a domain decomposition method for the exterior helmholtz problem a new domain decomposition method is presented for the exterior helmholtz problem the nonlocal dirichlet to neumann dtn map is used as a nonreflecting condition on the outer computational boundary the computational domain is divided into nonoverlapping subdomains with sommerfeld type conditions on the adjacent subdomain boundaries to ensure uniqueness an iterative scheme is developed where independent subdomain boundary value problems are obtained by applying the dtn operator to values from the previous iteration the independent problems are then discretized with finite elements and can be solved concurrently numerical results are presented for a two dimensional model problem and both the solution accuracy and convergence rate are investigated

finite element solution of compressible viscous flows using conservative variables abstract a finite element method for solving the compressible navier stokes equations is presented these equations are solved in conservation form and using conservative variables appropriate finite element approximations are discussed when a galerkin variational formulation is used for high speed flows the formulation is stabilized using the stream line upwind petrov galerkin method for which we propose an analytical expression for the matrix a new discontinuity capturing operator is also proposed to accurately solve flow problems exhibiting sharp gradients the non linear systems of equations arising from the discretization are solved using an iterative strategy based on the generalized minimal residual gmres algorithm numerical results for transonic and supersonic flows are presented that demonstrate the effectiveness of the proposed finite element method

enhanced discretization interface capturing technique edict for computation of unsteady flows with interfaces abstract we present the enhanced discretization interface capturing technique edict for computation of unsteady flow problems with interfaces such as two fluid and free surface flows in edict we solve over a non moving mesh the navier stokes equations together with an advection equation governing the evolution of an interface function with two distinct values identifying the two fluids the starting point for the spatial discretization of these equations are the stabilized finite element formulations which possess good stability and accuracy properties to increase the accuracy in modeling the interfaces we use finite element functions corresponding to enhanced discretization at and near the interface these functions are designed to have multiple components with each component coming from a different level of mesh refinement over the same computational domain the primary component of the functions for velocity and pressure comes from the base mesh called mesh 1 a subset of the elements in mesh 1 are identified to be at or near the interface and depending on where the interface is this subset could change from one time level to another a mesh 2 is constructed by patching together the second level meshes generated over this subset of elements and the second component of the functions for velocity and pressure comes from mesh 2 for the interface function we have a third component coming from a mesh 3 which is constructed by patching together the third level meshes generated over a subset of elements in mesh 2 with parallel computation of the test problems presented here we demonstrate that the edict can be used very effectively to increase the accuracy of the base finite element formulations

computational methods for risk averse undiscounted transient markov models the total cost problem for discrete time controlled transient markov models is considered the objective functional is a markov dynamic risk measure of the total cost two solution methods value and policy iteration are proposed and their convergence is analyzed in the policy iteration method we propose two algorithms for policy evaluation the nonsmooth newton method and convex programming and we prove their convergence the results are illustrated on a credit limit control problem

the pressurized hollow sphere problem in finite elastostatics for a class of compressible materials abstract this investigation is concerned with the problem of a hollow sphere subjected to uniform internal and external pressure within the equilibrium theory of finite elasticity the sphere is composed of homogeneous isotropic compressible materials of special type namely harmonic materials explicit closed form solutions for the deformation and stress fields are obtained the true stress distribution expressed as a function of the undeformed coordinates is shown to be essentially independent of material properties the two cases of internal pressure only and external pressure only are examined in detail in the former case there is a critical value of the applied pressure at which the maximum hoop stress in the sphere occurring at the inner surface becomes unbounded results appropriate for thin shells are also obtained for the case of external pressure only a critical value of the applied pressure exists for which the cavity closes the maximum hoop stress does not always occur at the cavity wall for nearly solid spheres or equivalently for a cavity in an unbounded medium explicit results are provided for the corresponding stress concentration factor for sufficiently small values of applied pressures all the foregoing results coincide with those of classical linear isotropic elastostatics

generic domain decomposition and iterative solvers for 3d bem problems summary in the past two decades considerable improvements concerning integration algorithms and solvers involved in boundary element formulations have been obtained first a great deal of efficient techniques for evaluating singular and quasi singular boundary element integrals have been definitely established and second iterative krylov solvers have proven to be advantageous when compared to direct ones also including non hermitian matrices the former fact has implied in cpu time reduction during the assembling of the system of equations and the latter fact in its faster solution in this paper a triangle polar co ordinate transformation and the telles co ordinate transformation applied in previous works independently for evaluating singular and quasi singular integrals are combined to increase the efficiency of the integration algorithms and so to improve the performance of the matrixassembly routines in addition the jacobi preconditioned biconjugate gradient j bicg solver is used to develop a generic substructuring boundary element algorithm in this way it is not only the system solution accelerated but also the computer memory optimized discontinuous boundary elements are implemented to simplify the coupling algorithm for a generic number of subregions several numerical experiments are carried out to show the performance of the computer code with regard to matrix assembly and the system solving in the discussion of results expressed in terms of accuracy and cpu time advantages and potential applications of the be code developed are highlighted copyright 2006 john wiley sons ltd

on consistency of stochastic dominance and mean semideviation models we analyze relations between two methods frequently used for modeling the choice among uncertain outcomes stochastic dominance and mean risk approaches new necessary conditions for stochastic dominance are developed these conditions compare values of a certain functional which contains two components the expected value of a random outcome and a risk term represented by the central semideviation of the corresponding degree if the weight of the semideviation in the composite objective does not exceed the weight of the expected value maximization of such a functional yields solutions which are efficient in terms of stochastic dominance the results are illustrated graphically

explicit solutions for multivariate discrete time control problems under uncertainty we consider discrete time control problems where only the support sets of the initial condition and of the disturbances are known we study the applicability of the dp method and as a counterpart of the lq problem of the stochastic setting we present a problem that admits an explicit analytic solution in particular we characterize a property of compatibility between the system dynamics and the norms of the spaces that is crucial to obtain the analytic solution also in the general multidimensional case

persistently optimal policies in stochastic dynamic programming with generalized discounting in this paper we study a markov decision process with a nonlinear discount function first we define a utility on the space of trajectories of the process in the finite and infinite time horizon and then take their expected values it turns out that the associated optimization problem leads to a nonstationary dynamic programming and an infinite system of bellman equations which result in obtaining persistently optimal policies our theory is enriched by examples

solution algorithms for nonlinear transient heat conduction analysis employing element by element iterative strategies abstract despite continuing advancements in computer technology there are many problems of engineering interest that exceed the combined capabilities of today s numerical algorithms and computational hardware the resources required by traditional finite element algorithms tend to grow geometrically as the problem size is increased thus for the forseeable future there will be problems of interest which cannot be adequately modeled using currently available algorithms for this reason we have undertaken the development of algorithms whose resource needs grow only linearly with problem size in addition these new algorithms will fully exploit the parallel processing capability available in the new generation of multi processor computers the approach taken in the element by element solution procedures is to approximate the global implicit operator by a product of lower order operators this type of product approximation originated with adi techniques and was further refined into the method of fraction steps the current effort involves the use of a more natural operator split for finite element analysis based on element operators this choice of operator splitting based on element operators has several advantages first it fits easily within the architecture of current finite element programs second it allows the development of parallel algorithms finally the computational expense varies only linearly with the number of elements the particular problems considered arise from nonlinear transient heat conduction the nonlinearity enters through both material temperature dependence and radiation boundary conditions the latter condition typically introduces a stiff component in the resultant matrix odes which precludes effective use of explicit solution techniques on the other hand typical implicit techniques involving direct equation solving can be prohibitively expensive instead the matrix equations are solved by combining a modified newton raphson iteration scheme for the nonlinear algebraic problem with an element by element preconditioned conjugate gradient procedure for the linear problems an adaptive intercommunicative strategy is developed for setting termination criteria for the nonlinear and linear equation solving algorithms errors and computational efficiency in the transient solution are controlled by an automatic time step selection strategy the resultant procedure has proven to be both accurate and reliable in the solution of medium size test problems

markov decision problems where means bound variances we identify a rich class of finite horizon markov decision problems mdps for which the variance of the optimal total reward can be bounded by a simple linear function of its expected value the class is characterized by three natural properties reward nonnegativity and boundedness existence of a do nothing action and optimal action monotonicity these properties are commonly present and typically easy to check implications of the class properties and of the variance bound are illustrated by examples of mdps from operations research operations management financial engineering and combinatorial optimization

a unified exact analysis for the poynting effects of cylindrical tubes made of hill s class of hookean compressible elastic materials at finite strain abstract a direct natural extension of hooke s law to finite strain was achieved by r hill in 1978 employing the notion of work conjugate measures of stress and strain with seth hill doyle ericksen class of finite strain measures this extension actually defines a broad class of compressible hyperelastic materials at finite strain each of which retains the simple linear structure of hooke s law as stress strain relationship several known simple elasticity models at finite strain are included as its particular examples with a novel idea of utilizing a suitable parametric variable here we present a unified study of the free end torsion problem poynting effects of thin walled cylindrical tubes made of the foregoing hill s class of hookean type hyperelastic materials we show that it is possible to derive a unified exact solution to the nonlinear coupling equations relating the torque the shear stress and the controlling deformation quantities including in particular the axial length change discussions and comparisons concerning various hookean type elasticity models are made based on the exact solution obtained

berge s theorem for noncompact image sets abstract for an upper semi continuous set valued mapping from one topological space to another and for a lower semi continuous function defined on the product of these spaces berge s theorem states lower semi continuity of the minimum of this function taken over the image sets it assumes that the image sets are compact for hausdorff topological spaces this paper extends berge s theorem to set valued mappings with possible noncompact image sets and studies relevant properties of minima

error estimates and automatic time step control for nonlinear parabolic problems i in this note we extend results by one of the authors on time discretization error estimates and related automatic time step control for stiff ordinary differential equations to the case of a nonlinear parabolic problem the method for time discretization is the so called discontinuous galerkin method based on using piecewise polynomials of degree q geqq 0 we consider in this note the case q 0 corresponding to a variant of the backward euler method we prove a new almost optimal error estimate and present a related new algorithm for automatic time step control this algorithm is very simple but yet is efficient and gives control of the global error

constitutive theory for some constrained elastic crystals abstract some of the observations of a 15 superconductors near cubic tetragonal phase transformations suggest treating them as thermoelastic bodies subject to certain material constraints here we begin to develop a theory of this kind

three dimensional finite element calculations in acoustic scattering using arbitrarily shaped convex artificial boundaries we report on a generalization of the bayliss gunzburger turkel non reflecting boundary conditions to arbitrarily shaped convex artificial boundaries for elongated scatterers such as submarines we show that this generalization can improve significantly the computational efficiency of finite element methods applied to the solution of three dimensional acoustic scattering problems copyright 2001 john wiley sons ltd

multi domain parallel computation of wake flows abstract we present a new multi domain parallel computational method for simulation of unsteady flows involving a primary object a long wake region and possibly a secondary object affected by the wake flow the method is based on the stabilized finite element formulation of the time dependent navier stokes equations of incompressible flows in the multi domain computational method the entire simulation domain is divided into an ordered sequence of overlapping subdomains the flow data computed over the leading subdomain is used for specifying the inflow boundary conditions for the next subdomain the subdomain corresponding to the wake would not involve any objects hence the mesh constructed over this domain would be structured a special purpose finite element implementation for structured meshes is used for the wake domain to achieve much higher computational speeds compared to a general purpose implementation we present verification studies for the multi domain method and special purpose implementation followed by two numerical examples the first example is the wake behavior behind a circular cylinder the second one is the aerodynamic effect of tip vortices released from a leading wing on a trailing wing placed in the far wake

risk averse control of undiscounted transient markov models we use markov risk measures to formulate a risk averse version of the undiscounted total cost problem for a transient controlled markov process using the new concept of a multikernel we derive conditions for a system to be risk transient that is to have finite risk over an infinite time horizon we derive risk averse dynamic programming equations satisfied by the optimal policy and we describe methods for solving these equations we illustrate the results on an optimal stopping problem and an organ transplantation problem

conditional risk mappings we introduce an axiomatic definition of a conditional convex risk mapping and we derive its properties in particular we prove a representation theorem for conditional risk mappings in terms of conditional expectations we also develop dynamic programming relations for multistage optimization problems involving conditional risk mappings

parallel finite element computations in fluid mechanics we provide an overview of the role of parallel finite element computations in fluid mechanics we emphasize the class of flow problems involving moving boundaries and interfaces some of the computationally most challenging flow problems such as fluid object and fluid structure interactions as well as free surface and two fluid flows belong to this class in the development of the methods targeting this class of problems the computational challenges involved need to be addressed in such a way that 3d computation of complex applications can be carried out efficiently on parallel computers this requirement has to be one of the key factors in designing various components of the overall solution approach such as solution techniques for the discretized equations and mesh update methods for handling the changes in the spatial domain occupied by the fluid this overview includes a description of how the computational challenges are addressed and how the computational schemes can be enhanced with special preconditioning techniques 2005 elsevier b v all rights reserved

hierarchical basis for stabilized finite element methods for compressible flows the quest for more accurate numerical simulations of the navier stokes equations has motivated the study of high order piecewise polynomial basis functions also known as k version finite element methods as a means to attain this accuracy in the most cost effective manner stabilized finite element methods e g streamline upwind petrov galerkin have been proven to attain optimal rates of convergence for any polynomial order basis as well as perform well on a variety of flows including turbulence applications we present a stabilized finite element formulation for fluid dynamics using mesh entity based hierarchical basis functions the implementation is shown to attain theoretical convergence results for the linear model problem as well as the navier stokes equations

from stochastic dominance to mean risk models semideviations as risk measures abstract two methods are frequently used for modeling the choice among uncertain outcomes stochastic dominance and mean risk approaches the former is based on an axiomatic model of risk averse preferences but does not provide a convenient computational recipe the latter quantifies the problem in a lucid form of two criteria with possible trade off analysis but cannot model all risk averse preferences in particular if variance is used as a measure of risk the resulting mean variance markowitz model is in general not consistent with stochastic dominance rules this paper shows that the standard semideviation square root of the semivariance as the risk measure makes the mean risk model consistent with the second degree stochastic dominance provided that the trade off coefficient is bounded by a certain constant similar results are obtained for the absolute semideviation and for the absolute and standard deviations in the case of symmetric or bounded distributions in the analysis we use a new tool the outcome risk o r diagram which appears to be particularly useful for comparing uncertain outcomes

adaptive finite element methods for parabolic problems i a linear model problem this paper is the first part in a series of papers on adaptive finite element methods for parabolic problems in this paper an adaptive algorithm is presented and analyzed for choosing the space a

risk forms representation disintegration and application to partially observable two stage systems we introduce the concept of a risk form which is a real functional of two arguments a measurable function on a polish space and a measure on that space we generalize the duality theory and the kusuoka representation to this setting for a risk form acting on a product of polish spaces we define marginal and conditional forms and we prove a disintegration formula which represents a risk form as a composition of its marginal and conditional forms we apply the proposed approach to two stage stochastic programming problems with partial information and decision dependent observation distribution

a multi element group preconditioned gmres algorithm for nonsymmetric systems arising in finite element analysis abstract a multi element group domain decomposition algorithm is presented for solving linear nonsymmetric systems arising in finite element analysis the iterative strategy employed is based on the generalized minimum residual gmres procedure originally proposed by saad and shultz two levels of preconditioning are investigated coding is presented which fully exploits vector architectured computers applications to problems of high speed compressible flow illustrate the effectiveness of the scheme

a space time coupled p version least squares finite element formulation for unsteady two dimensional navier stokes equations this paper presents a p version least squares finite element formulation for two dimensional unsteady fluid flow described by navier stokes equations where the effects of space and time are coupled the dimensionless form of the navier stokes equations are first cast into a set of first order differential equations by introducing auxiliary variables this permits the use of c0 element approximation the element properties are derived by utilizing the p version approximation functions in both space and time and then minimizing the error functional given by the space time integral of the sum of squares of the errors resulting from the set of first order differential equations this results in a true space time coupled least squares minimization procedure the application of least squares minimization to the set of coupled first order partial differential equations results in finding a solution vector which makes gradient of error functional with respect to a null vector this is accomplished by using newton s method with a line search a time marching procedure is developed in which the solution for the current time step provides the initial conditions for the next time step equilibrium iterations are carried out for each time step until the error functional and each component of the gradient of the error functional with respect to nodal degrees of freedom are below a certain prespecified tolerance the space time coupled p version approximation functions provide the ability to control truncation error which in turn permits very large time steps what literally requires hundreds of time steps in uncoupled conventional time marching procedures can be accomplished in a single time step using the present space time coupled approach the generality success and superiority of the present formulation procedure is demonstrated by presenting specific numerical examples for transient couette flow and transient lid driven cavity the results are compared with the analytical solutions and those reported in the literature the formulation presented here is ideally suited for space time adaptive procedures the element error functional values provide a mechanism for adaptive h p or hp refinements

convergence to steady state solutions for stabilized finite element simulations of compressible flows abstract the main objective of the paper is to compare the numerical performance of several pseudo time integration algorithms used for driving finite element solutions of compressible flow equations towards the steady state the algorithms are implementations of four strategies explicit linear implicit multistage linear implicit and nonlinear all except the explicit scheme employ a particular implementation of gmres to solve systems of linear equations the nonlinear algorithm uses at each time step two iterations of the newton method with an approximate jacobian the finite element formulation is a version of the stabilized fem with h adaptivity the comparison is done for three flow problems in three flow regimes subsonic transonic and supersonic final conclusions concerning relative performance of the methods are drawn

hill s class of compressible elastic materials and finite bending problems exact solutions in unified form abstract hill 1978 proposed a natural extension of hooke s law to finite deformations with all seth hill finite strains hill s natural extension presents a broad class of compressible hyperelastic materials over the whole deformation range we show that a number of known hookean type finite hyperelasticity models are included as particular cases in hill s class and that bell s and ericksen s constraints may be derived as natural consequences from hill s class subjected to internal constraints also we present a unified study of finite bending problems for elastic hill materials to date exact results are available for certain particular classes of compressible elastic materials which do not cover hill s class here with a novel idea of circumventing the strong nonlinearity we show that it is possible to derive exact solutions in unified form for the whole class of elastic hill materials reduced results are also given for cases subjected to internal constraints

stability results for stochastic programs and sensors allowing for discontinuous objective functions the paper examines the stability of the optimal value and the solutions of stochastic programming problems stability is checked with respect to variations in both the problem formulation and the probability distribution that describes the uncertainty of particular interest is the case where the payoff functions may be discontinuous these results are applied to analyze the stability of sensors that model the possibility of making inquiries to improve the probabilistic information available about the uncertain quantities

massively parallel finite element computations of three dimensional time dependent incompressible flows in materials processing systems abstract a parallel implementation of the galerkin finite element method for three dimensional incompressible flows is presented the inherent element by element parallelism of the method is exploited to make efficient use of the architecture of the cm 5 computer our implementation features a mixed formulation to expand the primitive variables using triquadratic brick elements with linear discontinuous pressure basis functions and the gmres method with diagonal preconditioning is employed to solve the linear system at each newton iteration transitions among flow states in the classical taylor couette system which are representative of the complexity of flows found in materials processing systems are computed as benchmark solutions and preliminary results are presented for flow in a large scale solution crystal growth system sustained calculation rates of up to 6 gigaflops are achieved on 512 processors of the cm 5

on a consistent finite strain plate theory based on three dimensional energy principle this paper derives a finite strain plate theory consistent with the principle of stationary three dimensional potential energy under general loadings with a fourth order error starting from the three dimensional nonlinear elasticity with both geometrical and material nonlinearity and by a series expansion we deduce a vector plate equation with three unknowns which exhibits the local force balance structure the success relies on using the three dimensional field equations and bottom traction condition to derive exact recursion relations for the coefficients associated weak formulations are considered leading to a two dimensional virtual work principle an alternative approach based on a two dimensional truncated energy is also provided which is less consistent than the first plate theory but has the advantage of the existence of a two dimensional energy function as an example we consider the pure bending problem of a hyperelastic block the comparison between the analytical plate solution and available exact one shows that the plate theory gives second order correct results compared with existing plate theories it appears that the present one has a number of advantages including the consistency order of correctness generality of loadings applicability to finite strain problems and no involvement of non physical quantities

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

the choice of objective rates in finite elastoplasticity general results on the uniqueness of the logarithmic rate a eulerian rate formulation of finite elastoplasticity is a composite one composed of a rate equation for elastic behaviour and a flow rule for plastic behaviour as well as an evolution equation for hardening behaviour in which objective eulerian tensor rates are used among a large variety of objective rates actually infinitely many how to choose suitable ones has been one of the crucial points in finite elastoplasticity it is realized that the foregoing composite formulation of elastoplasticity should fulfil certain consistency criteria in order to avoid inconsistencies or contradictions these criteria narrow the choice of objective rates these authors bruhns and co workers and xiao and co workers have recently introduced the self consistency criterion in a composite formulation of elastoplasticity the rate equation intended for characterization of elastic behaviour should be exactly integrable to deliver an elastic relation it has been demonstrated in the work of the aforementioned authors that if a composite formulation of elastoplasticity with objective rates is required to fulfil the just stated self consistency criterion as it should be then the newly discovered logarithmic rate is the only possible choice among all objective corotational rates including the zaremba jaumann rate and the green naghdi rate etc in the afore mentioned result non corotational rates including oldroyd rates cotter rivlin rate and truesdell rate etc are not taken into consideration in general it is the main goal of this paper to further establish the uniqueness of the logarithmic rate among all corotational and non corotational objective rates essential to the attainment of this goal is the use of the yielding stationarity criterion the vanishing of the stress rate implies that the yield function is stationary it is shown that the just stated criterion is necessary for a composite eulerian rate formulation of finite elastoplasticity to be consistent and means that the stress rate must be a corotational rate the main goal of this article is thus attained by combining the just stated result and the established result stated before

brief risk sensitive and minimax control of discrete time finite state markov decision processes this paper analyzes a connection between risk sensitive and minimax criteria for discrete time finite state markov decision processes mdps we synthesize optimal policies with respect to both criteria both for the finite horizon and the discounted infinite horizon problem a generalized decision making framework is introduced which includes as special cases a number of approaches that have been considered in the literature the framework allows for discounted risk sensitive and minimax formulations leading to stationary optimal policies on the infinite horizon we illustrate our results with a simple machine replacement problem

the dirichlet to neumann map for two dimensional crack problems a coupled analytic finite element method is presented for two dimensional crack problems two classes of problems are studied the first considers problems where non linear constitutive processes occur in a region near the crack tip and the remotely applied loading can be characterized by the linear elastic k field and perhaps the t stress in this case the finite element method is applied in a circular region around the crack tip where non linear constitutive response is occurring and stiffness contributions associated with a numerically implemented dirichlet to neumann map are imposed on the circular boundary to account for the large surrounding elastic domain and the remote applied loading the second class of problems considers entirely linear elastic domains with irregular external boundaries and or complex applied loadings here the discrete dirichlet to neumann map is used to represent a circular region surrounding the crack tip and finite elements are used for the external region in this case the mixed mode stress intensity factors and the t stress are retrieved from the map

algorithmic aspects of mean variance optimization in markov decision processes we consider finite horizon markov decision processes under performance measures that involve both the mean and the variance of the cumulative reward we show that either randomized or history based policies can improve performance we prove that the complexity of computing a policy that maximizes the mean reward under a variance constraint is np hard for some cases and strongly np hard for others we finally offer pseudopolynomial exact and approximation algorithms

process based risk measures and risk averse control of discrete time systems for controlled discrete time stochastic processes we introduce a new class of dynamic risk measures which we call process based their main feature is that they measure risk of processes that are functions of the history of a base process we introduce a new concept of conditional stochastic time consistency and we derive the structure of process based risk measures enjoying this property we show that they can be equivalently represented by a collection of static law invariant risk measures on the space of functions of the state of the base process we apply this result to controlled markov processes and we derive dynamic programming equations we also derive dynamic programming equations for multistage stochastic programming with decision dependent distributions

more risk sensitive markov decision processes we investigate the problem of minimizing a certainty equivalent of the total or discounted cost over a finite and an infinite horizon that is generated by a markov decision process mdp in contrast to a risk neutral decision maker this optimization criterion takes the variability of the cost into account it contains as a special case the classical risk sensitive optimization criterion with an exponential utility we show that this optimization problem can be solved by an ordinary mdp with extended state space and give conditions under which an optimal policy exists in the case of an infinite time horizon we show that the minimal discounted cost can be obtained by value iteration and can be characterized as the unique solution of a fixed point equation using a sandwich argument interestingly it turns out that in the case of a power utility the problem simplifies and is of similar complexity than the exponential utility case however has not been treated in the literature so far we also establish the validity and convergence of the policy improvement method a simple numerical example namely the classical repeated casino game is considered to illustrate the influence of the certainty equivalent and its parameters finally the average cost problem is also investigated surprisingly it turns out that under suitable recurrence conditions on the mdp for convex power utility the minimal average cost does not depend on the parameter of the utility function and is equal to the risk neutral average cost this is in contrast to the classical risk sensitive criterion with exponential utility

stabilized finite element interface capturing technique for parallel computation of unsteady flows with interfaces we present the stabilized finite element interface capturing sfe ic method developed for parallel computation of unsteady flow problems with two fluid interfaces and free surfaces the sfe ic method involves stabilized formulations an interface sharpening technique and the enforcement of global mass conservation for each fluid the sfe ic method has been efficiently implemented on the cray t3e parallel supercomputer a number of 2d test problems are presented to demonstrate how the sfe ic method works and the accuracy it attains we also show how the sfe ic method can be very effectively applied to 3d simulation of challenging flow problems such as two fluid interfaces in a centrifuge tube and operational stability of a partially filled tanker truck driving over a bump

on the existence and the uniqueness of the solution of a fluid structure interaction scattering problem the existence and uniqueness of the solution of a fluid structure interaction problem is investigated the proposed analysis distinguishes itself from previous studies by employing a weighted sobolev space framework the dtn operator properties and the fredholm theory the proposed approach allows to extend the range of validity of the standard existence and uniqueness results to the case where the elastic scatterer is assumed to be only lipschitz continuous which is of more practical interest

constitutive inequalities for an isotropic elastic strain energy function based on hencky s logarithmic strain tensor hencky s strain energy function for finite isotropic elasticity is obtained by the replacement of the infinitesimal strain measure occurring in the classical strain energy function of infinitesimal

dual stochastic dominance and related mean risk models we consider the problem of constructing mean risk models which are consistent with the second degree stochastic dominance relation by exploiting duality relations of convex analysis we develop the quantile model of stochastic dominance for general distributions this allows us to show that several models using quantiles and tail characteristics of the distribution are in harmony with the stochastic dominance relation we also provide stochastic linear programming formulations of these models

variance penalized markov decision processes we consider a markov decision process with both the expected limiting average and the discounted total return criteria appropriately modified to include a penalty for the variability in the stream of rewards in both cases we formulate appropriate nonlinear programs in the space of state action frequencies averaged or discounted whose optimal solutions are shown to be related to the optimal policies in the corresponding variance penalized mdp the analysis of one of the discounted cases is facilitated by the introduction of a cartesian product of two independent mdps

a block qmr algorithm for non hermitian linear systems with multiple right hand sides abstract many applications require the solution of multiple linear systems that have the same coefficient matrix but differ in their right hand sides instead of applying an iterative method to each of these systems individually it is often more efficient to employ a block version of the method that generates iterates for all the systems simultaneously in this paper we propose a block version of freund and nachtigal s quasi minimal residual qmr method for the iterative solution of non hermitian linear systems the block qmr method uses a novel lanczos type process for multiple starting vectors which was recently developed by aliaga boley freund and hernandez to compute suitable basis vectors for the underlying block krylov subspaces we describe the basic block qmr method and also give important implementation details in particular we show how to incorporate deflation to drop converged linear systems and to delete linearly and almost linearly dependent vectors in the underlying block krylov sequences numerical results are reported that illustrate typical features of the block qmr method

a globally convergent matrix free algorithm for implicit time marching schemes arising in finite element analysis in fluids a solution procedure for solving nonlinear time marching problems is presented the nonsymmetric systems of equations arising from a newton type linearization of these time marching problems are solved using an iterative strategy based on the generalized minimal residual gmres algorithm matrix free techniques leading to reduction in storage are presented incorporation of a linesearch algorithm in the newton gmres scheme is discussed an automatic time increment control strategy is developed to increase the stability of the time marching process high speed flow computations demonstrate the effectiveness of these algorithms

risk sensitive control of discrete time markov processes with infinite horizon in this paper we study existence of solutions to the bellman equation corresponding to risk sensitive ergodic control of discrete time markov processes using three different approaches also for particular classes of systems asymptotics for vanishing risk factor is investigated showing that in the limit the optimal value for an average cost per unit time is obtained

risk averse dynamic programming for markov decision processes we introduce the concept of a markov risk measure and we use it to formulate risk averse control problems for two markov decision models a finite horizon model and a discounted infinite horizon model for both models we derive risk averse dynamic programming equations and a value iteration method for the infinite horizon problem we develop a risk averse policy iteration method and we prove its convergence we also propose a version of the newton method to solve a nonsmooth equation arising in the policy iteration method and we prove its global convergence finally we discuss relations to min max markov decision models

enhanced approximation linear solution technique ealst abstract the enhanced discretization and solution techniques are among the advanced computational methods we rely on in simulation and modeling of complex flow problems including those with moving boundaries and interfaces the set of enhanced discretization and solution techniques includes those based on enhancement in spatial discretization enhancement in time discretization and enhancement in iterative solution of nonlinear and linear equation systems the enhanced approximation linear solution technique ealst was introduced to increase the performance of the iterative technique used in solution of the linear equation systems when some parts of the computational domain may offer more of a challenge for the iterative method than the others the ealst can be used for computations based on semi discrete or space time formulations

adaptive finite element methods for systems of reaction diffusion equations we consider an adaptive finite element method with quantitative error control for systems of reaction diffusion equations the adaptive algorithm is based on an a posteriori error estimate involving residuals of the computed solution and certain strong stability factors which are estimated by solving an associated linearized dual problem numerically to take into account that the stability properties in space and time are different separate stability factors are used for the space discretization and the time discretization

risk sensitive markov control processes we introduce a general framework for measuring risk in the context of markov control processes with risk maps on general borel spaces that generalize known concepts of risk measures in mathematical finance operations research and behavioral economics within the framework applying weighted norm spaces to incorporate unbounded costs also we study two types of infinite horizon risk sensitive criteria discounted total risk and average risk and solve the associated optimization problems by dynamic programming for the discounted case we propose a new discount scheme which is different from the conventional form but consistent with the existing literature while for the average risk criterion we state lyapunov like stability conditions that generalize known conditions for markov chains to ensure the existence of solutions to the optimality equation