design of two dimensional digital filters using singular value decomposition and balanced approximation method it is shown that the singular value decomposition svd of the sampled amplitude response of a two dimensional 2 d digital filter possesses a special structure every singular vector is either mirror image symmetric or antisymmetric with respect to its midpoint consequently the svd can be applied along with 1 d finite impulse response fir techniques for the design of linear phase 2 d filters with arbitrary prescribed amplitude responses which are symmetrical with respect to the origin of the omega psi omega sub 2 plane the balanced approximation method is applied to linear phase 2 d fir filters of the type that may be obtained by using the svd method the method leads to economical and computationally efficient filters usually infinite impulse response filters which have prescribed amplitude responses and whose phase responses are approximately linear

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

the fixed mesh ale approach for the numerical approximation of flows in moving domains in this paper we propose a method to approximate flow problems in moving domains using always a given grid for the spatial discretization and therefore the formulation to be presented falls within the category of fixed grid methods even though the imposition of boundary conditions is a key ingredient that is very often used to classify the fixed grid method our approach can be applied together with any technique to impose approximately boundary conditions although we also describe the one we actually favor our main concern is to properly account for the advection of information as the domain boundary evolves to achieve this we use an arbitrary lagrangian eulerian framework the distinctive feature being that at each time step results are projected onto a fixed background mesh that is where the problem is actually solved

on inf sup stabilized finite element methods for transient problems we consider the behavior of inf sup stabilization in the context of transient problems with multiple time scales our motivation for studying this setting is provided by reacting flows problems for which small time steps are necessary in the integration process we show that for algorithms defined through a process wherein spatial and temporal discretizations are separated the coupling of implicit time integration with spatial inf sup stabilization may lead to anomalous pressure behavior including the onset of spurious oscillations for very small time steps effectively this coupling introduces a stability criterion resulting in a dependence between the spatial grid size and the time step we illustrate our theoretical results by numerical examples that demonstrate the stability criterion 2004 elsevier b v all rights reserved

enforcement of constraints and maximum principles in the variational multiscale method abstract we present a new theoretical framework for the enforcement of constraints in variational multiscale vms analysis the theory is first presented in an abstract operator format and subsequently specialized for the steady advection diffusion equation the approach borrows heavily from results in constrained and convex optimization an exact expression for the fine scales is derived in terms of variational derivatives of the constraints lagrange multipliers and a fine scale green s function the methodology described enables the development of numerical methods which satisfy predefined attributes a practical and effective procedure for solving the steady advection diffusion equation is presented based on a vms inspired stabilized method weakly enforced dirichlet boundary conditions and enforcement of a maximum principle and conservation constraint

stochastic switching for partially observable dynamics and optimal asset allocation abstractin industrial applications optimal control problems frequently appear in the context of decision making under incomplete information in such framework decisions must be adapted dynamically to account for possible regime changes of the underlying dynamics using stochastic filtering theory markovian evolution can be modelled in terms of latent variables which naturally leads to high dimensional state space making practical solutions to these control problems notoriously challenging in our approach we utilise a specific structure of this problem class to present a solution in terms of simple reliable and fast algorithms the algorithms presented in this paper have already been implemented in an r package

error estimation and adaptive meshing in strongly nonlinear dynamic problems we present work aimed at developing a general framework for mesh adaption in strongly nonlinear possibly dynamic problems we begin by showing that the solutions of the incremental boundary value problem for a wide class of materials including nonlinear elastic materials compressible newtonian fluids and viscoplastic solids obey a minimum principle provided that the constitutive updates are formulated appropriately this minimum principle can be taken as a basis for asymptotic error estimation in particular we chose to monitor the error of a lower order projection of the finite element solution the optimal mesh size distribution then follows from a posteriori error indicators which are purely local i e can be computed element by element we demonstrate the robustness and versatility of the computational framework with the aid of convergence studies and selected examples of application

synthesis of 2 d state space digital filters with low sensitivity based on the fornasini marchesini model the balanced realization and low sensitivity structure of two dimensional recursive digital filters are considered in the framework of the fornasini marchesini local state space model a procedure is introduced for the balanced realization of 2 d recursive digital filters the sensitivities of a 2 d transfer function are investigated with respect to the coefficients in the local state space model the overall sensitivity is evaluated using the 2 d controllability and observability gramians the filter structure reducing the overall sensitivity is synthesized for two cases one free from l sub 2 scaling constraints on the state variables and the other under the scaling constraints these filter structures are shown to be closely related to the balanced realization an example is given to illustrate the utility of the proposed technique

adjoint weighted equation for inverse problems of incompressible plane stress elasticity the adjoint weighted equation awe formulation is applied to incompressible isotropic plane stress elasticity for the solution of inverse problems for the strong form of the problem to have a solution a restrictive strain compatibility condition must hold in the awe variational formulation on the other hand a much milder sufficient condition is that uniaxial stress states be precluded making the method more robust to noisy data we prove that the formulation leads to a stable converging numerical method and show through computations that the method performs well

a relationship between stabilized finite element methods and the galerkin method with bubble functions abstract a relation between stabilized finite element methods and the galerkin method employing interpolations with bubble functions is established for the advective diffusive model and for the linearized compressible navier stokes equations the bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy in particular for the advective diffusive model the galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline upwind petrov galerkin supg method in the diffusive limit

boundary lagrange multipliers in finite element methods error analysis in natural norms a finite element procedure for circumventing the babuska brezzi condition in mixed formulations with lagrange multipliers defined on the boundary is presented residual terms constructed from the euler lagrange equations are added to the classical galerkin formulation in order to attain coercivity in a mesh dependent norm convergence is proven for the primal variable and the multiplier in the natural mesh independent norm of the problem generalizing results of a previous paper

convergence analyses of galerkin least squares methods for symmetric advective diffusive forms of the stokes and incompressible navier stokes equations abstract symmetric advective diffusive forms of the stokes and incompressible navier stokes equations are presented the galerkin least squares method for advective diffusive equations is used for both systems and is related to other stabilized methods previously studied the presentation reveals that the convergence analysis for advective diffusive equations as applied before to a linearized form of the compressible navier stokes equations carries over in a straightforward manner to the stokes problem and to a linearized form of the incompressible navier stokes equations

studies of domain based formulations for computing exterior problems of acoustics a strategy must be devised to compute solutions over domains which are unbounded exact impedance conditions at an artificial external boundary are specified by the dtn method yielding an equivalent problem that is suitable for domain based computation the dtn boundary condition is non reflective giving rise to exact and thereby unique solutions the truncated dtn operator which is employed in practice fails to inhibit the reflection of higher modes so that non unique solutions may occur at their harmonics simple expressions determine a sufficient number of terms in the truncated operator for unique solutions at any given wave number there are three characteristic length scales in the computational problem the radius of the artificial boundary the geometry of the body represented by the internal boundary and the mesh size

an improved stable xfem is xfem with a novel enrichment function for the computational modeling of cohesive cracks abstract owing to the solution space enriched with a priori known knowledge through the partition of unity the extended or generalized finite element method xfem gfem has been widely applied to the modeling of localized failure in solids as far as cohesive cracks are concerned in this work on the one hand the xfem enriched with heaviside function or the shifted one with respect to nodal values is of optimal accuracy but is prone to the issue of ill conditioned or even singular system matrix for arbitrary crack propagation on the other hand the stable xfem s xfem circumvents the ill conditioning issues by introducing the residual heaviside function with respect to its linear interpolant at the cost of losing accuracy e g spurious stress locking for discontinuities with non uniform displacement jumps aiming to reconcile the incompatibility between accuracy of the solution and conditioning of the system matrix this work addresses a simple yet effective improved stable xfem is xfem with a novel enrichment function both the xfem and s xfem are recovered as its particular cases with different approximation schemes for the bridging scale which incorporates information from both the continuous coarse scale and the discontinuous fine scale in the proposed is xfem as the enrichment basis functions are not contained in the standard polynomial space conditioning of the resulting system matrix is nearly insensitive to the mesh discontinuity configuration even if the crack path gets close to element nodes furthermore the is xfem with a small stabilization parameter is almost of the same accuracy as the xfem particularly pathological numerical results polluted by spurious stress locking exhibited in the s xfem are not observed across a fully softened discontinuity with non uniform displacement jumps as only the enrichment function is modified the proposed is xfem together with appropriate crack propagation criterion and tracking algorithm can be implemented easily in the existing xfem codes several representative numerical simulations of element and structure benchmark tests are presented to validate the proposed is xfem regarding both accuracy of the solution and conditioning of the system matrix

stability and stability margin for a two dimensional system in this paper a necessary and sufficient condition is derived for the stability of the fornasini marchesini fm first model proposed for two dimensional 2 d dynamic system descriptions a connection has been established between the stability of this model and the structured singular value ssv of a constant matrix which is now widely known in control theories based on this connection a novel sufficient condition is obtained for the stability of the fm first model that is more computationally convenient in filter design numerical simulations show that this sufficient condition is usually less conservative than that of moreover the stability margin of the fm first model is also investigated it is shown that a 2 d system remains stable under parametric variations if and only if the ssv of a constant matrix is smaller than one

a bubble stabilized finite element method for dirichlet constraints on embedded interfaces we examine a bubble stabilized finite element method for enforcing dirichlet constraints on embedded interfaces by embedded we refer to problems of general interest wherein the geometry of the interface is assumed independent of some underlying bulk mesh as such the robust imposition of dirichlet constraints using a lagrange multiplier field is not trivial to focus issues we consider a simple one sided problem that is representative of a wide class of evolving interface problems the bulk field is decomposed into coarse and fine scales giving rise to coarse scale and fine scale one sided sub problems the fine scale solution is approximated with bubble functions permitting static condensation and giving rise to a stabilized form bearing strong analogy with a classical method importantly the method is simple to implement readily extends to multiple dimensions obviates the need to specify any free stabilization parameters and can lead to a symmetric positive definite system of equations the performance of the method is then examined through several numerical examples the accuracy of the lagrange multiplier is compared to results obtained using a local version of the domain integral method the variational multiscale approach proposed herein is shown to both stabilize the lagrange multiplier and improve the accuracy of the post processed fluxes copyright 2006 john wiley sons ltd

analysis of a new stabilized higher order finite element method for advection diffusion equations abstract we consider a singularly perturbed advection diffusion two point boundary value problem whose solution has a single boundary layer based on piecewise polynomial approximations of degree k 1 a new stabilized finite element method is derived in the framework of a variation multiscale approach the method coincides with the supg method for k 1 but differs from it for k 2 estimates for the error to an appropriate interpolant are given in several norms on different types of meshes for k 1 enhanced accuracy is achieved by superconvergence postprocessing guarantees the same estimates for the error to the solution itself

the geometry of weighted low rank approximations the low rank approximation problem is to approximate optimally with respect to some norm a matrix by one of the same dimension but smaller rank it is known that under the frobenius norm the best low rank approximation can be found by using the singular value decomposition svd although this is no longer true under weighted norms in general it is demonstrated here that the weighted low rank approximation problem can be solved by finding the subspace that minimizes a particular cost function a number of advantages of this parameterization over the traditional parameterization are elucidated finding the minimizing subspace is equivalent to minimizing a cost function on the grassmann manifold a general framework for constructing optimization algorithms on manifolds is presented and it is shown that existing algorithms in the literature are special cases of this framework within this framework two novel algorithms a steepest descent algorithm and a newton like algorithm are derived for solving the weighted low rank approximation problem they are compared with other algorithms for low rank approximation as well as with other algorithms for minimizing a cost function on a grassmann manifold

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

two dimensional system optimal realizations with l sub 2 sensitivity minimization an expression is derived for the error variance of transfer function of a two dimensional 2 d system the optimal realization problem is then formulated by minimizing this variance with respect to all possible realizations of the system this problem is shown to be equivalent to the minimization of a pure l sub 2 norm based sensitivity measure it is shown that the problem can be solved using any standard minimization algorithm

an absolutely stabilized finite element method for the stokes problem on presente une formulation a elements finis absolument stabilisee pour le probleme de stokes on etablit des estimations d erreurs optimales dans la norme l 2 pour l approximation des champs de vitesses et de pressions

optimal design of iir digital filters with robust stability using conic quadratic programming updates in this paper minimax design of infinite impulse response iir filters with prescribed stability margin is formulated as a conic quadratic programming cqp problem cqp is known as a class of well structured convex programming problems for which efficient interior point solvers are available by considering factorized denominators the proposed formulation incorporates a set of linear constraints that are sufficient and near necessary for the iir filter to have a prescribed stability margin a second order cone condition on the magnitude of each update that ensures the validity of a key linear approximation used in the design is also included in the formulation and eliminates a line search step collectively these features lead to improved designs relative to several established methods the paper then moves on to extend the proposed design methodology to quadrantally symmetric two dimensional 2 d digital filters simulation results for both one dimensional 1 d and 2 d cases are presented to illustrate the new design algorithms and demonstrate their performance in comparison with several existing methods

stability and error estimates for the successive projection technique with b splines in time abstract we study the successive projection technique with b splines proposed by takizawa and tezduyar in 2014 computational mechanics vol 53 the projection is considered for x valued functions with a banach space x stability and error estimates in the l 0 t x norm are studied for b spline basis functions of degree p 1 2 3 4 the quasi uniformity of partition is always assumed and the projection is stable if p 1 we prove that for p 2 3 4 the uniformity of partition is a sufficient condition for stability to hold furthermore we infer from numerical experiments that stability holds at least for p 5 6 7 we also prove the error estimate using the spline preserving property of the projector if the projection is stable

improved l sub 2 sensitivity for state space digital system an improved l sub 2 sensitivity measure for linear state space digital systems is presented it gives a more precise evaluation of the transfer function deviation spl delta h z between the infinite wordlength system and the finite wordlength system when the structure matrices a b c contain 0 and spl plusmn 1 coefficients this measure can be applied in the system optimization resulting in a computationally efficient and very low l sub 2 sensitivity structure the theoretical result is verified by a numerical example

segregated runge kutta time integration of convection stabilized mixed finite element schemes for wall unresolved les of incompressible flows in this work we develop a high performance numerical framework for the large eddy simulation les of incompressible flows the spatial discretization of the nonlinear system is carried out using mixed finite element fe schemes supplemented with symmetric projection stabilization of the convective term and a penalty term for the divergence constraint these additional terms introduced at the discrete level have been proved to act as implicit les models in order to perform meaningful wall unresolved simulations we consider a weak imposition of the boundary conditions using a nitsche s type scheme where the tangential component penalty term is designed to act as a wall law next segregated runge kutta srk schemes recently proposed by the authors for laminar flow problems are applied to the les simulation of turbulent flows by the introduction of a penalty term on the trace of the acceleration these methods exhibit excellent stability properties for both implicit and explicit treatment of the convective terms srk schemes are excellent for large scale simulations since they reduce the computational cost of the linear system solves by splitting velocity and pressure computations at the time integration level leading to two uncoupled systems the pressure system is a darcy type problem that can easily be preconditioned using a traditional block preconditioning scheme that only requires a poisson solver at the end only coercive systems have to be solved which can be effectively preconditioned by multilevel domain decomposition schemes which are both optimal and scalable the framework is applied to the taylor green and turbulent channel flow benchmarks in order to prove the accuracy of the convection stabilized mixed fes as les models and srk time integrators the scalability of the preconditioning techniques in space only has also been proven for one step of the srk scheme for the taylor green flow using uniform meshes moreover a turbulent flow around a naca profile is solved to show the applicability of the proposed algorithms for a realistic problem

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

implementation and comparison of three isogeometric navier stokes solvers applied to simulation of flow past a fixed 2d naca0012 airfoil at high reynolds number abstract implementation of three different navier stokes solvers in an isogeometric finite element framework is presented in this paper the three solvers chorin projection method and coupled formulation both with the spalart allmaras turbulence model and variational multiscale vms method have been applied to simulate flow past a two dimensional naca0012 airfoil at a high reynolds number r e 3 10 6 for four different angles of attack the predicted flow characteristics have been compared and the effects of increasing the order of the spline element on the accuracy of prediction and computational efficiency are evaluated in this study it turns out that flow separation does not take place up to an angle of attack of 16 up to this angle of attack all three solvers predict similar results in good agreement with each other and with available experimental results however a big spread in lift and drag coefficients is observed in the stall regime our study also shows that for linear spline elements all three solvers are computationally similar for quadratic spline elements the chorin solver compares favorably to the others based on the results presented here

an anisotropic gls stabilized finite element method for incompressible flow problems abstract we consider a stabilized finite element approximation of incompressible flow problems in primitive velocity pressure variables which is based on a gls formulation equal order interpolation for the velocity and the pressure can be employed with this formulation the method introduced here is specially developed to be used on anisotropic finite element meshes with large element aspect ratios rather than using a single stabilization parameter within each element the jacobian matrix of the affine transformation from the reference element is employed for stabilization purposes stability and anisotropic error estimates in a suitable mesh dependent norm are proved for the linear stokes problem numerical results confirm the accuracy and robustness of the proposed method compared to similar previous stabilized schemes

the localized reduced basis multiscale method for two phase flows in porous media summary in this work we propose a novel model order reduction approach for two phase flow in porous media by introducing a global pressure formulation in which the total mobility which realizes the coupling between saturation and pressure is regarded as a parameter to the pressure equation in our approach the mobility itself is an optimal fit of mobility profiles that are precomputed using the time of flight for the initial saturation using this formulation and the localized reduced basis multiscale method we obtain a low dimensional surrogate of the high dimensional pressure equation by applying ideas from model order reduction for parametrized partial differential equations we are able to split the computational effort for solving the pressure equation into a costly offline step that is performed only once and an inexpensive online step that is carried out in every time step of the two phase flow simulation which is thereby largely accelerated usage of elements from numerical multiscale methods allows us to displace the computational intensity between the offline and online steps to reach an ideal runtime at acceptable error increase for the two phase flow simulation this is achieved by constructing reduced dimensional local spaces that lead to a non conforming global approximation space as one example for a coupling on the global space we introduce a discontinuous galerkin scheme copyright 2014 john wiley sons ltd

separable denominator state space realization of two dimensional filters using a canonic form in this paper a procedure is developed for the computation of a state space realization of a two dimensional filter the transfer function of this realization has a separable denominator the procedure relies on a canonic form for the state space realization and utilizes a finite sequence of two dimensional pulse response coefficients markov parameters

state of the art a survey of partially observable markov decision processes theory models and algorithms this paper surveys models and algorithms dealing with partially observable markov decision processes a partially observable markov decision process pomdp is a generalization of a markov decision process which permits uncertainty regarding the state of a markov process and allows for state information acquisition a general framework for finite state and action pomdp s is presented next there is a brief discussion of the development of pomdp s and their relationship with other decision processes a wide range of models in such areas as quality control machine maintenance internal auditing learning and optimal stopping are discussed within the pomdp framework lastly algorithms for computing optimal solutions to pomdp s are presented

realisation and approximation of linear infinite dimensional systems with error bounds the class of linear infinite dimensional systems with finite dimensional inputs and outputs whose impulse response h satisfies h in l 1 cap l 2 0 infty mathbb c p times m and induces a nuclear hankel operator is said to be of nuclear type for this class of systems it is shown that balanced or output normal realisations always exist and their truncations converge to the original system in various topologies furthermore explicit l infty bounds on the transfer function errors l 1 and l 2 bounds on the impulse response errors and hilbert schmidt and nuclear bounds on the hankel operator errors are obtained these truncations also generate an approximating sequence to the optimal hankel norm approximations to the original system and various error bounds of these approximants are deduced

realization of 2 d linear phase fir filters by using the singular value decomposition the singular value decomposition svd technique is investigated for the realization of a general two dimensional 2 d linear phase fir filter with an arbitrary magnitude response a parallel realization structure consisting of a number of one dimensional 1 d fir subfilters is obtained by applying the svd to the impulse response of a 2 d filter it is shown that by using the symmetry property of the 2 d impulse response and by developing an appropriate unitary transformation an svd yielding linear phase constituent 1 d filters can always be obtained so that the efficient structures of the 1 d linear phase filters can be exploited for 2 d realization it is shown that when the 2 d filter to be realized has some specified symmetry in its magnitude response the proposed svd realization would yield a magnitude characteristic with the same symmetry an analysis is carried out to obtain tight upper bounds for the errors in the impulse response as well as in the frequency response of the realized filter it is shown that the number of parallel sections can be reduced significantly without introducing large errors even in the case of 2 d filters with nonsymmetric magnitude response

implementation of 2d explicit depth extrapolation fir digital filters for 3d seismic volumes using singular value decomposition we propose a new scheme for implementing predesigned 2d complex valued wavefield extrapolation finite impulse response fir digital filters which are used for extrapolating 3d seismic wavefields the implementation is based on singular value decomposition svd of quadrantally symmetric 2d fir filters extrapolators to simplify the svd computations for such afilter impulse response structure we apply a special matrix transformation on the extrapolation fir filter impulse responses where we guarantee the retentionoftheirwavenumberphaseresponse unliketheexisting 2d fir filter implementation methods that are used for this geophysical application such as the mcclellan transformationoritsimprovedversion thisimplementationviasvdresults in perfect circularly symmetrical magnitude and phase wavenumber responses in this paper we also demonstrate that the svd method can save depending on the filter size more than 23 of the number of multiplications per output sample and approximately 62 of the number of additions per output sample when compared to direct implementation with quadrantal symmetry via true 2d convolution finally anapplicationtoextrapolationofaseismicimpulseisshown toproveourtheoreticalconclusions

the shifted boundary method for embedded domain computations part ii linear advection diffusion and incompressible navier stokes equations abstract we propose a new embedded finite element method for the linear advection diffusion equation and the laminar and turbulent incompressible navier stokes equations the proposed method belongs to the class of surrogate approximate boundary algorithms and is based on the idea of shifting the location where boundary conditions are applied from the true to a surrogate boundary accordingly boundary conditions enforced weakly are appropriately modified to preserve optimal error convergence rates we include the full analysis of stability and convergence of the method in the linear advection diffusion equation and a battery of tests for the case of laminar and turbulent incompressible navier stokes equations we also discuss the conservation properties of the proposed method in all cases

a posteriori optimization of parameters in stabilized methods for convection diffusion problems part i abstract stabilized finite element methods for convection dominated problems require the choice of appropriate stabilization parameters from numerical analysis often only their asymptotic values are known this paper presents a general framework for optimizing stabilization parameters with respect to the minimization of a target functional exemplarily this framework is applied to the supg finite element method and the minimization of a residual based error estimator an error indicator and a functional including the crosswind derivative of the computed solution benefits of the basic approach are demonstrated by means of numerical results

l sub 2 sensitivity analysis and minimization of 2 d separable denominator state space digital filters for two dimensional 2 d state space digital filters that are separable in the denominator the coefficient sensitivity is analyzed by using a pure l sub 2 norm and then the problem of minimizing the l sub 2 sensitivity is considered first a novel expression is developed in closed form for the evaluation of the l sub 2 sensitivity next an iterative procedure is presented for synthesizing the optimal filter structures that minimize the l sub 2 sensitivity finally a numerical example is given to illustrate the utility of the proposed technique

optimal stopping of partially observable markov processes a filtering based duality approach in this note we develop a numerical approach to the problem of optimal stopping of discrete time continuous state partially observable markov processes pomps our motivation is to find approximate solutions that provide lower and upper bounds on the value function such that the gap between the bounds can provide a practical measure of the quality of the solutions to this end we develop a filtering based duality approach which relies on the martingale duality formulation of the optimal stopping problem and the particle filtering technique we show that this approach complements an asymptotic lower bound derived from a suboptimal stopping time with an asymptotic upper bound on the value function we carry out error analysis and illustrate the effectiveness of our method on an example of pricing american options under partial observation of stochastic volatility

bubble functions prompt unusual stabilized finite element methods a second order linear scalar differential equation including a zero th order term is approximated using first the standard galerkin method enriched with bubble functions static condensation of the bubbles suggest an unusual stabilized finite element method for which we establish a convergence study and obtain successful numerical simulations the method is generalized to allow for a convection operator in the equation this work may be employed as a starting point for simulation of nonlinear equations governing turbulence phenomena flows with chemical reactions and other important problems

a new family of stable elements for nearly incompressible elasticity based on a mixed petrov galerkin finite element formulation adding to the classical hellinger reissner formulation another residual form of the equilibrium equation a new petrov galerkin finite element method is derived it fits within the framework of a mixed finite element method and is proved to be stable for rather general combinations of stress and displacement interpolations including equal order discontinuous stress and continuous displacement interpolations which are unstable within the galerkin approach error estimates are presented using the babuska brezzi theory and numerical results confirm these estimates as well as the good accuracy and stability of the method

computation of maxwell singular solution by nodal continuous elements abstract in this paper we propose and analyze a nodal continuous and h 1 conforming finite element method for the numerical computation of maxwell s equations with singular solution in a fractional order sobolev space h r where r may take any value in the most interesting interval 0 1 the key feature of the method is that mass lumping linear finite element l 2 projections act on the curl and divergence partial differential operators so that the singular solution can be sought in a setting of l 2 space we shall use the nodal continuous linear finite elements enriched with one element bubble in each element to approximate the singular and non h 1 solution discontinuous and nonhomogeneous media are allowed in the method some error estimates are given and a number of numerical experiments for source problems as well as eigenvalue problems are presented to illustrate the superior performance of the proposed method

adaptive variational multiscale methods for incompressible flow based on two local gauss integrations we consider variational multiscale vms methods with h adaptive technique for the stationary incompressible navier stokes equations the natural combination of vms with adaptive strategy retains the best features of both methods and overcomes many of their deficits a reliable a posteriori projection error estimator is derived which can be computed by two local gauss integrations at the element level finally some numerical tests are presented to illustrate the method s efficiency

realization of 3 d separable denominator digital filters with low l_2 sensitivity three dimensional 3 d digital filters find applications in a variety of image and video signal processing problems this paper presents a coefficient sensitivity analysis for a wide class of 3 d digital filters with separable denominators in local state space that leads to an analytic formulation for sensitivity minimization and to present two solution techniques for the sensitivity minimization problem at hand to this end a vector matrix vector decomposition of a given 3 d transfer function that separates the three variables and leads to a state space realization in a form convenient for subsequent analysis an l2 sensitivity analysis is then performed the result is a computationally tractable formula of the overall l2 sensitivity for 3 d digital filters the l2 sensitivity is minimized subject to l2 scaling constraints by using one of the two solution methods proposed one relaxes the constraints into a single trace constraint and solves the relaxed problem with an effective matrix iteration scheme while the other converts the contained optimization problem at hand into an unconstrained problem and solves it using a quasi newton algorithm a case study is presented to illustrate the validity and effectiveness of the proposed techniques

using convex switching techniques for partially observable decision processes we present and examine a novel method for obtaining solutions to specific discrete time optimal control problems our approach is based on linear state dynamics and convexity assumptions commonly satisfied in practical applications we show that the important class of optimal switching problems under partial observation is covered by our methodology and we exploit specific model features to achieve simple algorithmic form of a numerical solution

pathwise stochastic optimal control this paper approaches optimal control problems for discrete time controlled markov processes by representing the value of the problem in a dual lagrangian form the value is expressed as an infimum over a family of lagrangian martingales of an expectation of a pathwise supremum of the objective adjusted by the lagrangian martingale term this representation opens up the possibility of numerical methods based on monte carlo simulation which may be advantageous in high dimensional problems or in problems with complicated constraints

a stochastic mixed finite element heterogeneous multiscale method for flow in porous media a computational methodology is developed to efficiently perform uncertainty quantification for fluid transport in porous media in the presence of both stochastic permeability and multiple scales in order to capture the small scale heterogeneity a new mixed multiscale finite element method is developed within the framework of the heterogeneous multiscale method hmm in the spatial domain this new method ensures both local and global mass conservation starting from a specified covariance function the stochastic log permeability is discretized in the stochastic space using a truncated karhunen loeve expansion with several random variables due to the small correlation length of the covariance function this often results in a high stochastic dimensionality therefore a newly developed adaptive high dimensional stochastic model representation technique hdmr is used in the stochastic space this results in a set of low stochastic dimensional subproblems which are efficiently solved using the adaptive sparse grid collocation method asgc numerical examples are presented for both deterministic and stochastic permeability to show the accuracy and efficiency of the developed stochastic multiscale method

l sub 2 sensitivity minimization of one and two dimensional state space digital filters subject to l sub 2 scaling constraints this paper investigates the problem of minimizing an l sub 2 sensitivity measure subject to l sub 2 norm dynamic range scaling constraints for one dimensional 1 d as well as a class of two dimensional 2 d state space digital filters where the 2 d digital filters are described by a transposed structure of the fornasini marchesini second local state space model in each case a novel iterative technique is developed to solve the constraint optimization problem directly the proposed solution methods are largely based on the use of a lagrange function and some matrix theoretic techniques numerical examples are presented to demonstrate the effectiveness of the proposed techniques

virtual bubbles and galerkin least squares type methods ga l s abstract the equivalence between stabilized finite element methods or galerkin least squares tyoe methods ga l s and the standard galerkin method with bubble functions is established in an abstract framework the results are applicable to various finite element spaces including high order elements and applications to the advective diffusive model and to the stokes problem are presented illustrating the potential of the abstract theory introduced here

modeling of steep layers in singularly perturbed diffusion reaction equation via flexible fine scale basis abstract we present a new stabilized method for the diffusion reaction equation which develops sharp boundary and or internal layers for the reaction dominated case i e singularly perturbed case the method relies on an improved expression for the stabilization parameter that is derived via the fine scale variational formulation facilitated by the variational multiscale vms framework the proposed fine scale basis consists of enrichment functions which may be nonzero at element edges the derived stabilization parameter enjoys spatial variation over element interiors and along inter element boundaries that helps model the rapid variation of the residual of the euler lagrange equations over the domain this feature also facilitates consistent stabilization across boundary and internal layers as well as capturing anisotropic refinement effects the method is able to better satisfy the maximum principle as compared to other existing methods we present a priori mathematical analysis of the stability and convergence of the method for the diffusion reaction equation optimal convergence on meshes comprised of linear triangles and bilinear quadrilateral elements are presented for smooth problems as well as for problems with steep boundary layers stability and accuracy features of the method for problems with discontinuous forcing function internal layers and boundary layers are shown and its performance on unstructured and distorted meshes comprised of quadrilateral and triangular elements is highlighted

a fic based stabilized finite element formulation for turbulent flows abstract we present a new stabilized finite element fem formulation for incompressible flows based on the finite increment calculus fic framework onate 1998 in comparison to existing fic approaches for fluids this formulation involves a new term in the momentum equation which introduces non isotropic dissipation in the direction of velocity gradients we also follow a new approach to the derivation of the stabilized mass equation inspired by recent developments for quasi incompressible flows onate et al 2014 the presented fic fem formulation is used to simulate turbulent flows using the dissipation introduced by the method to account for turbulent dissipation in the style of implicit large eddy simulation

balanced realization of separable denominator multidimensional systems we present a general framework for internal balancing and model order reduction for an important class separable denominator of multidimensional systems it is shown that the internally balanced realizations for denominator separable n dimensional digital systems can be obtained by solving certain coupled lyapunov equations the proposed balancing and order reduction technique is illustrated by applying it to obtain low order approximations of gaussian and laplacian gaussian infinite impulse response filters

svd based design and new structures for variable fractional delay digital filters this paper shows that the problem of designing one dimensional 1 d variable fractional delay vfd digital filter can be elegantly reduced to the easier subproblems that involve one dimensional 1 d constant filter subfilter designs and 1 d polynomial approximations by utilizing the singular value decomposition svd of the variable design specification we prove that both 1 d constant filters and 1 d polynomials possess either symmetry or anti symmetry simultaneously therefore a vfd filter can be efficiently obtained by designing 1 d constant filters with symmetrical or antisymmetrical coefficients and performing 1 d symmetrical or antisymmetrical approximations to perform the weighted least squares wls vfd filter design a new wls svd method is also developed moreover an objective criterion is proposed for selecting appropriate subfilter orders and polynomial degrees our computer simulations have shown that the svd based design and wls svd design can achieve much higher design accuracy with significantly reduced filter complexity than the existing wls design method another important part of the paper proposes two new structures for efficiently implementing the resulting vfd filter which require less computational complexity than the so called farrow structure

optimal stochastic switching under convexity assumptions we address a method of approximate calculation of optimal control policy applicable to a particular class of stochastic control problems whose stochastic dynamics exhibit a certain convexity preserving property problems of this type appear in many applications and encompass important examples arising in the area of optimal stopping and in the framework of control based on partial observations utilizing this specific structure we suggest a numerical method which enjoys a number of desirable properties in particular we work out a remarkably strong method for calculation of the value function within our numerically well trackable approach we show a convergence to the value function of the original problem uniformly on compact sets this issue can be of great advantage particularly for high dimensional control problem where the only competing methods from least squares monte carlo family are able to serve merely l p convergence under several restrictions since the presented algorithm is simpl

variational multiscale residual based turbulence modeling for large eddy simulation of incompressible flows we present an les type variational multiscale theory of turbulence our approach derives completely from the incompressible navier stokes equations and does not employ any ad hoc devices such as eddy viscosities we tested the formulation on forced homogeneous isotropic turbulence and turbulent channel flows in the calculations we employed linear quadratic and cubic nurbs a dispersion analysis of simple model problems revealed nurbs elements to be superior to classical finite elements in approximating advective and diffusive processes which play a significant role in turbulence computations the numerical results are very good and confirm the viability of the theoretical framework

minimization of frequency weighted l_ 2 sensitivity subject to l_ 2 scaling constraints for two dimensional state space digital filters this paper investigates the problem of frequency weighted l2 sensitivity minimization subject to l2 scaling constraints for two dimensional 2 d state space digital filters described by the roesser model it is shown that the fornasini marchesini second model can be imbedded in the roesser model two iterative methods are developed to solve the constrained optimization problem encountered the first iterative method introduces a lagrange function and optimizes it using some matrix theoretic techniques and an efficient bisection method the second iterative method converts the problem into an unconstrained optimization formulation by using linear algebraic techniques and solves it by applying an efficient quasi newton algorithm the optimal filter structure with minimum frequency weighted l2 sensitivity and no overflow is then synthesized by an appropriate coordinate transformation case studies are presented to demonstrate the validity and effectiveness of the proposed techniques

a stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations in this paper a stabilized finite element method to deal with incompressibility in solid mechanics is presented a mixed formulation involving pressure and displacement fields is used and a continuous linear interpolation is considered for both fields to overcome the babuska brezzi condition a stabilization technique based on the orthogonal sub scale method is introduced the main advantage of the method is the possibility of using linear triangular or tetrahedral finite elements which are easy to generate for real industrial applications results are compared with standard galerkin and q1p0 mixed formulations for nearly incompressible problems in the context of linear elasticity

boundedness of multidimensional filters over a prescribed frequency domain signal processing often requires the magnitude of a filter simultaneously upper and lower bounded on some specified frequency domains in this paper on the basis of the structure of the span of a multivariate matrix polynomial a sufficient condition is derived for the boundedness of a multidimensional multiple input multiple output mimo infinite impulse response iir filter over a cuboid frequency domain this condition is expressed through a linear matrix inequality lmi and can be proved to be less conservative than a condition derived from an upper bound of matrix structured singular value moreover using parameter dependent lmis and the linear fractional transformation structure of the filter two necessary and sufficient conditions are also obtained for this boundedness verification problem which are again expressed by lmis furthermore lmi based conditions are derived for filter output matrix and direct transmission matrix which are applicable to filter design numerical examples are included to illustrate the efficiency and characteristics of the derived theoretical results

an efficient solver for space time isogeometric galerkin methods for parabolic problems abstract in this work we focus on the preconditioning of a galerkin space time isogeometric discretization of the heat equation exploiting the tensor product structure of the basis functions in the parametric domain we propose a preconditioner that is the sum of kronecker products of matrices and that can be efficiently applied thanks to an extension of the classical fast diagonalization method the preconditioner is robust w r t the polynomial degree of the spline space and the time required for the application is almost proportional to the number of degrees of freedom for a serial execution by incorporating some information on the geometry parametrization and on the equation coefficients we keep high efficiency with non trivial domains and variable thermal conductivity and heat capacity coefficients

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

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