upwind function the upwind function chosen for the new method provokes its degeneration into the supg or cau methods depending on the approximate solution s regularity the accuracy and stability of the new formulation for the linear and scalar advection diffusion equation is demonstrated in several numerical examples

measurable rigidity of actions on infinite measure homogeneous spaces ii we consider the problems of measurable isomorphisms and join ings measurable centralizers and quotients for certain classes of ergodic group actions on infinite measure spaces our main focus is on systems of algebraic origin actions of lattices and other discrete subgroups g on homoge neous spaces g h where h is a sufficiently rich unimodular subgroup in a semi simple group g we also consider actions of discrete groups of isometries isom x of a pinched negative curvature space x acting on the space of horospheres hor x for such systems we prove that the only measurable isomorphisms joinings quotients etc are the obvious algebraic or geometric ones this work was inspired by the previous work of shalom and steger but uses completely different techniques which lead to more general results 1 introduction and statement of the main results

bisimulation through probabilistic testing abstract we propose a language for testing concurrent processes and examine its strength in terms of the processes that are distinguished by a test by using probabilistic transition systems as the underlying semantic model we show how a testing algorithm can distinguish with a probability arbitrarily close to one between processes that are not bisimulation equivalent we also show a similar result in a slightly stronger form for a new process relation called 2 3 bisimulation which lies strictly between that of simulation and bisimulation finally the ultimately strength of the testing language is shown to identify a new process relation called probabilistic bisimulation which is strictly stronger than bisimulation

a brief survey on numerical methods for solving singularly perturbed problems in the present paper a brief survey on computational techniques for the different classes of singularly perturbed problems is given this survey is a continuation of work performed earlier by the first author and contains the literature of the work done by the researchers during the years 2000 2009 however some older important relevant papers are also included in this survey we also mentioned those papers which are not surveyed in the previous survey papers by the first author of this paper see appl math comput 30 1989 223 259 130 2002 457 510 134 2003 371 429 for details thus this survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems

eigenvalues of the laplacian the first betti number and the congruence subgroup problem theorem 1 1 let f be an arithmetic lattice in the real lie group so n 1 n 2 if n 7 then assume r does not come from the twisted forms 3 6d4 if n 3 and f comes from the units of a quaternion algebra over a number field l with a unique complex embedding then assume l has a subfield of index 2 then for some finite index congruence subgroup fo of r the commutator quotient is infinite equivalently 1 fo the first betti number of the manifold fo hn is nonzero when 1 so n 1 so n is the n dimensional hyperbolic space

the ergodic theory of discrete isometry groups on manifolds of variable negative curvature this paper studies the ergodic theory at infinity of an arbitrary discrete isometry group acting on any hadamard manifold h of pinched variable negative curvature most of the results obtained by sullivan in the constant curvature case are generalized to the case of variable curvature we describe connections between measures supported on the limit set of dynamics of the geodesic flow and the geometry of m h we explore the relationship between the growth exponent of the group the hausdorff dimension of the limit set and the topological entropy of the geodesic flow the equivalence of various descriptions of an analogue of the hopf dichotomy is proved as applications we settle a question of j feldman and m ratner about the horocycle flow on a finite volume surface of negative curvature and obtain an asymptotic formula for the counting function of lattice points at the end of this paper we apply our results to the study of some rigidity problems more applications to mostow rigidity for discrete subgroups of rank 1 noncompact semisimple lie groups with infinite covolume will be published in subsequent papers by the author notations h is a hadamard manifold with pinched sectional curvature k 2 k k 1 k2 k1 0 is a non elementary discrete isometry group acting on h freely and properly discontinuously which is called fuchsian h is the ideal boundary of h m h is a complete riemannian manifold sh or sm is the unit tangent bundle g is the geodesic flow on sh or sm v t is the unique geodesic in sh resp sm with the initial velocity v 0 v sh resp sm v resp v is the asymptotic class of the geodesic v t resp v t l is the limit set of on h l is the radical limit set of in l is the nonwandering set of the geodesic flow on sm received by the editors may 7 1995 1991 mathematics subject classification primary 58f17 secondary 58f11 58f15 20h10 research at msri supported by nsf grant dms 8505550 also partially supported by nsf grant dms 9403870 and sfb 170 c 1996 american mathematical society

algebraic laws for nondeterminism and concurrency since a nondeterministic and concurrent program may in general communicate repeatedly with its environment its meaning cannot be presented naturally as an input output function as is often done in the denotational approach to semantics in this paper an alternative is put forth first a definition is given of what it is for two programs or program parts to be equivalent for all observers then two program parts are said to be observation congruent if they are in all program contexts equivalent the behavior of a program part that is its meaning is defined to be its observation congruence class the paper demonstrates for a sequence of simple languages expressing finite terminating behaviors that in each case observation congruence can be axiomatized algebraically moreover with the addition of recursion and another simple extension the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties

rule formats for distributivity this paper proposes rule formats for structural operational semantics guaranteeing that certain binary operators are left distributive with respect to a set of binary operators examples of left distributivity laws from the literature are shown to be instances of the provided formats some conditions ensuring the invalidity of the left distributivity law are also offered

turning sos rules into equations abstract many process algebras are defined by structural operational semantics sos indeed most such definitions are nicely structured and fit the gsos format of bloom et al j assoc comput mach to appear we give a procedure for converting any gsos language definition to a finite complete equational axiom system possibly with one infinitary induction principle which precisely characterizes strong bisimulation of processes

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

modeling subgrid viscosity for advection diffusion problems we analyse the effect of the subgrid viscosity on a finite element discretisation with piecewise linear elements of a linear advection diffusion scalar equation we point out the importance of a proper tune up of the viscosity coefficient and we propose a heuristic method for obtaining reasonable values for it the extension to more general problems is then hinted in the last section

rigidity of group actions on homogeneous spaces iii consider homogeneous g h and g f for an s algebraic group g a lattice acts on the left strictly conservatively the following rigidity results are obtained morphisms factors and joinings defined apriori only in the measurable category are in fact algebraically constrained arguing in an elementary fashion we manage to classify all the measurable commuting with the action assuming ergodicity we find they are algebraically defined