higher order characteristics based method for incompressible flow computation on unstructured grids an algorithm for numerical simulation of incompressible flows on three dimensional unstructured grids is presented it is an upwind finite volume method based on the method of characteristics which is made possible with the introduction of chorin s artificial compressibility formulation flow variables are calculated along characteristics and their initial values are interpolated based on the signs of the corresponding characteristics in addition an upwind biased interpolation method of third order accuracy is used for interpolating flow variables on unstructured grids with these inherent upwinding techniques for evaluating convection fluxes at control volume surfaces no artificial viscosity is required the discretized equations are solved by an explicit multistage runge kutta time stepping scheme which is found to be efficient in terms of cpu and memory overheads a computer code has been developed using the numerical methods presented a number of test cases including two dimensional three dimensional inviscid and viscous flows have been calculated to validate the code and to evaluate the performance of the numerical algorithm

generation of viscous grids at ridges and corners an extension of lohner aiaa 93 3348 cp 1993 for the generation of high aspect ratio volume grids on surfaces with ridges and corners is presented for reynolds averaged navier stokes computations multiple point normals are introduced along ridges and corners the original technique generates a semi structured boundary layer of prismatic elements growing along point normals therefore extra degenerated faces must be introduced to take into account the multiple growth curves at ridges and corners and produce a valid topological surface triangulation the major task of the algorithm consists in recovering conformity in the surface mesh triangulation which has been lost due to the introduction of the virtual faces the procedure relies on a topological taxonomy of an arbitrary combination of concave and convex ridges each case is highlighted in detail special boundary conditions such as symmetry planes and periodic boundary conditions are also handled several complex geometries have been chosen to illustrate the proposed procedure and timings are given showing that the new module does not place any extra burden on the previous semi structured approach copyright 2008 john wiley sons ltd

benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

transient behavior analysis of vibrationally controlled nonlinear parabolic systems with neumann boundary conditions the transient behavior of vibrationally controlled distributed parameter systems governed by parabolic partial differential equations pdes with neumann boundary conditions is analyzed the analysis uses a certain mapping and a time invariant pde whose trajectories under this mapping yield the approximate moving averages along the trajectories of the vibrationally controlled system this approach considerably enhances the understanding of the behavior of vibrationally controlled distributed parameter systems and facilitates a selection of the parameters of stabilizing vibrations that ensure transient behavior with more desirable properties

non trivial effect of fast vibration on the dynamics of a class of non linearly damped mechanical systems the effect of very high frequency excitation on the slow dynamics of a class of non linearly damped mechanical oscillators is considered two different models of damping namely piecewise linear and pth power damping are considered fast excitation is modelled as triangular sinusoidal and random base excitation the effect of fast excitation is theoretically analyzed using the method of direct partition of motion mdpm and direct simulation the method of numerical averaging is also used where damping characteristics or excitations are not amenable to analytical techniques fast excitation has the non trivial effect of increasing and decreasing the low velocity damping of hard and soft dampers respectively the effect of fast excitation on the transient and steady state slow dynamics of the system is investigated by direct numerical integration of the equation of motion

vibrational control of nonlinear systems vibrational stabilizability in this work the theory of vibrational control for nonlinear systems is developed the present paper gives criteria for stabilizability of nonlinear systems by linear multiplicative vibrations by almost periodic forcing and by vector additive vibrations illustrative examples are also considered in a subsequent paper the problem of vibrational controllability and transient behavior will be addressed

adaptive distributed parameter systems identification with enforceable identifiability conditions and reduced order spatial differentiation presents the synthesis of adaptive identifiers for distributed parameter systems dps with spatially varying parameters described by partial differential equations pdes of parabolic elliptic and hyperbolic type the features of the pde setting are utilized to obtain the not directly intuitive parameter estimation algorithms that use spatial derivatives of the output data with the order reduced from that of the highest spatial plant derivative the tunable identifier parameters are passed through the integrator block which forms their orthogonal expansions the latter are shown to be pointwise plant parameter estimates in this regard the approach of the paper is in the spirit of finite dimensional observer realization in integrating rather than differentiating the output data only applied to the spatial rather than temporal domain the constructively enforceable identifiability conditions formulated in terms of the sufficiently rich input signals referred to as generators of persistent excitation are shown to guarantee the existence of a unique zero steady state for the parameter errors under such inputs the tunable parameters in the adaptive identifiers proposed are shown to converge to plant parameters in l sub 2 and the orthogonal expansions of these tunable parameters pointwise

a new class of nonmonotone conjugate gradient training algorithms in this paper we propose a new class of conjugate gradient algorithms for training neural networks which is based on a new modified nonmonotone scheme proposed by shi and wang 2011 the utilization of a nonmonotone strategy enables the training algorithm to overcome the case where the sequence of iterates runs into the bottom of a curved narrow valley a common occurrence in neural network training process our proposed class of methods ensures sufficient descent avoiding thereby the usual inefficient restarts and it is globally convergent under mild conditions our experimental results provide evidence that the proposed nonmonotone conjugate gradient training methods are efficient outperforming classical methods proving more stable efficient and reliable learning

edges stars superedges and chains abstract several possibilities for the reduction of indirect addressing operations within edge based solvers are discussed it is shown that indirect addressing operations may be reduced by a factor in excess of 1 4 if edges are grouped and linked together tests of benchmark loops on two common engineering computer platforms reveal that cpu saving factors ranging from 1 3 to 3 5 may be realized when switching from edge based to superedge or chain based loops

diagonal implicit multigrid algorithm for the euler equations a multigrid implementation of the alternating direction implicit algorithm has been developed to solve the euler equations of inviscid compressible flow the equations are approximated using a finite volume spatial approximation with added dissipation provided by an adaptive blend of second and fourth differences for computational efficiency the equations are diagonalized by a local similariity transformation so that only a decoupled system of scalar pentadiagonal systems need be solved along each line results are computed for transonic flows past airfoils and include pressure distributions to verify the accuracy of the basic scheme and convergence histories to demonstrate the efficiency of the method

asymptotic behavior of a nonlinear kirchhoff type equation with spring boundary conditions in this paper we consider the initial boundary value problem for a nonlinear kirchhoff type equation with the damping term and spring boundary conditions we establish the global existence and uniqueness of solutions to this problem in time and give an example and simulation to illustrate our results for the proof we use the faedo galerkin approximate method finally we study the asymptotic behavior of solutions and some of its simulation results results of this paper are able to apply industrial parts such as a typical model widely used to represent threads wires magnetic tapes belts band saws and so on

multigrid solution of the two dimensional euler equations on unstructured triangular meshes a multigrid algorithm has been developed to accelerate the convergence of the euler equations to a steady state on unstructured triangular meshes the method operates on a sequence of coarse and fine unstructured meshes and assumes no relation exists between the various meshes a tree search algorithm is used to efficiently identify regions of overlap between coarse and fine grid cells the multigrid method is applied to two different discretizations of the euler equations and results about multi element airfoils are presented for both discretization schemes convergence is accelerated by an order of magnitude resulting in convergence rates comparable to those obtained with structured multigrid algorithms

stability of fast periodic systems with time lags the stability criterion of r bellman et al 1985 for fast periodic linear systems is extended to systems with time delays applying the results of j hale 1966 the asymptotic stability criterion for a class of time lag systems is derived a comparison to a nondelay case is made and it is demonstrated that small delays can significantly affect the stability properties of this class of systems

parallel processing for the simulation of problems involving scattering of electromagnetic waves abstract the three dimensional simulation of the scattering of electromagnetic waves by obstacles of arbitrary geometrical shape is considered maxwell s curl equations are solved in the time domain on an unstructured mesh of linear tetrahedral elements the discrete equations are formed by a galerkin procedure with a lax wendroff consistent numerical flux function and explicit time stepping parallelisation of the procedure is achieved by mesh decomposition and the use of a single program multiple data model the approach is first validated and is then applied to problems involving the scattering of plane electromagnetic waves by a complete aircraft

a nonlinear conjugate gradient method with a strong global convergence property conjugate gradient methods are widely used for unconstrained optimization especially large scale problems the strong wolfe conditions are usually used in the analyses and implementations of conjugate gradient methods this paper presents a new version of the conjugate gradient method which converges globally provided the line search satisfies the standard wolfe conditions the conditions on the objective function are also weak being similar to those required by the zoutendijk condition

mesh generation and adaptivity for the solution of compressible viscous high speed flows an implicit explicit procedure for the solution of the compressible navier stokes equations on unstructured triangular and tetrahedral meshes is outlined a procedure for constructing continuous lines made up of edges in the mesh is employed and the implicit equation system is solved via line relaxation the problem of generating and adapting unstructured meshes for viscous flow simulations is addressed a number of examples are included which demonstrate the numerical performance of the proposed procedures

direct adaptive control of parabolic systems algorithm synthesis and convergence and stability analysis this paper presents a model reference adaptive control of a class of distributed parameter systems described by linear n dimensional parabolic partial differential equations unknown parameters appearing in the system equation are either constant or spatially varying distributed sensing and actuation are assumed to be available adaptation laws are obtained by the lyapunov redesign method it is shown that the concept of persistency of excitation which guarantees the parameter error convergence to zero in finite dimensional adaptive systems in infinite dimensional adaptive systems should be investigated in relation to time variable spatial variable and also boundary conditions unlike the finite dimensional case in infinite dimensional adaptive systems even a constant input is shown to be persistently exciting in the sense that it guarantees the convergence of parameter errors to zero averaging theorems for two time scale systems which involve a finite dimensional slow system and an infinite dimensional fast system are developed the exponential stability of the adaptive system which is critical in finite dimensional adaptive control in terms of tolerating disturbances and unmodeled dynamics is shown by applying averaging

three dimensional unstructured multigrid for the euler equations the three dimensional euler equations are solved on unstructured tetrahedral meshes using a multigrid strategy the driving algorithm consists of an explicit vertex based finite element scheme which employs an edge based data structure to assemble the residuals the multigrid approach employs a sequence of independently generated coarse and fine meshes to accelerate the convergence to steady state of the fine grid solution variables residuals and corrections are passed back and forth between the various grids of the sequence using linear interpolation the addresses and weights for interpolation are determined in a preprocessing stage using an efficient graph traversal algorithm the preprocessing operation is shown to require a negligible fraction of the cpu time required by the overall solution procedure whereas gains in overall solution efficiencies greater than an order of magnitude are demonstrated on meshes containing up to 350 000 vertices solutions using globally regenerated fine meshes as well as adaptively refined meshes are given

vibration control of an euler bernoulli beam under unknown spatiotemporally varying disturbance in this article the vibration suppression of an euler bernoulli beam system is considered by using the adaptive boundary control technique the dynamics of the beam are represented by a partial differential equation and four ordinary differential equations involving functions of both space and time by using lyapunov synthesis the robust boundary control with a disturbance observer is first proposed to suppress the vibration and attenuate the effect of the external disturbances to compensate for both the system parametric uncertainties and the disturbances uncertainties the adaptive boundary control is developed with the proposed boundary control the state of the beam system is proven to be uniformly ultimately bounded and converge to a small neighbourhood of zero by appropriately choosing the design parameters the effectiveness of the proposed control is successfully verified by numerical simulations

stabilization of infinte dimensional systems with periodic feedback gains and sampled output abstract a novel control technique periodic output feedback is investigated in the context of infinite dimensional linear dynamic systems with unbounded input and output operators this control scheme differs from classical control schemes in that the output of the system in question need not be monitored continuously but only monitored at sampling instants it is shown that for systems satisfying an analog of detectability and stabilizability periodic output feedback provides a stabilization scheme which is robust under perturbations of the sampling time sequence and is easily implementable

on the gain margin improvement using dynamic compensation based on generalized sampled data hold functions this paper shows that the use of dynamic compensation based on generalized sampled data hold functions gshf can arbitrarily improve the gain margin for continuous time nonminimum phase linear systems the gshf compensator is a particular periodic digital controller the effect of sampling period on the gain margin is analyzed furthermore it is proved that under a mild condition the gain margin improvement can be achieved without forcing the sampling period small an important advantage of periodic compensation over lti compensation is found to be the capability of reducing conflict between gain margin and sensitivity

technical communique periodic compensation of a class of decentralized systems with fixed modes this paper first finds that the high frequency w periodic controller suggested in lee meerkov and runolfsson 1987 for fixed mode removal and pole and zero placement of a class of decentralized systems a b i c i all the strongly interconnected channels of which satisfy c ib i 0 causes large o w oscillations in the outputs next it proposes an alternative controller a dual of the above that achieves the compensation with oscillations of o 1 only

a new conjugate gradient method with guaranteed descent and an efficient line search a new nonlinear conjugate gradient method and an associated implementation based on an inexact line search are proposed and analyzed with exact line search our method reduces to a nonlinear version of the hestenes stiefel conjugate gradient scheme for any inexact line search our scheme satisfies the descent condition bf g k sf t bf d k le frac 7 8 bf g k 2 moreover a global convergence result is established when the line search fulfills the wolfe conditions a new line search scheme is developed that is efficient and highly accurate efficiency is achieved by exploiting properties of linear interpolants in a neighborhood of a local minimizer high accuracy is achieved by using a convergence criterion which we call the approximate wolfe conditions obtained by replacing the sufficient decrease criterion in the wolfe conditions with an approximation that can be evaluated with greater precision in a neighborhood of a local minimum than the usual sufficient decrease criterion numerical comparisons are given with both l bfgs and conjugate gradient methods using the unconstrained optimization problems in the cute library

application of vibrational control to linear quadratic control problems abstract the application of the theory of vibrational control to linear quadratic control problems is developed the solution of the matrix riccati differential equation rde and the optimal trajectory are found approximately as power series of a small parameter the minimizing effect of vibrations on the maximal solution of rde and the cost functional is studied the region of attraction of the maximal solution of rde for the case of hamiltonian matrix with imaginary axis eigenvalues is found special attention is paid to the application of vibrations to the linear quadratic problem of stabilization with respect to a part of variables and transfer of the other variables to a given position a problem of vibrational stabilization and optimal control of a carriage with an inverted pendulum is solved as an example

high resolution finite volume computation of turbulent transonic flow past airfoils the objective is to develop a high resolution numerical scheme for calculating turbulent transonicows past airfoils the numerical scheme essentially combines a multigrid explicit nite volume time marching scheme with a convective upwind split pressure cusp scheme for controlling arti cial dissipation and convergence rate is further enhanced by using local time stepping and implicit residual smoothing one and two equation turbulence models areincorporated into thenumerical scheme to assess the ability of various turbulencemodels in the prediction of turbulent transonicow over airfoils within the framework of the cusp formulation of arti cial dissipation animplicit factored upwind biasednumericalschemeisusedfortheintegrationoftheturbulence eld equations transonic viscousows around the rae 2822 airfoil are computed using this scheme the results show reasonably good agreement with existing experimental data and an improved resolution of transonicviscousows he structure of turbulent transonicow around an airfoil is complex because of the presence of shock waves and vis cous layers when one computes thisow eld numerically it is important to establish a high resolution algorithm for the solution of turbulent transonicows so as to improve the numerical pre diction capabilities of the algorithm whereas a variety of ef cient numerical solution procedures have been proposed for the solution of navier stokes equations the focus of this work is on explicit nite volume numerical schemes that require an explicit addition of arti cial dissipative terms to ensure numerical stability and to resolve discontinuities and shear layers in theow eld the intro duction of numerical dissipation could lead to the contamination of the physical dissipation and excessive smearing of shock waves all oftheseaffecttheaccuracyofthesolutionofviscousowproblems hence there is a need to control the amount of arti cial dissipation without affecting numerical stability one approach is to reduce the arti cial dissipation through the use ofthe velocity scaling ofthe ar ti cial dissipation such as kunz 1 and varma and caughey 2 orofthe matrix value dissipation of turkel and vatsa 3 although the matrix valued dissipation produces better resolution ofow features than

correlation free forms for nonlinear stochastic systems abstract an asymptotic method for analysis of nonlinear systems with wide band and high frequency stochastic perturbation is developed correlation free ito limiting equations are derived and a generalization of the wong zakai correction for the drift term is obtained a correction for the diffusion term is also shown to exist several illustrative examples are considered

a spectral conjugate gradient method for solving large scale unconstrained optimization abstract this paper establishes a spectral conjugate gradient method for solving unconstrained optimization problems where the conjugate parameter and the spectral parameter satisfy a restrictive relationship the search direction is sufficient descent without restarts in per iteration moreover this feature is independent of any line searches under the standard wolfe line searches the global convergence of the proposed method is proved when k k f r holds the preliminary numerical results are presented to show effectiveness of the proposed method

vibrational feedback control of time delay systems this paper applies vibrational feedback control to time lag systems averaging theory for differential delay systems is presented and then applied to aid in the design of periodic controllers both stabilization and transient issues are discussed an illustrative example is given which demonstrates that the proposed controller 1 provides superior robustness properties in comparison to time invariant controllers when applied correctly 2 is not robust with respect to unmodeled delays and 3 does not have zero placement capabilities in the sense defined in the paper

multigrid acceleration of the flux split euler equations multigrid acceleration is applied to a flux split algorithm for solving the euler equations in three dimensions the basic algorithm is an implicit spatially split approximate factorization method the stability and performance of the scheme in comparison to other factorizations are examined results are presented for three dimensional flows that demonstrate substantially unproved convergence with the multigrid algorithm

some general effects of strong high frequency excitation stiffening biasing and smoothening abstract mechanical high frequency hf excitation provides a working principle behind many industrial and natural applications and phenomena this paper concerns three particular effects of hf excitation that may change the apparent characteristics of mechanical systems 1 stiffening by which the apparent linear stiffness associated with an equilibrium is changed along with derived quantities such as stability and natural frequencies 2 biasing by which the system is biased towards a particular state static or dynamic which does not exist or is unstable in the absence of the hf excitation and 3 smoothening referring to a tendency for discontinuities to be effectively smeared out by hf excitation illustrating first these effects for a few specific systems analytical results are provided that quantify them for a quite general class of mechanical systems this class covers systems that can be modelled by a finite number of second order ordinary differential equations generally non linear with periodically oscillating excitation terms of high frequency and small amplitude the results should be useful for understanding the effects in question in a broader perspective than is possible with specific systems for calculating effects for specific systems using well defined formulas and for possibly designing systems that display prescribed characteristics in the presence of hf excitation

condition of vibrational stabilizability for a class of nonlinear systems a notion of vibrational stabilizability for a class of nonlinear systems is introduced and analyzed

edge based finite element techniques for non linear solid mechanics problems edge based data structures are used to improve computational efficiency of inexact newton methods for solving finite element non linear solid mechanics problems on unstructured meshes edge based data structures are employed to store the stiffness matrix coefficients and to compute sparse matrix vector products needed in the inner iterative driver of the inexact newton method numerical experiments on three dimensional plasticity problems have shown that memory and computer time are reduced respectively by factors of 4 and 6 compared with solutions using element by element storage and matrix vector products copyright 2001 john wiley sons ltd

optimal control of a co rotating vortex pair averaging and impulsive control abstract the problem of controlling the position of a pair of point vortices using a strain field or a field of a single source sink is considered the problem dimension is reduced by averaging over the fast rotation of vortices around the center of vorticity control is assumed to be function of rotation phase only for the case of the strain field actuation optimal control problem is posed in three different settings control input whose integral over a cycle of vortex rotation is bounded bounded control input and mixed problem where both integral over a cycle and control magnitude are bounded it is shown that optimal solutions in integral setting are impulsive they consist of dirac delta functions applied at optimal phases during the cycle of vortex rotation if a bound on the control magnitude is added to the constraints the mixed problem a solution is obtained for which control is at the maximum amplitude except possibly for intervals during which it is zero these results are obtained by direct optimization for the case of a source sink field we pose the optimal control problem of the averaged equations through the use of the pontryagin maximum principle an obtained solution is a set of dirac delta pulses at optimal phases of the vortex rotation cycle a discussion of these results in the context of vortex merger control is given impulsive control arises here naturally as an optimal control design once averaging method is used

global convergence properties of conjugate gradient methods for optimization this paper explores the convergence of nonlinear conjugate gradient methods without restarts and with practical line searches the analysis covers two classes of methods that are globally convergent on smooth nonconvex functions some properties of the fletcher reeves method play an important role in the first family whereas the second family shares an important property with the polak ribiere method numerical experiments are presented

vibrational control without averaging the standard approach to vibrational control applies first order averaging methods to find an open loop periodic input that stabilizes an unstable equilibrium point while the capability of stabilization without feedback is appealing this formulation has drawbacks from a design perspective an alternative design framework based on stability maps for second order linear periodic systems is not as general but has significant potential advantages the averaging approach only guarantees that a solution exists the designer must then find that solution by other means furthermore the frequencies required may be too high for practical implementation use of stability maps makes a broader class of stabilizing inputs accessible allowing for example the use of lower frequency signals application to nonlinear and higher order systems is demonstrated with two examples the first is stabilization of the classical vertically forced inverted pendulum the second is delay of a pitchfork bifurcation in a fourth order nonlinear system in the second example we show that the averaging based approach necessarily fails to delay the bifurcation while the alternative method achieves significant extension of the stable operating region

periodic compensation of continuous time plants this note presents a periodic compensator which achieves robust stability for single input single output siso linear time invariant lti plants having both right half plane rhp poles and zeros a job lti controllers fail to do in addition for strictly proper plants this controller achieves model matching ensuring at the same time that the periodic oscillations present in the plant output are insignificant in magnitude the design steps are straightforward and linear algebraic in nature

an implicit finite element method for high speed flows a fast algorithm is presented for constructing continuous lines made up of element sides which pass once through each node of a general unstructured triangular mesh and which are generally aligned in prescribed directions the lines are used as the basis of an adaptive fully implicit unstructured grid procedure for the solution of two dimensional problems of steady compressible inviscid and laminar viscous high speed flows where the equation system is solved by line relaxation using a block tridiagonal equation solver for three dimensional laminar viscous simulations it is proposed to utilize an implicit explicit finite element formulation in the vicinity of solid walls a grid exhibiting structure in the normal direction is employed while away from this region the grid will be totally unstructured in the structured region lines in the normal direction to the wall are readily identified while lines in the surfaces parallel to the solid wall are constructed using the proposed two dimensional procedure the implicit algorithm is then used in the structured region and the equation solution is achieved via line relaxation an explicit form of the solution algorithm is used elsewhere to illustrate the performance of the proposed method solutions are obtained for both transonic inviscid and transonic and hypersonic laminar viscous problems in two dimensions the application of the proposed procedure to the solution of three dimensional hypersonic laminar viscous flow over a double ellipsoid configuration is also described

vibrational stabilization of linear time delay systems and its robustness with respect to the delay size abstract the purpose of this paper is to investigate the effectiveness of vibrational stabilization for a class of linear systems with time delay the total vibrational stabilizability conditions are formulated the robustness of an oscillatory stabilizing effect with respect to the magnitudes of the delays and the parameters of oscillations is also investigated on the basis of numerical examples

cost translation and a lifting approach to the multirate lqg problem it is shown how to translate an instance of a multirate sampled data lqg problem into an equivalent modified single rate shift invariant problem via a lifting isomorphism approach using this approach one can solve the multirate lqg problem without using periodic system theory or solving periodic riccati equations and without suffering any increases in state dimension this translation procedure shows the correct way to translate rms noise specification to the lifted domain for a multirate q design computer aided design package

two descent hybrid conjugate gradient methods for optimization in this paper we propose two new hybrid nonlinear conjugate gradient methods which produce sufficient descent search direction at every iteration this property depends neither on the line search used nor on the convexity of the objective function under suitable conditions we prove that the proposed methods converge globally for general nonconvex functions the numerical results show that both hybrid methods are efficient for the given test problems from the cute library

vibrational control of linear time lag systems with arbitrarily large but bounded delays it is shown that vibrational stabilization can be effective for linear systems with large bounded delays theorems are given that define the procedures for the search of the stabilizing vibrations robust oscillatory stabilization insensitive to the delay size is also shown to take place for some classes of systems

three dimensional adaptive grid embedding euler technique a new three dimensional adaptive grid euler procedure is presented that automatically detects high gradient regions in the flow and locally subdivides the computational grid in these regions to provide a uniform high level of accuracy over the entire domain a tunable semistructured data system is utilized that provides global topological unstructured grid flexibility along with the efficiency of a local structured grid system in addition this data structure allows for the flow solution algorithm to be executed on a wide variety of parallel vector computing platforms an explicit lime marching control volume procedure is used to integrate the euler equations to steady state

global convergence of a modified fletcher reeves conjugate gradient method with armijo type line search in this paper we are concerned with the conjugate gradient methods for solving unconstrained optimization problems it is well known that the direction generated by a conjugate gradient method may not be a descent direction of the objective function in this paper we take a little modification to the fletcher reeves fr method such that the direction generated by the modified method provides a descent direction for the objective function this property depends neither on the line search used nor on the convexity of the objective function moreover the modified method reduces to the standard fr method if line search is exact under mild conditions we prove that the modified method with armijo type line search is globally convergent even if the objective function is nonconvex we also present some numerical results to show the efficiency of the proposed method

vibrational control of systems with arrhenius dynamics abstract a nonlinear system with s shape steady state characteristic is referred to as a system with arrhenius dynamics the negative slope part of the s shape curve represents a set of unstable steady states using two examples of arrhenius systems catalytic reactor and continuous stirred tank reactor it is shown that introduction of sufficiently fast oscillations in the parameters of the system generates a new arrhenius system the steady state characteristic of which has a smaller negative slope part results of analytical investigation as well as numerical simulation are presented it is shown that vibrational stabilization of arrhenius systems gives an increase in productivity of the plants

vibrational control of nonlinear systems vibrational controllability and transient behavior in the first part of this work 1 the criteria for the existence of stabilizing parametric oscillations have been derived in the present paper the problem of choosing the stabilizing vibrations is addressed and the properties of transient behavior of vibrationally controlled nonlinear systems are analyzed

steady state behavior in the vibrational control of a class of nonlinear systems by ap forcing vibrational control is an open loop control technique that uses zero mean parametric vibrations for shaping the response of a linear or nonlinear dynamical system several theoretical results are available based on averaging techniques assuring the possibility of modifying the equilibrium properties of a system for nonlinear systems computational difficulties arise and theoretical results cannot easily be applied in this note the stationary behavior of a class of nonlinear systems vibrationally controlled by ap forcing is investigated a practical formula linking the amplitude and the frequency of the vibration and the amplitude of the steady state oscillation in the controlled variable is obtained as test cases the well known rayleigh equation a catalytic reactor equation and the phase locked loop equation are considered

three dimensional unstructured adaptive multigrid scheme for the euler equations we present a solution adaptive multigrid scheme for the three dimensional euler equations the procedure begins with an initial coarse mesh and enriches this mesh by h refinement in regions of high solution gradient this adaptive procedure is used to generate the multigrid levels required by the solver new boundary nodes are added in a way to reflect the underlying surface representation of the geometry the h refinement procedure is extremely fast and results in a scheme where only a small percentage of the overall cpu time is spent in the meshing and refinement part of the algorithm the multigrid flow solver typically reduces the cpu time by an order of magnitude over the same case without multigrid

vibrational control of chemical reactions in a cstr with delayed recycle stream vibrational control is a method of modification of dynamic properties obtained by introducing zero mean oscillations into system parameters this paper shows that by introducing oscillations into the flow rates of a continuous stirred tank reactor with delayed recycle stream it is possible to operate reactions in the vicinity of previously unstable steady states

three dimensional unstructured adaptive multigrid scheme for the navier stokes equations a solution adaptive multigrid scheme for solving the three dimensional navier stokes equations on unstructured meshes is presented the algorithm solves the equations on a fully unstructured mesh of tetrahedral elements using a multigrid time marching scheme the initial unstructured mesh is successively refined based on gradients in the flow solution with the multigrid levels being determined by the refinement procedure important issues related to solving viscous flows on unstructured meshes are discussed these include calculation of the viscous stress terms in a manner that prevents wiggles calculation of the time steps to include both inviscid and viscous effects numerical smoothing considerations minimization of computer storage requirements and implementation of the k e turbulence model solutions are presented for several examples of industrial importance that illustrate the potential of the method including transonic flow about an aircraft engine nacelle and in both rotating and nonrotating turbomachinery passages

globally convergent modified perry s conjugate gradient method abstract conjugate gradient methods are probably the most famous iterative methods for solving large scale optimization problems in scientific and engineering computation characterized by the simplicity of their iteration and their low memory requirements in this paper we propose a new conjugate gradient method which is based on the mbfgs secant condition by modifying perry s method our proposed method ensures sufficient descent independent of the accuracy of the line search and it is globally convergent under some assumptions numerical experiments are also presented

a three dimensional parametric mesher with surface boundary layer capability abstract a novel parametric surface meshing technique is presented its distinctive feature relies on successive approximations of the cad geometry through a hierarchical process where geometric information is gathered incrementally a detailed review of zero and first order surface approximations and their impact on parametric surface meshing algorithms is performed the proposed approach emphasizes the use of three dimensional information in order to be as independent as possible of the parametrization to overcome limitations of meshing purely in the parametric plane the presented technique includes semi structured boundary layer surface mesh generation which is a critical capability for accurate solutions to flows around geometries that have leading edge features numerous examples illustrate the method s robustness and ability to high quality meshes for complex cad geometries

flatness and defect of non linear systems introductory theory and examples we introduce flat systems which are equivalent to linear ones via a special type of feedback called endogenous their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of kalman s controllability the distance to flatness is measured by a non negative integer the defect we utilize differential algebra where flatness and defect are best defined without distinguishing between input state output and other variables many realistic classes of examples are flat we treat two popular ones the crane and the car with n trailers the motion planning of which is obtained via elementary properties of plane curves the three non flat examples the simple double and variable length pendulums are borrowed from non linear physics a high frequency control strategy is proposed such that the averaged systems become flat

fundamental theorems of averaging for functional differential equations abstract in this paper we improve on classical averaging theorems for functional differential equations by proposing new averaged models specifically we present averaged models which retain functional dependence on state variables delays and additional parametric dependence as shown in three examples the new models often yield improvements in approximation accuracy

vibrational control of a class of nonlinear systems by nonlinear multiplicative vibrations vibrational control is a nonclassical control principle which proposes a utilization of zero mean parametric excitation of a dynamical system for control purposes this paper extends nonlinear vibrational control theory developed in 8 9 to systems controlled by nonlinear multiplicative vibrations condition for partial vibrational stabilization with respect to a component of a steady state vector the choice of stabilizing vibrations and the transient motions are discussed for a certain practically important class of nonlinear vibrationally controlled systems the application of the results is demonstrated on the example of a catalytic reactor using a combination of numerical and analytical techniques

simultaneous stabilization of two discrete time plants using a 2 periodic controller a generic method for designing a 2 periodic controller for the simultaneous placement of the closed loop poles of two single input single output discrete shift invariant plants at the origin is presented the method consists of first recasting the simultaneous pole placement problem as one of solving a coupled pair of linear polynomial equations involving three unknown polynomials and then obtaining the controller parameters in terms of the coefficients of these polynomials the isolated cases for which such pole placement is not possible have been listed simulation results show that the performances of systems thus compensated are superior to their performances when compensated using the higher periodicity controllers suggested in literature

mpdata an edge based unstructured grid formulation we present an advancement in the evolution of mpdata multidimensional positive definite advection transport algorithm over the last two decades mpdata has proven successful in applications using single block structured cuboidal meshes viz cartesian meshes while employing homeomorphic mappings to accommodate time dependent curvilinear domains motivated by the strengths of the cartesian mesh mpdata we develop a new formulation in an arbitrary finite volume framework with a fully unstructured polyhedral hybrid mesh in mpdata as in any taylor series based integration method for pde the choice of data structure has a pronounced impact on the technical details of the algorithm aiming at a broad range of applications with a large number of control volume cells we select a general compact and computationally efficient edge based data structure this facilitates the use of mpdata for problems involving complex geometries and or inhomogeneous anisotropic flows where mesh adaptivity is advantageous in this paper we describe the theory and implementation of the basic finite volume mpdata and document extensions important for applications a fully monotone scheme diffusion scheme and generalization to complete flow solvers theoretical discussions are illustrated with benchmark results in two and three spatial dimensions

on line parameter estimation for infinite dimensional dynamical systems the on line or adaptive identification of parameters in abstract linear and nonlinear infinite dimensional dynamical systems is considered an estimator in the form of an infinite dimensional linear evolution system having the state and parameter estimates as its states is defined convergence of the state estimator is established via a lyapunov estimate the finite dimensional notion of a plant being sufficiently rich or persistently excited is extended to infinite dimensions convergence of the parameter estimates is established under the additional assumption that the plant is persistently excited a finite dimensional approximation theory is developed and convergence results are established numerical results for examples involving the estimation of both constant and functional parameters in one dimensional linear and nonlinear heat or diffusion equations and the estimation of stiffness and damping parameters in a one dimensional wave equation with kelvin voigt viscoelastic damping are presented

vss version of energy based control for swinging up a pendulum abstract a new algorithm ensuring global attractivity of the upright unstable equilibrium of a pendulum based on the variable structure system version of the energy speed gradient method is proposed it is shown that global attractivity cannot be obtained with continuous static state feedback a detailed global analysis of the transient behavior of the closed loop system is presented in addition it is shown that the global attractivity of the upright equilibrium can be achieved by applying a control of arbitrarily small magnitude

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

analysis and design of continuous time multivariable periodic controllers an mathcal h _ infty ltr based approach this article proposes a new high frequency continuous time two degrees of freedom dof periodic control scheme to compensate linear time invariant lti square nonsquare multivariable plants the proposed scheme is more effective when the plant is nonminimum phase or has more inputs than outputs it is proved that in averaged sense the design of periodic controller can be recast as designing a 2 dof lti controller for an equivalent lti plant the conditions for which this equivalent plant becomes minimum phase are also obtained when this plant is minimum phase and has no more inputs than outputs the synthesis of the above mentioned lti controller is carried out using an linear matrix inequality based mathcal h infty loop transfer recovery ltr approach to achieve linear quadratic regulator lqr loop behavior asymptotically the design method being based on ltr the reference input to output transfer function of the averaged compensated system becomes same as that using lqr the periodic controller is shown to exhibit negligible ripples in the plant output but o 1 ripples in control input suitable examples are considered to show the superiority of the proposed control

vibrational feedback control zeros placement capabilities it is shown that in addition to closed loop pole placement vibrational feedback controllers lead in the sense specified below to a possibility of open loop zeros assignability on this basis the superior performance characteristics of continuous time periodic controllers discovered in 3 6 are explained

application of averaging method for integro differential equations to model reference adaptive control of parabolic systems abstract an averaging theorem for integro differential equations is applied to the convergence analysis of controller parameters of a model reference adaptive control algorithm for a class of parabolic partial differential equations with constant coefficients the stability of an adaptive control algorithm is proven as well

vibrational control of nonlinear time lag systems vibrational stabilization and transient behavior abstract this paper addresses two problems of control of nonlinear time lag systems i an existence and a synthesis of parametric vibrations for their stabilization and ii the transient behavior analysis of the vibrationally controlled nonlinear systems with time lags in this work stabilizability conditions for two vibration types are formulated and procedures for the synthesis of the corresponding stabilizing vibrations are proposed the method for the transient behavior analysis of vibrationally controlled systems on a finite time interval is developed as well several examples are given to support the theory presented

semistructured mesh generation for three dimensional navier stokes calculations to mesh complex geometries efficiently is the authors view that a fully unstructured mesh generation technique holds the most promise there are many papers detailing mesh generation and flow solutions for inviscid flows on unstructured meshes however the computation of viscous flows on unstructured meshes is a relatively new area of research to accurately and efficiently compute viscous flows highly stretched cells aligned in the proper direction are required in the viscous layers many of the currently available unstructured mesh generators provide at most a limited ability to create these cells in the current work a method that builds layers of highly stretched prismatic cells on an existing unstructured surface triangulation is described the outer surface of this inflated triangulation provides a natural starting point for the advancing front algorithm used to fill the interior with tetrahedra care is taken to limit the possibility of a crossed over mesh in concave geometrical regions if the mesh does cross over then the offending cells are removed the combined algorithm of surface inflation and advancing front is demonstrated on a range of internal and external flow test cases a limited number of flow solutions are also presented

high frequency nonlinear vibrational control this paper discusses the feasibility of high frequency nonlinear vibrational control such control has the advantage that it does not require state measurement and processing capabilities that are required in conventional feedback control bellman et al 1986 investigated nonlinear systems controlled by linear vibrational controllers and proved that vibrational control is not feasible if the jacobian matrix has a positive trace this paper extends previous work to include nonlinear vibrational controllers a stability criteria is derived for nonlinear systems with nonlinear controllers and it is shown that a nonlinear vibrational controller can stabilize a system even if the jacobian matrix has a positive trace

operator based preconditioning of stiff hyperbolic systems we introduce an operator based scheme for preconditioning stiff components encountered in implicit methods for hyperbolic systems of pdes posed on regular grids the method is based on a directional splitting of the implicit operator followed by a characteristic decomposition of the resulting directional parts this approach allows for the solution of any number of characteristic components from the entire system to only the fastest stiffness inducing waves we apply the preconditioning method to stiff hyperbolic systems arising in magnetohydrodynamics and gas dynamics we then present numerical results showing that this preconditioning scheme works well on problems where the underlying stiffness results from the interaction of fast transient waves with slowly evolving dynamics scales well to large problem sizes and numbers of processors and allows for additional customization based on the specific problems under study

asymptotic behavior analysis of a coupled time varying system application to adaptive systems asymptotic behavior of a partial state of a coupled ordinary and or partial differential equation is investigated it is specifically shown that if a signal x t is a solution to a dynamic system existing for all t spl ges 0 in an abstract banach space and pth p spl ges 1 power integrable then x t spl rarr 0 as t spl rarr spl infin the system is allowed to be nonautonomous and assumes the existence of a lyapunov function since the derivative of the lyapunov function is negative semidefinite stability or uniform stability in the sense of lyapunov would be concluded however this paper further asserts that the partial state which remains in the time derivative of the lyapunov function converges to zero asymptotically

vibrational stabilization of nonlinear parabolic systems with neumann boundary conditions the conditions for the existence of the stabilizing vibrations for a class of distributed parameter systems governed by parabolic partial differential equations with neumann boundary conditions are derived the guidelines for the choice of the vibration parameters that ensure stabilization are given examples of vibrational stabilization of unstable systems by linear multiplicative and vector additive vibrations are given to support the theory

delay independent stability conditions and decay estimates for time varying functional differential equations this paper presents sufficient delay independent conditions that guarantee stability of nonlinear time varying functional differential equations fde s estimates on the rate of decay of solutions are also obtained

periodic discrete time systems stability analysis and robust control using zero placement a simple method based on floquet theory for obtaining the characteristic equation and hence stability of periodic discrete time systems is presented using this method it is shown that 2 periodic controllers can be used to relocate the zeros of siso plants some examples are considered to illustrate the use of 2 periodic controllers for robust control of finite gain margin problems

evaluation of navier stokes solutions using the integrated effect of numerical dissipation a method for evaluating the quality of solutions to the navier stokes equations is developed and illustrated with representative examples in solutions to the navier stokes equations it is important that added numerical dissipation does not overwhelm the real viscous dissipation to verify this it is necessary to be able to estimate quantitatively the effect of numerical dissipation a method for estimating the integrated effect of numerical dissipation on solutions to the navier stokes equations is developed in this paper the method is based on integration of the momentum equations and the computation of corrections due to numerical dissipation to the drag integral these corrections can then be considered as estimates of the error due to dissipation solutions to the navier stokes equations for laminar and turbulent flows over airfoils are used to illustrate the method the errors due to numerical dissipation are compared with the total numerical errors in the solutions the effect of mach number scaling of the numerical dissipation terms is discussed he evaluation of the quality of any numerical solution of the navier stokes equations and the validation of the computer code that yielded the solution necessarily require an estimation of the errors in the solution as hoist 1 has pointed out these errors fall under two broad categories physical modeling errors and numerical errors the physical modeling errors include among others those arising from the approximations involved in the navierstokes equations themselves or their thin layer approximation as well as those introduced by any model for the effects of turbulence the numerical errors include those due to the basic discretization scheme including any implicit or explicit numerical dissipation and are dependent upon the fineness and distribution of the grid physical modeling errors can be quantified only by comparison with the results of experiments or with the results of direct numerical simulations in which the corresponding approximations are not made before these comparisons can be meaningful however it is important to understand the level of numerical error and this can be done without recourse to comparison with experiments it is with these numerical errors and in particular with the effects of numerical dissipation that the present article is concerned the calculation of fluxes in several widely used finite volume schemes used to solve the euler and navier stokes equations can be shown to be equivalent to central differencing such schemes applied to the euler equations do not contain any inherent dissipation to prevent odd even point decoupling and oscillations near shock waves or stagnation points numerical dissipation terms must be added when solving the euler equations the navierstokes equations on the other hand possess dissipative properties due to the presence of the viscous terms but the physical dissipation provided by these terms in regions far away from the surface is usually small and the addition of numerical dissipation terms is still necessary to ensure the stability and robustness of the schemes while the added dissipation terms must be large enough for this purpose they must also be small enough not to overwhelm

a folding unfolding algorithm for the construction of semi structured layers in hybrid grid generation abstract a method is presented for generating semi structured layers in hybrid grids suitable for high reynolds number flow simulations it can produce superior quality grids around convex and concave ridges of the domain compared to a standard prismatic or advancing layers generator in a first step hybrid quadrilateral triangular grids are employed to cluster the surface grid towards sharp corners and ridges starting from this surface grid as an initial front for the volume grid generation a prismatic and hexahedral layers generation technique is used containing degenerate faces to add or remove elements in convex or concave areas of the geometry respectively the method can automatically create structured like grids in concave gaps and better discretize the space around convex ridges to improve overall accuracy the final grid remains conforming to not complicate the solver and post processing requirements several examples illustrate the application of the method

analysis and design of oscillatory control systems this paper presents analysis and design results for control systems subject to oscillatory inputs i e inputs of large amplitude and high frequency the key analysis results are a series expansion characterizing the averaged system and various lie algebraic conditions that guarantee the series can be summed various example systems provide insight into the results with regards to design we recover and extend a variety of point stabilization and trajectory tracking results using oscillatory controls we present novel developments on stabilization of systems with positive trace and on tracking for second order underactuated systems

non euclidian metrics and the robust stabilization of systems with parameter uncertainty this paper considers from a complex function theoretic point of view certain kinds of robust synthesis problems in particular we use a certain kind of metric on the disk the hyperbolic metric which allows us to reduce the problem of robust stabilization of systems with many types of real and complex parameter variations to an easily solvable problem in non euclidian geometry it is shown that several apparently different problems can be treated in a unified general framework a new result on the gain margin problem for multivariable plants is also given finally we apply our methods to systems with real zero or pole variations

vibrational control of nonlinear time lag systems with bounded delay averaging theory stabilizability and transient behavior this paper develops the theory of vibrational control of nonlinear time lag systems with arbitrarily large but bounded delay averaging theory for fast oscillating differential delay equations is presented and then applied to vibrational control conditions are given which ensure the existence of parametric vibrations that stabilize nonlinear time lag systems transient behavior is also discussed illustrative examples are given which show 1 the feasibility of the theory to important applications and 2 the differences in the theory presented and the existing known theory for vibrational control of ordinary differential equations