stabilized finite element schemes with lbb stable elements for incompressible flows we study stabilized fe approximations of supg type to the incompressible navier stokes problem revisiting the analysis for the linearized model we show that for conforming lbb stable elements the design of the stabilization parameters for many practical flows differs from that commonly suggested in literature and initially designed for the case of equal order approximation then we analyze a reduced supg scheme often used in practice for lbb stable elements to provide the reduced scheme with appropriate stability estimates we introduce a modified lbb condition which is proved for a family of fe approximations the analysis is given for the linearized equations numerical experiments for some linear and nonlinear benchmark problems support the theoretical results

an analysis of the time integration algorithms for the finite element solutions of incompressible navier stokes equations based on a stabilised formulation abstract this work is concerned with the analysis of time integration procedures for the stabilised finite element formulation of unsteady incompressible fluid flows governed by the navier stokes equations the stabilisation technique is combined with several different implicit time integration procedures including both finite difference and finite element schemes particular attention is given to the generalised method and the linear discontinuous in time finite element scheme the time integration schemes are first applied to two model problems represented by a first order differential equation in time and the one dimensional advection diffusion equation and subjected to a detailed mathematical analysis based on the fourier series expansion in order to establish the accuracy and efficiency of the time integration schemes for the navier stokes equations a detailed computational study is performed of two standard numerical examples unsteady flow around a cylinder and flow across a backward facing step it is concluded that the semi discrete generalised method provides a viable alternative to the more sophisticated and expensive space time methods for simulations of unsteady flows of incompressible fluids governed by the navier stokes equations

boundary recovery for three dimensional conforming delaunay triangulation we present an efficient boundary recovery method for conforming delaunay triangulation of three dimensional domains our method combines local transformations like edges faces swappings and modified constrained delaunay refinement like edges faces splittings to recover the missing boundary edges and faces its convergence is theoretically proved its effectiveness is also demonstrated through some meshing examples

generation of tetrahedral mesh of variable element size by sphere packing over an unbounded 3d domain this paper describes an algorithm for the generation of tetrahedral mesh of specified element size over an unbounded three dimensional domain starting from an arbitrary point in space defined as the origin and guided by the concept of advancing front spheres of size compatible with the specified element size are packed tightly together one by one to form a cluster of spheres of different sizes the compactness of the cluster of spheres is achieved by packing spheres at a site closest to the origin in a densest manner with tangent but no overlapping with as many other spheres as possible in view of these criteria a rotational mechanism between spheres is innovated which allows the newly inserted sphere to follow the path by rotation between existing spheres until the lowest point is reached the centres of the packing spheres provide ideal locations for delaunay point insertion to form a triangulation of tetrahedral elements of size compatible with the specified value spheres of random size distribution or of size specified by a node spacing function are packed by the proposed algorithm in all test examples high quality tetrahedral elements of size consistent with the specified node spacing are generated the process is fast and robust and the time complexity for mesh generation is expected to be almost linear however in the present implementation a quasi linear time relationship is observed as a search for the nearest node on the front is proposed in the sphere packing process the memory requirement has been kept to a minimum as no additional data structure other than the adjacency relationship of the tetrahedral elements as required by the delaunay triangulation is stored the structure of the advancing frontal surface needs not be explicitly constructed nor updated as it is simply not required in the sphere packing process

fast and robust delaunay tessellation in periodic domains an algorithm is presented for constructing three dimensional delaunay tessellations in periodic domains applications include mesh generation for periodic transport problems and geometric decomposition for modelling particulate structures the algorithm is a point insertion technique and although the general framework is similar to point insertion in a convex hull a number of new issues are introduced by periodicity these issues are discussed in detail in the context of the computational algorithm examples are given for the tessellation of random points and random sphere packings performance data for the algorithm are also presented these data show an empirical scaling of the computation time with size of o n1 11 and tessellation rates of 7000 14000 tetrahedrons per second for the problems studied up to 105 points a breakdown of the performance is given which shows the computational load is shared most heavily by two specific parts of the point insertion procedure copyright 2002 john wiley sons ltd

dynamic journeying under uncertainty abstract we introduce a journey planning problem in multi modal transportation networks under uncertainty the goal is to find a journey possibly involving transfers between different transport services from a given origin to a given destination within a specified time horizon due to uncertainty in travel times the arrival times of transport services at public transport stops are modeled as random variables if a transfer between two services is rendered unsuccessful the commuter has to reconsider the remaining path to the destination the problem is modeled as a markov decision process in which states are defined as paths in the transport network the main contribution is a backward induction method that generates an optimal policy for traversing the public transport network in terms of maximizing the probability of reaching the destination in time by assuming history independence and independence of successful transfers between services we obtain approximate methods for the same problem analysis and numerical experiments suggest that while solving the path dependent model requires the enumeration of all paths from the origin to the destination the proposed approximations may be useful for practical purposes due to their computational simplicity in addition to on time arrival probability we show how travel and overdue costs can be taken into account making the model applicable to freight transportation problems

error exponents of modulo additive noise channels with side information at the transmitter consider the optimum strategy for using channel state side information in transmission over a modulo additive noise channel with state dependent noise where the receiver does not have access to the side information si previous work showed that capacity wise the optimum transmitter shifts each code letter by a prediction of the noise sample based on the si we show that this structure achieves also the random coding error exponent and therefore is optimum at some range of rates below capacity specifically the optimum transmitter predictor minimizes the renyi entropy of the prediction error the renyi order depends on the rate and goes to one corresponding to shannon entropy for rates close to capacity in contrast it is shown that this prediction strategy may not be optimal at low transmission rates

a boundary integral modification of the galerkin least squares formulation for the stokes problem abstract a new boundary integral term is added to the galerkin least squares gls formulation the new formulation compensates for a lack of consistency noted for the traditional gls method when bilinear interpolation is used on quadrilateral elements exact solutions at the nodes are obtained for poiseuille flow and another test problem and the pressure singularity for the driven cavity is better captured

metric based mesh adaptation for 2d lagrangian compressible flows in this paper we present a method to compute compressible flows in 2d it uses two steps a lagrangian step and a metric based triangular mesh adaptation step computational mesh is locally adapted according to some metric field that depends on physical or geometrical data this mesh adaptation step embeds a conservative remapping procedure to satisfy consistency with euler equations the whole method is no more lagrangian after describing mesh adaptation patterns we recall the metric formalism then we detail an appropriate remapping procedure which is first order and relies on exact intersections we give some hints about the parallel implementation finally we present various numerical experiments which demonstrate the good properties of the algorithm

note an improved conditional monte carlo technique for the stochastic shortest path problem this paper describes a simulation procedure for estimating the distribution function of the shortest path length in a network with random arc lengths the method extends the concept of conditional monte carlo utilizing special properties of the uniformly directed cutsets and the unique arcs the objective here is to reduce the sampling effort and utilize known probability information to derive multivariate integrals of lower dimension the experimental results show that the proposed method is substantially cost effective and performs better than traditional monte carlo and conditional methods

hp adaptive time integration based on the bdf for viscous flows this paper presents a procedure based on the backward differentiation formulas of order 1 to 5 to obtain efficient time integration of the incompressible navier stokes equations the adaptive algorithm performs both stepsize and order selections to control respectively the solution accuracy and the computational efficiency of the time integration process the stepsize selection h adaptivity is based on a local error estimate and an error controller to guarantee that the numerical solution accuracy is within a user prescribed tolerance the order selection p adaptivity relies on the idea that low accuracy solutions can be computed efficiently by low order time integrators while accurate solutions require high order time integrators to keep computational time low the selection is based on a stability test that detects growing numerical noise and deems a method of order p stable if there is no method of lower order that delivers the same solution accuracy for a larger stepsize hence it guarantees both that 1 the used method of integration operates inside of its stability region and 2 the time integration procedure is computationally efficient the proposed time integration procedure also features a time step rejection and quarantine mechanisms a modified newton method with a predictor and dense output techniques to compute solution at off step points

a new stabilization of adaptive step trapezoid rule based on finite difference interrupts the adaptive step trapezoid rule tr is a generally effective numerical integrator but it is prone to ringing instability and solution stall we introduce a new stabilization algorithm based on finite difference interrupts fdi that reduces ringing and prevents stall unlike previously reported stabilization schemes our algorithm achieves stability and second order accuracy without incurring significant computational cost or spurious diffusion tr with fdi is at least as stable and accurate as existing methods when solving the prototypical scalar problem we demonstrate that it has better stability accuracy and cost when solving the tightly coupled system describing free surface flows of viscoelastic liquids though we demonstrate tr with fdi in the context of a finite element method of lines it is applicable to any tr based algorithm

least squares finite element formulations for viscous incompressible and compressible fluid flows abstract we present least squares based finite element formulations for the numerical solution of viscous fluid flows governed by the navier stokes equations as an alternate approach to the well known weak form galerkin finite element formulations the use of least squares principles leads to a variational unconstrained minimization problem where compatibility conditions between approximation spaces never arise and the resulting linear algebraic problem will have a symmetric positive definite coefficient matrix we address the issue of norm equivalence of the least squares functional and its implications on the resulting finite element model in particular we develop an understanding of the compromise that must exist between the optimality and practicality of the finite element model the latter measured in terms of c k regularity across inter element boundaries we show through numerical examples that for the traditional c 0 basis such a compromise is possible when high p levels are used to span the finite element spaces when a low p level solution is desired guidelines are presented to obtain a reliable least squares collocation solution numerical examples are presented to demonstrate the high and low p level approaches these include incompressible flow past two circular cylinders in a side by side arrangement for gap sizes s d 2 0 and 0 85 incompressible flow past a square cylinder and subsonic transonic and supersonic compressible flow past a circular cylinder in addition we present a discontinuous least squares formulation where c k regularity across inter element boundaries is enforced in a weak sense through the least squares functional allowing for h and p type non conformities in the computational domain

a binary analog to the entropy power inequality let x sub n y sub n be independent stationary binary random sequences with entropy h x h y respectively let h zeta zeta log zeta 1 zeta log 1 zeta 0 or sigma x sigma y where sigma z h sup 1 h z and alpha beta alpha 1 beta beta 1 alpha when y sub n are independent identically distributed this reduces to mrs gerber s lemma from a d wyner and j ziv 1973

a least squares finite element formulation for unsteady incompressible flows with improved velocity pressure coupling in the weak form galerkin formulation for incompressible flows the pressure has a well understood role at all times it may be interpreted as a lagrange multiplier that enforces the divergence free constraint on the velocity field this is not the case in least squares formulations for incompressible flows where the divergence free constraint is enforced in a least squares sense in a variational setting of residual minimization thus the role of the pressure in a least squares formulation is rather vague we find that this lack of velocity pressure coupling in least squares formulations may induce spurious temporal pressure oscillations when using the non stationary form of the equations we present a least squares formulation with improved velocity pressure coupling based on the use of a regularized divergence free constraint a first order system least squares fosls approach based on velocity pressure and vorticity is used to allow the use of practical c0 element expansions in the finite element model we use high order spectral element expansions in space and second and third order time stepping schemes excellent conservation of mass and accuracy of computed pressure metrics are demonstrated in the numerical results

stochastic shortest path problems with piecewise linear concave utility functions this paper considers a stochastic shortest path problem where the arc lengths are independent random variables following a normal distribution in this problem the optimal path is one that maximizes the expected utility with the utility function being piecewise linear and concave such a utility function can be used to approximate nonlinear utility functions that capture risk averse behaviour for a wide class of problems the principal contribution of this paper is the development of exact algorithms to solve large problem instances two algorithms are developed and incorporated in labelling procedures computational testing is done to evaluate the performance of the algorithms overall both algorithms are very effective in solving large problems quickly the relative performance of the two algorithms is found to depend on the curvature of the piecewise linear utility function

a new family of projection schemes for the incompressible navier stokes equations with control of high frequency damping abstract a simple spatially discrete model problem consisting of mass points and dash pots is presented which allows for the assessment of the properties of different projection schemes for the solution of the incompressible navier stokes equations in particular the temporal accuracy the stability and the numerical damping are investigated the present study suggests that it is not possible to formulate a second order accurate projection pressure correction scheme which possesses any high frequency damping motivated by this observation two new families of projection schemes are proposed which are developed from the generalised midpoint rule and from the generalised method respectively and offer control over high frequency damping both schemes are investigated in detail on the basis of the model problem and subsequently implemented in the context of a finite element formulation for the incompressible navier stokes equations comprehensive numerical studies of the flow in a lid driven cavity and the flow around a cylinder are presented the observations made are in agreement with the conclusions drawn from the model problem

a better consistency for low order stabilized finite element methods abstract the standard implementation of stabilized finite element methods with a piece wise function space of order lower than the highest derivative present in the partial differential equation often suffers from a weak consistency that can lead to reduced accuracy the popularity of these low order elements motivates the development of a new stabilization operator which globally reconstructs the derivatives not present in the local element function space this new method is seen to engender a stronger consistency leading to better convergence and improved accuracy applications to the navier stokes equations are given which illustrate the improvement at a negligible additional cost

finite element stabilization parameters computed from element matrices and vectors abstract we propose new ways of computing the stabilization parameters used in the stabilized finite element methods such as the streamline upwind petrov galerkin supg and pressure stabilizing petrov galerkin pspg formulations the parameters are computed based on the element level matrices and vectors which automatically take into account the local length scales advection field and the reynolds number we describe how we compute these parameters in the context of first a time dependent advection diffusion equation and then the navier stokes equations of unsteady incompressible flows

delaunay s mesh of a convex polyhedron in dimension d application to arbitrary polyhedra this paper presents a method for creating a delaunay triangulation connected to a set of specified points the theoretical aspect is recalled for an arbitrary dimension and the method is discussed in order to derive a practical approach valid for dimensions 2 and 3 which is simple robust and well adapted to computation convex polyhedral and arbitrary polyhedral situations are introduced

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

fast iterative solvers for buoyancy driven flow problems we outline a new class of robust and efficient methods for solving the navier stokes equations with a boussinesq model for buoyancy driven flow we describe a general solution strategy that has two basic building blocks an implicit time integrator using a stabilized trapezoid rule with an explicit adams bashforth method for error control and a robust krylov subspace solver for the spatially discretized system we present numerical experiments illustrating the efficiency of the chosen preconditioning schemes with respect to the discretization parameters

implicit finite incompressible elastodynamics with linear finite elements a stabilized method in rate form abstract we propose a stabilization method for linear tetrahedral finite elements suitable for the implicit time integration of the equations of nearly and fully incompressible nonlinear elastodynamics in particular we derive and discuss a generalized framework for stabilization and implicit time integration that can comprehensively be applied to the class of all isotropic hyperelastic models in this sense the presented development can be considered an important extension and complement to the stabilization approach proposed by the authors in previous work which was instead focused on explicit time integration and simple neo hookean models for nearly incompressible elasticity with the goal of computational efficiency we also present a two step block gauss seidel strategy for the time update of displacements velocities and pressures specifically a mixed system of equations for the velocity and pressure is updated implicitly in a first stage and the displacements are updated explicitly in a second stage the proposed mixed formulation is then embedded in newton type strategies for the nonlinear solution of the equations of motion various implicit time integration strategies are considered and particularly we focus on high frequency dissipation time integrators which are preferable in transient mechanics applications an extensive set of numerical computations with linear tetrahedral elements is presented to demonstrate the performance of the proposed approach

consistent supg method for transient transport problems stability and convergence we consider the time space discretization of the transient advection equation discretization in space is performed by the streamline upwind petrov galerkin method and in time we use an a stable finite difference operator the formulation is strongly consistent in the sense that the time derivative is included in the stabilization term uniform stability of the general formulation is proved under a regularity condition on data or a moderate inverse cfl condition that allows for optimal choices of the discretization parameters both the backward euler method bdf1 the crank nicolson scheme and the second order backward differentiation formula bdf2 enter the framework and quasi optimal convergence is proved for these schemes

feedback does not increase the capacity of discrete channels with additive noise we consider discrete time finite alphabet channels with additive random noise we show that output feedback does not increase the capacity of such channels this result holds in the most general case i e for arbitrary additive noise processes

technical note a note on the stochastic shortest route problem an optimality index for choosing the shortest route in an acyclic stochastic network has recently been proposed the present note identifies certain anomalies in using that index and proposes another optimality index the results of using these indices are compared in a simple example

arc reduction and path preference in stochastic acyclic networks the paper presents a heuristic for determining the path that maximizes the expected utility of a stochastic acyclic network the focus is on shortest route problems where a general nonlinear utility function is used to measure outcomes for such problems enumerating all feasible paths is the only way to guarantee that the global optimum has been found alternatively we develop a reduction algorithm based on stochastic dominance to speed up the computations monte carlo simulation is used to evaluate the approach in all 70 test problems comprising 20 to 60 nodes are randomly generated and analyzed the results indicate that the heuristic produces significant computational saving as the size of the network grows and that the quality of the reduced network solutions are better than those obtained from the original formulation

coupling stabilized finite element methods with finite difference time integration for advection diffusion reaction problems abstract we present some numerical schemes for the unsteady advection diffusion reaction linear problem in one space dimension we investigate two possible different ways of combining the discretization in time and in space where the sequence of the discretizations is interchanged discretization in time is performed by using the crank nicolson finite difference scheme while for the space discretization we consider three classical stabilized finite element schemes and the more recent link cutting bubble strategy proposed in f brezzi g hauke l d marini g sangalli link cutting bubbles for the stabilization of convection diffusion reaction problems math models methods appl sci 13 2003 445 461 numerical experiments are presented to assess and valuate the capabilities of the proposed methods an l 1 error analysis of the link cutting bubble strategy for solving the steady problem is included

an adaptive remeshing strategy for flows with moving boundaries and fluid structure interaction the primary objective of this work is to extend the capability of the arbitrary lagrangian eulerian ale based strategy for solving fluid structure interaction problems this is driven by the fact that the ale mesh movement techniques will not be able to treat problems in which fluid structure interface experiences large motion in addition for certain problems the need arises to capture accurately flow features such as a region with high gradients of the solution variables this can be achieved by incorporating an adaptive remeshing procedure into the solution strategy as in our previous works comput methods appl mech eng 2006 195 1633 1666 comput methods appl mech eng 2006 195 5754 5779 here the fluid flow is governed by the incompressible navier stokes equations and modelled by using stabilized low order velocity pressure finite elements the motion of the fluid domain is accounted for by an arbitrary lagrangian eulerian ale strategy the flexible structure is represented by means of appropriate standard finite element formulations while the motion of the rigid body is described by rigid body dynamics for temporal discretization of both fluid and solid bodies the discrete implicit generalized method is employed the resulting strongly coupled set of non linear equations is then solved by means of a novel partitioned solution procedure which is based on the newton raphson methodology and incorporates full linearization of the overall incremental problem within the adaptive solution strategy the quality of fluid mesh and the solution quality indicator are evaluated regularly and compared against the appropriate remeshing criteria to decide whether a remeshing step is required the adaptive remeshing procedure follows closely the standard computational procedure in which the adaptive remeshing process produces a mesh that can capture salient features of the flow field for the problems under consideration in this work the motion of the fluid boundary very often results in boundaries with very high curvatures and a fluid domain that contain areas with small cross sections to be able to generate meshes that give result with acceptable accuracy these local geometrical features need to be included in determining the element density distribution the numerical examples demonstrate the robustness and efficiency of the methodology copyright 2007 john wiley sons ltd

adaptive time stepping for incompressible flow part ii navier stokes equations we outline a new class of robust and efficient methods for solving the navier stokes equations we describe a general solution strategy that has two basic building blocks an implicit time integrator using a stabilized trapezoid rule with an explicit adams bashforth method for error control and a robust krylov subspace solver for the spatially discretized system we present numerical experiments illustrating the potential of our approach

a time domain unstructured grid approach to the simulation of electromagnetic scattering in piecewise homogeneous media abstract the simulation of the scattering of plane electromagnetic waves by obstacles constructed from piecewise homogeneous material media is considered the governing equations are maxwell s equations which are expressed in a conservation form the solution is obtained on a grid consisting of an unstructured assembly of linear triangular elements in 2d by modifying a technique developed originally for the solution of the compressible euler equations the computed solution is used to determine the radar scattering width of the obstacle

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

shape reconstruction and volume meshing for complex solids the reconstruction of a solid surface from a series of cross sections and the generation of a volume mesh that conforms with a prescribed surface are issues that arise in numerous applications we describe an approach to both these problems that is based on the generation of a tetrahedral mesh which automatically captures a triangulation of the surface points a simple algorithm for introducing a set of interior points permits a simple partition of the volume mesh into two disjoint sets of tetrahedra such that one set determines the interior of the solid while the second determines the exterior

analysis of the block gauss seidel solution procedure for a strongly coupled model problem with reference to fluid structure interaction the block gauss seidel procedure is widely used for the resolution of the strong coupling in the computer simulation of fluid structure interaction based on a simple model problem this work presents a detailed analysis of the convergence behaviour of the method in particular the model problem is used to highlight some aspects that arise in the context of the application of the block gauss seidel method to fsi problems thus the effects of the time integration schemes chosen of relaxation techniques of physical constraints and non linearities on the convergence of the iterations are investigated

centroidal voronoi tessellation based finite element superconvergence in this article a finding on finite element superconvergence is reported the laplacian operator with dirichlet boundary condition is considered the linear finite element solutions have an o h2 0 5 superconvergence in l2 norm at nodes on an almost equilateral triangular mesh generated based on centroidal voronoi tessellation for an arbitrary 2d bounded domain extensive numerical examples are presented to demonstrate the superconvergence property copyright 2008 john wiley sons ltd

stabilized shock hydrodynamics i a lagrangian method abstract a new supg stabilized formulation for lagrangian hydrodynamics of materials satisfying mie gruneisen equation of state is proposed it allows the use of simplex type triangular tetrahedral meshes as well as the more commonly used brick type quadrilateral hexahedral meshes the proposed method yields a globally conservative formulation in which equal order interpolation p1 or q1 isoparametric finite elements is applied to velocities displacements and pressure as a direct consequence and in contrast to traditional cell centered multidimensional hydrocode implementations the proposed formulation allows a natural representation of the pressure gradient on element interiors the supg stabilization involves additional design requirements specific to the lagrangian formulation a discontinuity capturing operator in the form of a noh type viscosity with artificial heat flux is used to preserve stability and smoothness of the solution in shock regions a set of challenging shock hydrodynamics benchmark tests for the euler equations of gas dynamics in one and two space dimensions is presented in the two dimensional case computations performed on quadrilateral and triangular grids are analyzed and compared these results indicate that the new formulation is a promising technology for hydrocode applications

a new finite element formulation for computational fluid dynamics x the compressible euler and navier stokes equations a space time element method is presented for solving the compressible euler and navier stokes equations the proposed formulation includes the variational equation predictor multi corrector algorithms and boundary conditions the variational equation is based on the time discontinuous galerkin method in which the physical entropy variables are employed a least squares operator and a discontinuity capturing operator are added resulting in a high order accurate and unconditionally stable method implicit explicit predictor multi corrector algorithms applicable to steady as well as unsteady problems are presented techniques are developed to enhance their efficiency implementation of boundary conditions is addressed in particular a technique is introduced to satisfy nonlinear essential boundary conditions and a consistent method is presented to calculate boundary fluxes numerical results are presented to demonstrate the performance of the method

transient adaptivity applied to two phase incompressible flows an anisotropic adaptation process is applied to a three dimensional incompressible two phase flow solver the solver uses a level set finite element method on unstructured tetrahedral meshes we show how the level set function can be used to build an anisotropic mesh with good properties some computations with a strong transient character and large densities ratios 1 1000 are presented we show that the efficiency of the computations can be deeply enhanced by mesh adaptations

a fictitious domain distributed lagrange multiplier based fluid structure interaction scheme with hierarchical b spline grids abstract we present a numerical scheme for fluid structure interaction based on hierarchical b spline grids and fictitious domain distributed lagrange multipliers the incompressible navier stokes equations are solved over a cartesian grid discretised with b splines the fluid grid near the immersed solids is refined locally using hierarchical b splines the immersed solid is modelled as geometrically exact beam discretised with standard linear lagrange shape functions the kinematic constraint at the fluid solid interface is enforced with distributed lagrange multipliers the unconditionally stable and second order accurate generalised method is used for integration in time for both the fluid and solid domains a fully implicit and fully coupled solution scheme is developed by using the newton raphson method to solve the non linear system of equations obtained with galerkin weak formulation first the spatial and temporal convergence of the proposed scheme is assessed by studying steady and unsteady flow past a fixed cylinder then the scheme is applied to several benchmark problems to demonstrate the efficiency and robustness of the proposed scheme the results obtained with the present scheme are compared with the reference values

space time coupled spectral hp least squares finite element formulation for the incompressible navier stokes equations we consider least squares finite element models for the numerical solution of the non stationary navier stokes equations governing viscous incompressible fluid flows the paper presents a formulation where the effects of space and time are coupled resulting in a true space time least squares minimization procedure as opposed to a space time decoupled formulation where a least squares minimization procedure is performed in space at each time step the formulation is first presented for the linear advection diffusion equation and then extended to the navier stokes equations the formulation has no time step stability restrictions and is spectrally accurate in both space and time to allow the use of practical c0 element expansions in the resulting finite element model the navier stokes equations are expressed as an equivalent set of first order equations by introducing vorticity as an additional independent variable and the least squares method is used to develop the finite element model of the governing equations high order element expansions are used to construct the discrete model the discrete model thus obtained is linearized by newton s method resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix free form spectral convergence of the l2 least squares functional and l2 error norms in space time is verified using a smooth solution to the two dimensional non stationary incompressible navier stokes equations numerical results are presented for impulsively started lid driven cavity flow oscillatory lid driven cavity flow transient flow over a backward facing step and flow around a circular cylinder the results demonstrate the predictive capability and robustness of the proposed formulation even though the space time coupled formulation is emphasized we also present the formulation and numerical results for least squares space time decoupled finite element models the numerical results show that the space time coupled formulation has superior predictive capabilities for flows demanding high space time resolution exemplified here by the transient flow over a backward facing step

bounding the project completion time distribution in pert networks we consider the pert model of a project composed of activities whose durations are random variables with known distributions for the situations in which the activity durations are completely independent we present a new method for obtaining a probability distribution function that bounds the exact probability distribution of the project completion time from below the bounding distribution can be used to obtain an upper bound on the mean completion time of the project we also prove and illustrate that this bounding distribution is better tighter than any of the existing lower bounds implying that the corresponding upper bound on the mean completion time is tighter than any of the existing upper bounds

delaunay triangulation in computational fluid dynamics abstract a method which utilises the delaunay criterion is described by which computational grids consisting of assemblies of triangles or tetrahedra can be constructed an algorithm is briefly outlined to construct the triangulation and its dual the voronoi diagram issues related to how to construct boundary conforming grids from such a triangulation are addressed and details are presented of how grid points within the domain can be generated automatically the point generation algorithm utilises either the given boundary point distribution or for grid adaption a background mesh computational aspects of constructing the triangulation in both 2 and 3 dimensions are covered examples of meshes and flow computations for a range of aerospace geometries are presented

a generalized α method for integrating the filtered navier stokes equations with a stabilized finite element method abstract a generalized method is developed and analyzed for linear first order systems the method is then extended to the filtered navier stokes equations within the context of a stabilized finite element method the formulation is studied through the application to laminar flow past a circular cylinder and turbulent flow past a long transverse groove the method is formulated to obtain a second order accurate family of time integrators whose high frequency amplification factor is the sole free parameter such an approach allows the replication of midpoint rule zero damping gear s method maximal damping or anything in between

anisotropic mesh adaptation with optimal convergence for finite elements using embedded geometries this paper presents a numerical study of a recent technique that consists in modeling embedded geometries by a level set representation in combination with local anisotropic mesh refinement the local anisotropic mesh procedure is suitable for various orders p of finite element approximations this method proves beneficial in simulations involving complex geometries as it suppresses the need for the tedious process of body fitted mesh generation without altering the finite element formulation nor the prescription of boundary conditions the first part of the study deals with a simple laplace problem featuring a planar interface on which a dirichlet boundary condition is imposed it is shown that the appropriate amount of local isotropic refinement yields the optimal convergence rate for various finite element orders p unlike uniform refinement anisotropic refinement further ensures geometric convergence and limits the growth of the number of unknowns then we explain how to use metric based anisotropic adaptation to obtain nearly body fitted meshes with arbitrary geometries the optimal rate of convergence both for the solution and the geometry is demonstrated on 2d and 3d academic laplace problems involving curved boundaries finally applications in the field of fluid dynamics and material science are presented the results for these simulations successfully converge towards data from the literature analytical solutions or values obtained with body fitted meshes

fast and accurate simulations of air cooled structures there are fields of engineering for which the cad based navier stokes solvers are too expensive architecture and medicine for blood flows are two such examples mesh generation and adaptation is also a bottleneck because the users are not expected to have the know how we report here on a navier stokes solver for incompressible temperature and time dependent flows dedicated to architectural applications the building blocks are not new a finite element method with time implicit pressure projection steps and mesh adaptativity but putting them together in an easy to use and efficient 3d code is the challenge which motivates this paper for non engineering applications the user interface is a big problem in an earlier attempt we designed freefem3d based on a fictitious domain discretization thus avoiding boundary fitted mesh however it turned out that the display of the solutions requires a boundary fitted mesh it is possible to generate a feasible surface mesh for graphics but it is much more difficult to generate a feasible surface mesh for fem in this project the user interface is taken from freefem3d then with a marching cube algorithm we produce a graphic only feasible mesh finally a surface mesh adapted to a fem computation is constructed with an adaptation module and the result is used as input to a delaunay volumic mesh generator the solver is optimized and parallelized all modules are the authors work three applications are presented for which the data preparation takes less than a day and results are obtained overnight on a pc cluster one of the application is presented in details it is an air cooling system for a canister containing radio nucleides

fourier analysis of semi discrete and space time stabilized methods for the advective diffusive reactive equation i supg abstract in this paper the work initiated in part one and two is extended to the transient subgrid scale gradient subgrid scale sgs gsgs stabilized method temporal accuracy and stability of semi discrete and time discontinuous space time versions of the method are examined for transient advection diffusion reaction problems also for the above methods predictor multi corrector algorithms are analyzed with special emphasis on mass and source lumping which has been shown to enhance both stability and accuracy of explicit stabilized methods it will be shown that the parent supg sgs and sgs gsgs methods perform very similarly and that explicit predictor multi corrector mass source lumping practically retains the accuracy of the parent method while gaining stability

comparison of some finite element methods for solving the diffusion convection reaction equation abstract in this paper we describe several finite element methods for solving the diffusion convection reaction equation none of them is new although the presentation is non standard in an effort to emphasize the similarities and differences between them in particular it is shown that the classical supg method is very similar to an explicit version of the characteristic galerkin method whereas the taylor galerkin method has a stabilization effect similar to a sub grid scale model which is in turn related to the introduction of bubble functions

a stabilised immersed boundary method on hierarchical b spline grids abstract in this work an immersed boundary finite element method is proposed which is based on a hierarchically refined cartesian b spline grid and employs the non symmetric and penalty free version of nitsche s method to enforce the boundary conditions the strategy allows for h and p refinement and employs a so called ghost penalty term to stabilise the cut cells an effective procedure based on hierarchical subdivision and sub cell merging which avoids excessive numbers of quadrature points is used for the integration of the cut cells a basic laplace problem is used to demonstrate the effectiveness of the cut cell stabilisation and of the penalty free nitsche method as well as their impact on accuracy the methodology is also applied to the incompressible navier stokes equations where the supg pspg stabilisation is employed simulations of the lid driven cavity flow and the flow around a cylinder at low reynolds number show the good performance of the methodology excessive ill conditioning of the system matrix is robustly avoided without jeopardising the accuracy at the immersed boundaries or in the field

a computational framework for free surface fluid flows accounting for surface tension abstract this work is concerned with the simulation of incompressible newtonian fluid flow problems with free surfaces in the presence of surface tension the computational framework presented is based on the stabilised velocity pressure finite element method the movement and deformation of the computational domain are accounted for by employing the arbitrary lagrangian eulerian ale description of the fluid kinematics the numerical model is extended to incorporate surface tension effects a novel partitioned solution procedure is developed based on the newton raphson methodology which incorporates full linearisation of the overall incremental problem several numerical examples are provided to demonstrate the efficiency of the methodology

compressible flowfield solutions with unstructured grids generated by delaunay triangulation a method is described that constructs three dimensional unstructured tetrahedral meshes using the delaunay triangulation criterion the approach includes an automatic point creation technique and ensures that given an initial surface triangulation which bounds a domain a valid boundary conforming assembly of tetrahedra is produced the efficiency of the proposed procedure reduces the computer time for the generation of realistic unstructured tetrahedral grids to the order of minutes on workstations of modest computational capabilities the grids generated are used with two finite element algorithms to simulate inviscid transonic compressible flows flow solutions for aerospace configurations are presented and computed results compared with experimental data

a general formula for channel capacity a formula for the capacity of arbitrary single user channels without feedback not necessarily information stable stationary etc is proved capacity is shown to equal the supremum over all input processes of the input output inf information rate defined as the liminf in probability of the normalized information density the key to this result is a new converse approach based on a simple new lower bound on the error probability of m ary hypothesis tests among equiprobable hypotheses a necessary and sufficient condition for the validity of the strong converse is given as well as general expressions for spl epsiv capacity

a comparison of time discretization linearization approaches for the incompressible navier stokes equations abstract this paper presents a numerical study of two ways for discretizing and linearizing the time dependent incompressible navier stokes equations one approach consists in first applying a semi discretization in time by a fully implicit scheme then in each discrete time the equations are linearized by a fixed point iteration the number of iterations to reach a given stopping criterion is a priori unknown in this approach in the second approach rosenbrock schemes with s stages are used as temporal discretization the non linearity of the navier stokes equations is treated internally in the rosenbrock methods in each discrete time exactly s linear systems of equations have to be solved the numerical study considers five two dimensional problems with distinct features four implicit time stepping schemes and five rosenbrock methods are involved

efficient three dimensional delaunay triangulation with automatic point creation and imposed boundary constraints a method is described which constructs three dimensional unstructured tetrahedral meshes using the delaunay triangulation criterion several automatic point creation techniques will be highlighted and an algorithm will be presented which can ensure that given an initial surface triangulation which bounds a domain a valid boundary conforming assembly of tetrahedra will be produced statistics of measures of grid quality are presented for several grids the efficiency of the proposed procedure reduces the computer time for the generation of realistic unstructured tetrahedral grids to the order of minutes on workstations of modest computational capabilities

the capacity cost function of discrete additive noise channels with and without feedback we consider modulo q additive noise channels where the noise process is a stationary irreducible and aperiodic markov chain of order k we begin by investigating the capacity cost function c spl beta of such additive noise channels without feedback we establish a tight upper bound to c spl beta which holds for general not necessarily markovian stationary q ary noise processes this bound constitutes the counterpart of the wyner ziv lower bound to the rate distortion function of stationary sources with memory we also provide two simple lower bounds to c spl beta which along with the upper bound can be easily calculated using the blahut algorithm for the computation of channel capacity numerical results indicate that these bounds form a tight envelope on c spl beta we next examine the effect of output feedback on the capacity cost function of these channels and establish a lower bound to the capacity cost function with feedback c sub fb spl beta we show both analytically and numerically that for a particular feedback encoding strategy and a class of markov noise sources the lower bound to c sub fb spl beta is strictly greater than c spl beta this demonstrates that feedback can increase the capacity cost function of discrete channels with memory

finite element euler computations in three dimensions an explicit finite element solution procedure for the three dimensional euler equations is presented the solution domain is automatically meshed using a tetrahedral mesh generator which is an extension of our previous two dimensional work several examples are included to illustrate the performance of the generator and solver an adaptive mesh regeneration procedure is used for the first time in three dimensions

estimating network characteristics in stochastic activity networks this paper describes a monte carlo method based on the theory of quasirandom points for estimating the distribution functions and means of network completion time and shortest path time in a stochastic activity network in particular the method leads to estimators whose absolute errors converge as log kn k where k denotes the number of replications collected in the experiment and n is the number of dimensions for sampling this rate compares favorably with the standard error of estimate o1 k1 2 which obtains for experiments that use random sampling moreover since quasirandom points are nonrandom the upper bound log kn k is deterministic in contrast to the random sampling rate o1 k1 2 which is probabilistic the paper demonstrates how the use of a cutset of the network reduces n in the bound when estimating the distribution functions two examples illustrate the benefits and costs of using quasirandom points

regridding surface triangulations an advancing front surface gridding technique that operates on discretely defined surfaces i e triangulations is presented different aspects that are required to make the procedure reliable for complex geometries are discussed notable among these are a the recovery of surface features and discrete surface patches from the discrete data b filtering based on point and side normals to remove undesirable data close to cusps and corners c the proper choice of host faces for ridges and d fast interpolation procedures suitable for complex geometries post generation surface recovery or repositioning techniques are discussed several examples ranging from academic to industrial demonstrate the utility of the proposed procedure forab initiosurface meshing from discrete data such as those encountered when the surface description is already given as discrete the improvement of existing surface triangulations as well as remeshing applications during runs exhibiting significant change of domain

necessary and sufficient condition for capacity of the discrete time gaussian channel to be increased by feedback the problem of whether the capacity of a discrete time gaussian channel is increased by feedback or not is considered it is well known that the capacity of a white gaussian channel under an average power constraint is not changed by feedback the necessary condition under which the capacity of a nonwhite gaussian channel with blockwise white noise is increased by feedback is given

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

capacity of burst noise erasure channels with and without feedback and input cost a class of burst noise erasure channels which incorporate both errors and erasures during transmission is studied the channel whose output is explicitly expressed in terms of its input and a stationary ergodic noise erasure process is shown to have a so called quasi symmetry property under certain invertibility conditions as a result it is proved that a uniformly distributed input process maximizes the channel s block mutual information resulting in a closed form formula for its non feedback capacity in terms of the noise erasure entropy rate and the entropy rate of an auxiliary erasure process the feedback channel capacity is also characterized showing that the feedback does not increase capacity and generalizing prior related results the capacity cost function of the channel with and without feedback is next investigated a sequence of finite letter upper bounds for the capacity cost function without feedback is derived finite letter lower bonds for the capacity cost function with feedback are obtained using a specific encoding rule based on these bounds it is demonstrated both numerically and analytically that feedback can increase the capacity cost function for a class of channels with markov noise erasure processes

exact algorithms for the stochastic shortest path problem with a decreasing deadline utility function in this paper the stochastic shortest path problem of determining a path that maximizes the expected utility is considered the nature of the utility function used to evaluate paths is of a decreasing deadline type the principal contribution of this paper is the development of exact algorithms that use two types of pruning techniques that are incorporated in labeling procedures one type of pruning makes use of the concept of local preference relations while the other type makes use of relaxations specifically two algorithms are developed each containing the same preference relation but two different relaxations our extensive computational testing indicate that both these algorithms are able to solve even large size problems quickly more importantly even for large problems both the algorithms solved them by enumerating a very small percentage of all paths

a computational framework for fluid structure interaction finite element formulation and applications abstract this work is concerned with the modelling of the interaction of fluid flow with flexibly supported rigid bodies the fluid flow considered is governed by the incompressible navier stokes equations and modelled by employing stabilised low order velocity pressure finite elements the motion of the fluid domain is accounted for by an arbitrary lagrangian eulerian ale strategy the rigid body motion excited by the fluid flow is restricted by the elastic and damping properties of the supports for the temporal discretisation the discrete implicit generalised method is employed the resulting strongly coupled set of nonlinear equations is solved by means of a novel partitioned solution procedure which is based on the newton raphson methodology and incorporates full linearisation of the overall incremental problem the strong coupling is resolved and optimal convergence of the residuals is achieved several numerical examples are presented to demonstrate the robustness and efficiency of the methodology the examples clearly capture the phenomena of vortex induced oscillations and galloping

a space time galerkin least squares finite element formulation of the navier stokes equations for moving domain problems a space time galerkin least squares finite element formulation of the navier stokes equations is presented for the analysis of free surface flows moving spatial configurations and deforming fluid structure interfaces the variational equation is based on the time discontinuous galerkin method employing the physical entropy variables the space time elements are oriented in time to accommodate the spatial deformations if the elements are oriented along the particle paths the formulation is lagrangian and if they are fixed in time it is eulerian consequently this formulation is analogous to the arbitrary lagrangian eulerian ale technique a novel mesh rezoning strategy is presented to orient the elements in time and adapt the fluid mesh to the changing spatial configuration numerical results are presented to show the performance of the method

a novel energy based approach for merging finite elements a novel approach for merging two intersecting finite elements is presented and demonstrated the solution mimics concepts from biology and uses principles rooted in continuum mechanics the problem of attaching or merging two coincident finite elements is common when using the plastering technique as part of the advancing front method this problem is particularly challenging for 3 d meshes of non convex shapes some automatic meshing methods require portions of the partially formed mesh to coincide and merge this problem is generally solved with heuristic rules which lack generality and may have difficulties with unforeseen situations the problem of merging two overlapping polyhedra may also appear in other applications such as computer graphics and cad software a new approach to address the problem of merging is presented here this solution does not utilize heuristic rules but rather uses an approach based on minimization of strain energy a fully automatic merging routine has been created that can address in an optimum way any situation of two nearby or overlapping elements that are to be merged this approach with minor adjustments is suitable for most types of 3 d elements

a stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation abstract a stabilized finite element formulation for incompressible viscous flows is derived the starting point are the modified navier stokes equations incorporating naturally the necessary stabilization terms via a finite increment calculus fic procedure application of the standard finite element galerkin method to the modified differential equations leads to a stabilized discrete system of equations overcoming the numerical instabilities emanating from the advective terms and those due to the lack of compatibility between approximate velocity and pressure fields the fic method also provides a natural explanation for the stabilization terms appearing in all equations for both the navier stokes and the simpler stokes equations transient solution schemes with enhanced stabilization properties are also proposed finally a procedure for computing the stabilization parameters is presented

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100