optimum sensitivity derivatives of objective functions in nonlinear programming the feasibility of eliminating second derivatives from the input of optimum sensitivity analyses of optimization problems is demonstrated this elimination restricts the sensitivity analysis to the first order sensitivity derivatives of the objective function it is also shown that when a complete first order sensitivity analysis is performed second order sensitivity derivatives of the objective function are available at little additional cost an expression is derived whose application to linear programming is presented

experiments with implicit upwind methods for the euler equations abstract a number of implicit integration schemes for the one dimensional euler equations with conservative upwind spatial differencing are tested on a problem of steady discontinuous flow fastest convergence quadratic for the first order backward euler scheme is obtained with the upwind switching provided by van leer s differentiable split fluxes which easily linearize in time with roe s nondifferentiable split flux differences the iterations may get trapped in a limit cycle this also happens in a second order scheme with split fluxes if the matrix coefficients arising in the implicit time linearization are not properly centered in space the use of second order terms computed from split fluxes degrades the accuracy of the solution especially if these are subjected to a limiter for the sake of monotonicity preservation second order terms computed from the characteristic variables perform best

geometric programming for aircraft design optimization formulating conceptual stage aircraft design problems as geometric programs which are a specific type of convex optimization problem is proposed recent advances in convex optimization offer sign

improving the efficiency of aerodynamic shape optimization the computational efficiency of an aerodynamic shape optimization procedure that is based on discrete sensitivity analysis is increased through the implementation of two improvements the first improvement involves replacing a grid point based approach for surface representation with a bezier bernstein polynomial parameterization of the surface explicit analytical expressions for the grid sensitivity terms are developed for both approaches the second improvement proposes the use of newton s method in lieu of an alternating direction implicit methodology to calculate the highly converged flow solutions that are required to compute the sensitivity coefficients

robust adaptive boundary control of a flexible marine riser with vessel dynamics in this paper robust adaptive boundary control for a flexible marine riser with vessel dynamics is developed to suppress the riser s vibration to provide an accurate and concise representation of the riser s dynamic behavior the flexible marine riser with vessel dynamics is described by a distributed parameter system with a partial differential equation pde and four ordinary differential equations odes boundary control is proposed at the top boundary of the riser based on lyapunov s direct method to regulate the riser s vibration adaptive control is designed when the system parametric uncertainty exists with the proposed robust adaptive boundary control uniform boundedness under the ocean current disturbance can be achieved the proposed control is implementable with actual instrumentation since all the required signals in the control can be measured by sensors or calculated by a backward difference algorithm the state of the system is proven to converge to a small neighborhood of zero by appropriately choosing design parameters simulations are provided to illustrate the applicability and effectiveness of the proposed control

on the stability of the reduced basis method for stokes equations in parametrized domains we present an application of reduced basis method for stokes equations in domains with affine parametric dependence the essential components of the method are i the rapid convergence of global reduced basis approximations galerkin projection onto a space wn spanned by solutions of the governing partial differential equation at n selected points in parameter space ii the off line on line computational procedures decoupling the generation and projection stages of the approximation process the operation count for the on line stage in which given a new parameter value we calculate an output of interest depends only on n typically very small and the parametric complexity of the problem the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation design optimization and real time control particular attention is given i to the pressure treatment of incompressible stokes problem ii to find an equivalent inf sup condition that guarantees stability of reduced basis solutions by enriching the reduced basis velocity approximation space with the solutions of a supremizer problem iii to provide algebraic stability of the problem by reducing the condition number of reduced basis matrices using an orthonormalization procedure applied to basis functions iv to reduce computational costs in order to allow real time solution of parametrized problem

aerodynamic design optimization using sensitivity analysis and computational fluid dynamics a new and efficient method is presented for aerodynamic design optimization which is based on a computational fluid dynamics cfd sensitivity analysis algorithm the method is applied to design a simplified scramjet afterbody configuration for an optimized axial thrust the euler equations are solved for the inviscid analysis of the flow which provides the objective function and the constraints of the optimization problem the cfd analysis is then coupled with the optimization procedure that used a constrained minimization method the sensitivity coefficients i e gradients of the objective function and the constraints needed for the optimization are obtained using a quasi analytic al method rather than the traditional finite difference approximations during the one dimensional search of the optimization procedure an approximate flow analysis predicted flow based on a first order taylor series expansion is used to reduce the computational cost finally the sensitivity of the optimum objective function to various flowfield problem parameters such as the mach number which are kept constant during the optimization is computed to predict new optimum solutions the flow analysis of the demonstrative example are compared with the experimental data it is shown that the method is more efficient than the traditional methods

problem formulation for multidisciplinary optimization this paper is about multidisciplinary design optimization or mdo the coupling of two or more analysis disciplines with numerical optimization the paper has three goals first it is an expository introduction to mdo aimed at those who do research on optimization algorithms since the optimization community has much to contribute to this important class of computational engineering problems second this paper presents to the mdo research community a new abstraction for multidisciplinary analysis and design problems as well as new decomposition formulations for these problems third the individual discipline feasible idf approaches introduced here make use of existing specialized analysis codes and they introduce significant opportunities for coarse grained computational parallelism particularly well suited to heterogeneous computing environments the key distinguishing characteristic of the three fundamental approaches to mdo formulation discussed here is the kind of disciplinary feasibility that

sensitivity analysis of the aeroacoustic response of turbomachinery blade rows a method for computing the change or sensitivity of the aeroacoustic response of a cascade to small changes in airfoil and cascade geometry is presented the steady flow is modeled by the full potential equation which is discretized using a variational finite element technique a streamline computational grid is generated as part of the steady solution newton iteration is used to solve for the nonlinear steady flow and grid equations with lower upper lu matrix decomposition plus one forward and one back substitution used to solve the resulting matrix equations similarly the unsteady small disturbance flow about the nonlinear mean flow is modeled by the linearized potential equation together with rapid distortion theory to account for vortical gusts these linearized equations are discretized using finite elements and solved with a single lu decomposition the sensitivities of the steady and unsteady flowfields to small changes in geometry are computed by perturbing the discretized equations about the nominal solutions the resulting linear system of equations can be solved very efficiently because the lu factors of the resulting matrix equations are computed as part of the nominal steady and unsteady solution results are presented in this paper to show the accuracy and efficiency of the method and the implications for aeroacoustic design of turbomachinery blades are discussed

natural norm a posteriori error estimators for reduced basis approximations we present a technique for the rapid and reliable prediction of linear functional outputs of coercive and noncoercive linear elliptic partial differential equations with affine parameter dependence the essential components are i rapidly convergent global reduced basis approximations galerkin projection onto a space wn spanned by solutions of the governing partial differential equation at n judiciously selected points in parameter space ii a posteriori error estimation relaxations of the error residual equation that provide inexpensive yet sharp bounds for the error in the outputs of interest and iii offiine online computational procedures methods which decouple the generation and projection stages of the approximation process the operation count for the online stage in which given a new parameter value we calculate the output of interest and associated error bound depends only on n typically very small and the parametric complexity of the problem in this paper we propose a new natural norm formulation for our reduced basis error estimation framework that a greatly simplifies and improves our inf sup lower bound construction offline and evaluation online a critical ingredient of our a posteriori error estimators and b much better controls significantly sharpens our output error bounds in particular through deflation for parameter values corresponding to nearly singular solution behavior we apply the method to two illustrative problems a coercive laplacian heat conduction problem which becomes singular as the heat transfer coefficient tends to zero and a non coercive helmholtz acoustics problem which becomes singular as we approach resonance in both cases we observe very economical and sharp construction of the requisite natural norm inf sup lower bound rapid convergence of the reduced basis approximation reasonable effectivities even for near singular behavior for our deflated output error estimators and significant several order of magnitude online computational savings relative to standard finite element procedures

an efficient feasible directions algorithm for design synthesis a nonlinear optimization algorithm is described that combines the best features of the method of feasible directions and the generalized reduced gradient method the algorithm uses the direction finding subproblem from the method of feasible directions to find a search direction that is equivalent to that of the generalized reduced gradient method but without the need to add a large number of slack variables associated with inequality constraints this leads to a core efficient algorithm for the solution of optimization problems with a large number of inequality constraints also during the one dimensional search it is not necessary to separate the design space into dependent and independent variables using the present method the concept of infrequent gradient calculations is introduced as a means of gaining further optimization efficiency finally it is shown that using the basic direction finding algorithm contained in this method the sensitivity of the optimum design with respect to problem parameters can be obtained without the need for second derivatives or lagrange multipliers the optimization algorithm and sensitivity analysis is demonstrated by numerical example

technical communique exponential stabilization of an axially moving string by linear boundary feedback the system modeled by an axially moving string and a mass damper spring mds controller applied at the right hand side rhs boundary of the string is considered the feature of the controller is not restricted at all and is determined by the system implicitly the mathematical model of this system is composed of an ordinary differential equation ode describing the mds and a partial differential equation pde describing the string the c 0 semigroup theory provides an elegant state space representation for the analysis of the coupled system the exponential stability is verified through the total mechanical energy dissipation and the semigroup theory the lower bound of the feedback gain is obtained

absolute stability results in infinite dimensions we derive absolute stability results of popov and circle criterion type for infinite dimensional systems in an input output setting our results apply to feedback systems in which the linear part is the series interconnection of an input output stable linear system and an integrator and the nonlinearity satisfies a sector condition which in particular allows for saturation and deadzone effects we use the input output theory developed to derive state space results on absolute stability applying to feedback systems in which the linear part is the series interconnection of an exponentially stable well posed infinite dimensional system and an integrator

comparison of newton s and quasi newton s method solvers for the navier stokes equations the results of a computational evaluation of several newton s and quasi newton s method solvers are discussed and analyzed computer time and memory requirements for iterating a solution to the steady state are recorded for each method roe s flux difference splitting together with the spekreijse van albada continuous limiter is used for the spatial discretization sparse matrix inversions are performed using a modified version of the boeing real sparse library routines and the conjugate gradient squared algorithm the methods are applied to exact and approximate newton s method jacobian systems for flat plate and flat plate wedge type ge ometries results indicate that the quasi newton s method solvers do not exhibit quadratic convergence but can be more efficient than the exact newton s method in select cases consistent goal of computational fluid dynamics cfd research has been to improve the efficiency of numerical algorithms one measure of this efficiency is the log of the residual which varies linearly with iteration count for typical cfd techniques these methods can be expected to converge at the same rate no matter how close they are to the final solution an exception to this behavior is the quadratic convergence newton s method for which the convergence rate actually increases as the final solution is approached when quadratic convergence has been attained the number of cor rect digits in the solution doubles with each iteration this behavior has been illustrated by several researchers who have obtained solutions of the potential equation 1 the euler equa tions 2 5 and the navier stokes equations 2 4 6 13 unfortu nately the number of iterations is a less important measure of the efficiency of a code than the total computation time quadratic convergence rates are typically accompanied by significant increases in algorithm complexity and hence in creased per iteration computational requirements it was the intent of this research to explore how the conver gence rate and per iteration efficiency vary for similar new ton s and quasi newton s method solvers so that the most efficient computational strategy can be identified to accom plish this goal the quadratic convergence newton s method solver developed by orkwis and mcrae6 8 was modified to create several quasi newton s method solvers approxima tions were made to the form of the jacobian and to the jacobian matrix inversion process the resulting schemes are evaluated based on their robustness and efficiency for two test problems

three dimensional aerodynamic shape optimization using discrete sensitivity analysis an aerodynamic shape optimization procedure based on discrete sensitivity analysis is extended to treat three dimensional geometries the function of sensitivity analysis is to directly couple computational fluid dynamics cfd with numerical optimization techniques which facilitates the construction of efficient direct design methods the development of a practical three dimensional design procedures entails many challenges such as 1 the demand for significant efficiency improvements over current design methods 2 a general and flexible three dimensional surface representation and 3 the efficient solution of very large systems of linear algebraic equations it is demonstrated that each of these challenges is overcome by 1 employing fully implicit newton methods for the cfd analyses 2 adopting a bezier bernstein polynomial parameterization of two and three dimensional surfaces and 3 using preconditioned conjugate gradient like linear system solvers whereas each of these extensions independently yields an improvement in computational efficiency the combined effect of implementing all the extensions simultaneously results in a significant factor of 50 decrease in computational time and a factor of eight reduction in memory over the most efficient design strategies in current use the new aerodynamic shape optimization procedure is demonstrated in the design of both two and three dimensional inviscid aerodynamic problems including a two dimensional supersonic internal external nozzle two dimensional transonic airfoils resulting in supercritical shapes three dimensional transport wings and three dimensional supersonic delta wings each design application results in realistic and useful optimized shapes

a combined genetic algorithm and nonlinear least squares method for material characterization using elastic waves abstract the inverse problem of material characterization is formulated as a parameter identification problem in which a set of parameters corresponding to the material property can be found by minimizing error functions formulated using the measured displacement response and the one computed by a forward solver based on projected candidates of parameters a hybrid numerical method is employed as the forward solver to calculate the dynamic displacement response on the surface of the composite plate for given material property a combined method is used as the inverse operator to determine the material property of composite plate in this method genetic algorithm is first used to select a set of better solutions close to the optima then the nonlinear least squares method is applied using these better solutions as the initial guesses finally the identification results can be determined from the solutions of nonlinear least squares method by comparing their corresponding error function values actual material characterizations of composites demonstrate the higher efficiency of the present method

optimal shape design of a two dimensional asymmetric diffuser in turbulent flow an optimal shape of two dimensional asymmetric diffuser with maximum pressure recovery at the exit is numerically obtained using a mathematical theory based on the variational calculus and gradient algorithm the initial diffuser is taken to be a two dimensional asymmetric diffuser for which much experimental and numerical data are available the reynolds number based on the bulk mean velocity and the channel height at the diffuser entrance is 1 8 10 4 f rom this initial shape optimal diffuser shapes are designed for six different geometric constraints such as the streamwise length and height of the diffuser the optimality condition for maximum pressure recovery is obtained to be zero skin friction along the diffuser wall the turbulent flow inside the diffuser is predicted using the k v2 f model and optimal shapes are obtained through iterative procedures to satisfy the optimality condition with the shape design flow separation that appeared in the initial diffuser is completely removed or significantly reduced for one of the optimal diffuser shapes obtained large eddy simulation is carried out to validate the result of the shape design the wall shear stress wall pressure mean velocity and turbulence quantities obtained from large eddy simulation are in good agreement with those from the simulation using the turbulence model

rapid inverse parameter estimation using reduced basis approximation with asymptotic error estimation this paper presents a rapid and reliable approach to solve inverse problems of parameter estimation for structural systems using reduced basis method rbm a reduced basis model is first developed with asymptotic error estimation and is used for fast computation of solving forward mechanics problems of solids and structures a genetic algorithm ga is then used in the inverse search procedure for parameter estimation the approach is applied to a typical inverse problem of estimating the crack location length and orientation inside a cantilever beam the displacements measured at five points on the lower surface of the beam which can also be evaluated by our fast rbm solver are used as inputs for constructing objective functions of error the genetic algorithm is used to search these parameters of the crack inside cantilever beam that minimize the objective function an example has been presented it is found that the estimated results are very accurate and reliable due to the use of rbm forward model with an effective and robust error estimation and detailed sensitivity analysis the present procedure is 460 times faster than the full fem model used inverse procedure

reduced basis approximation and a posteriori error estimation for stress intensity factors we develop reduced basis approximations rigorous a posteriori error bounds and offline online computational procedures for the accurate fast and reliable prediction of stress intensity factors or strain energy release rates for mode i linear elastic crack problems relevant to fracture mechanics we demonstrate the efficiency and rigor of our numerical method in several examples

cfd shape optimization using an incomplete gradient adjoint formulation a design methodology based on the adjoint approach for flow problems governed by the incompressible euler equations is presented the main feature of the algorithm is that it avoids solving the adjoint equations which saves an important amount of cpu time furthermore the methodology is general in the sense it does not depend on the geometry representation all the grid points on the surface to be optimized can be chosen as design parameters in addition the methodology can be applied to any type of mesh the partial derivatives of the flow equations with respect to the design parameters are computed by finite differences in this way this computation is independent of the numerical scheme employed to obtain the flow solution once the design parameters have been updated the new solid surface is obtained with a pseudo shell approach in such a way that local singularities which can degrade or inhibit the convergence to the optimal solution are avoided some 2d and 3d numerical examples are shown to demonstrate the proposed methodology copyright 2001 john wiley sons ltd

time varying and adaptive integral control of infinite dimensional regular linear systems with input nonlinearities closing the loop around an exponentially stable single input single output regular linear system subject to a globally lipschitz nondecreasing actuator nonlinearity and compensated by an integral controller with time dependent gain k t is shown to ensure asymptotic tracking of a constant reference signal r provided that a the steady state gain of the linear part of the system is positive b the reference value r is feasible in an entirely natural sense and c the function t mapsto k t monotonically decreases to zero at a sufficiently slow rate this result forms the basis of a simple adaptive control strategy that ensures asymptotic tracking under conditions a and b

algorithm developments for discrete adjoint methods this paper presents a number of algorithm developments for adjoint methods using the discrete approach in which the discretisation of the non linear equations is linearised and the resulting matrix is then transposed with a new iterative procedure for solving the adjoint equations exact numerical equivalence is maintained between the linear and adjoint discretisations the incorporation of strong boundary conditions within the discrete approach is discussed as well as a new application of adjoint methods to linear unsteady flow in turbomachinery

arbitrary decay rate for euler bernoulli beam by backstepping boundary feedback we consider a problem of stabilization of the euler bernoulli beam the beam is controlled at one end using position and moment actuators and has the ldquoslidingrdquo boundary condition at the opposite end we design the controllers that achieve any prescribed decay rate of the closed loop system removing a long standing limitation of classical ldquoboundary damperrdquo controllers the idea of the control design is to use the well known representation of the euler bernoulli beam model through the schrodinger equation and then adapt recently developed backstepping designs for the latter in order to stabilize the beam we derive the explicit integral transformation and its inverse of the closed loop system into an exponentially stable target system the transformation is of a novel volterra fredholm type the design is illustrated with simulations

backstepping boundary control of burgers equation with actuator dynamics in this paper we propose a backstepping boundary control law for burgers equation with actuator dynamics while the control law without actuator dynamics depends only on the signals u 0 t and u 1 t the backstepping control also depends on ux 0 t ux 1 t uxx 0 t and uxx 1 t making the regularity of the control inputs the key technical issue of the paper with elaborate lyapunov analysis we prove that all these signals are suciently regular and the closed loop system including the boundary dynamics is globally h 3 stable and well posed c 2000 elsevier science b v all rights reserved

using an adjoint approach to eliminate mesh sensitivities in computational design an adjoint algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced the method eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables an expense that has hindered large scale design optimization for practical applications the effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation followed by an explicit matrix vector product whose cost scales with the number of design variables and the resolution of the parameterized surface grid the methodology augments the current practice of using adjoints solely for the flowfield and leads to a dramatic computational savings the accuracy of the implementation is established and several sample design optimizations are shown

adaptive vibration isolation for axially moving strings theory and experiment high speed transport of continuous materials such as belts webs filaments or bands can cause unwanted vibration vibration control for these systems often focuses on restricting the response resulting from external disturbances e g support roller eccentricity or aerodynamic excitation to areas not requiring high precision positioning this paper introduces vibration controllers for an axially moving string system consisting of a controlled span coupled to a disturbed span via an actuator the system model includes a partial differential equation for the two spans and an ordinary differential equation for the actuator exact model knowledge and adaptive isolation controllers based on lyapunov theory regulate the controlled span from bounded disturbances in the adjacent uncontrolled span assuming distributed damping in the uncontrolled span the exact model knowledge and adaptive controllers exponentially and asymptotically drive the controlled span displacement to zero respectively while ensuring bounded uncontrolled span displacement and control force experiments demonstrate the effectiveness of the proposed controller in isolating the controlled span from disturbances and damping the controlled span displacement

efficient aerodynamic design method using a tightly coupled algorithm an efe cient aerodynamic design optimization method for the compressible euler equations is presented a gradient based optimization method is used to e nd the optimal design in conjunction with a continuous adjoint sensitivity analysis method to improve the efe ciency of the design method a tightly coupled algorithm based on a step size estimation isproposed the efe ciency of thepresentmethod is demonstrated through drag minimizations of a wing and an airfoil the result shows that the cost of the present method is signie cantly lower than that of the loosely coupled algorithm nomenclature ci e ux jacobian matrix in the computational domain d design variables vector fi e ux vector in the computational domain fi e ux vector in the physical domain g gradient vector of the object function i object function q conservative e ow variables vector r residual vector in the computational domain s searching direction step size along the searching direction s a lagrangian multiplier vector subscript face value at cell face superscript t transpose of vector or matrix

continuous adjoint sensitivities for optimization with general cost functionals on unstructured meshes a continuous adjoint approach is developed to obtain the sensitivity derivatives for the euler equations the completederivationofthecostateequations andtheirtransversality boundary conditionsarepresented both the state and the costate equations are second order e nite volume discretized for unstructured meshes and they are coupled with a constrained optimization algorithm also integrated into the overall methodology are a geometry parameterization method for the shape optimization and a dynamic unstructured mesh method for the shape evolution and the consequent volume mesh adaptations for the proof of concept three transonic airfoil optimization problems are presented this method accepts general cost functionals which are not necessarily functions of pressure only it is also shown that a switch to the natural coordinate system in conjunction with the reduction of the governing state equation to the control surface results in sensitivity integrals that are only a function of the tangential derivativesof the state variables thisapproach eliminates the need fornormal derivativecomputations that can be erroneous

a numerical approach for shape optimization of fluid flow domains abstract a numerical method for the shape optimization of fluid flow domains is presented and analyzed the procedure is based on a flow solver a mathematical optimization tool and a technique for shape variation which are combined into an integrated procedure the flow solver relies on the discretization of the incompressible navier stokes equations by means of the finite volume method for block structured boundary fitted grids with multi grid acceleration the optimization tool is an implementation of a trust region based derivative free method it is designed to minimize smooth functions whose evaluations are considered expensive and whose derivatives are not available or not desirable to approximate the shape variation is obtained by deforming the computational grid employed by the flow solver for this purpose displacement fields scaled by the design variables are added to the initial grid the displacement vectors are computed once before starting the optimization cycle by using a free form deformation technique applications illustrating the functionality and the properties of the method are presented for some examples of engineering interest such as the minimization of a pressure drop the maximization of a lift force and the optimization of a wall temperature

an online coupled state input parameter estimation approach for structural dynamics abstract in many practical structural applications unknown states inputs and parameters are present however most methods require one or more of these variables to be known in order to estimate the other s in this research an estimation technique which employs physical models is proposed to perform coupled state input parameter estimation in order to obtain a modeling technique which allows the estimation of a wide range of parameters in a generic fashion at a minimal computational cost even real time the use of a parametric model reduction technique is proposed the reduced model is coupled to an extended kalman filter ekf with augmented states for the unknown inputs and parameters this leads to a very efficient framework for estimation in structural dynamics problems special attention is also given to the measurement requirements in order to obtain an adequate observability of all unknown quantities and the necessity for at least one displacement level measurement is shown the proposed methodology is validated numerically and experimentally the approach is shown to be easy to tune and provides good results with different measurement methods

a novel reduced basis method with upper and lower bounds for real time computation of linear elasticity problems abstract this paper presents a novel reduced basis method for analyzing problems of linear elasticity in a systematical rapid and reliable fashion for solutions with both upper and lower bounds to the exact solution in the form of energy norm or compliance output the lower bound of the solution output is obtained form the well known reduced basis method based on the galerkin projection used in the finite element method which is termed as gp rbm for the upper bound a new reduced basis approach is developed by the combination of the reduced basis method and a smoothed galerkin projection used in the linearly conforming point interpolation method and it is thus termed as sgp rbm to examine the present sgp rbm we first conduct a theoretical study on the very important upper bound property reduced basis models for both gp rbm and sgp rbm are constructed with the aid of an asymptotic error estimation and greedy adaptive procedure the gp rbm and the newly proposed sgp rbm are applied to analyze a cantilever beam with an oblique crack to verify the proposed rbm technique in terms of accuracy convergence bound properties and computational savings both theoretical analysis and numerical results have demonstrated that the present method is a very efficient method for real time solutions providing exact output bounds

existence and asymptotic behaviour of solutions to weakly damped wave equations of kirchhoff type with nonlinear damping and source terms in this paper we consider the existence of a local solution in time to a weakly damped wave equation of kirchhoff type with the damping term and the source term utt t m tu t 2 u t 2ut t ut t put t u t qu t x p 0 q 0 2 0 with an initial value u 0 u0 ut 0 u1 and the dirichlet boundary condition u t x 0 where is an open bounded domain in rn with smooth boundary and m s is a locally lipschitz function we also discuss the global existence and exponential asymptotic behaviour of solutions

absolute stability of the kirchhoff string with sector boundary control this paper addresses the stability problem of the nonlinear kirchhoff string with nonlinear boundary control the nonlinear boundary control is the negative feedback of the transverse velocity of the string at one end which satisfies a sector constraint employing the integral type multiplier method we establish explicit absolute exponential stability of the kirchhoff string system

aerodynamic shape optimization using preconditioned conjugate gradient methods in an effort to further improve upon the latest advancements made in aerodynamic shape optimization procedures a systematic study is performed to examine several current solution methodologies as applied to various aspects of the optimization procedure it is demonstrated that preconditioned conjugate gradient like methodologies dramatically decrease the computational efforts required for such procedures the design problem investigated is the shape optimization of the upper and lower surfaces of an initially symmetric naca 0012 airfoil in inviscid transonic flow and at zero degrees angle of attack the complete surface shape is represented using a bezier bernstein polynomial

boundary control of a timoshenko beam system with input dead zone in this paper boundary control is designed for a timoshenko beam system with the input dead zone by the hamilton s principle the dynamics of the timoshenko beam system is represented by a distributed parameter model with two partial differential equations and four ordinary differential equations the bounded part is separated from the input dead zone and then forms the disturbance like term together with the boundary disturbance which finally acts on the timoshenko beam system boundary control based on the lyapunov s direct method is proposed to ensure the timoshenko beam converge into a small neighbourhood of zero where stability of the system is also analysed besides the existence and uniqueness of the solution of the timoshenko beam system are proved simulations are provided to reveal the applicability and effectiveness of the proposed control scheme

infeasible path optimal design methods with applications to aerodynamic shape optimization we consider optimal design of physical systems described by a nonlinear boundary value problem we propose a sequential quadratic programming method specifically tailored to the solution of this class of design problems a particular representation of the null space of the constraint jacobian that exploits its specific structure is employed the resulting method avoids resolution of nonlinear behavior at the optimization iterations while keeping the size of the problem as small as that of conventional approaches three variants of the method are developed and discussed these entail the solution of either two or three linear systems involving the jacobian matrix of the discretized form of the boundary value problem the method is used to solve aerodynamic design problems involving nonlinear transonic flow no special provisions are made for treating discontinuities and therefore the present implementation of the method is limited to problems with no shocks problems with up to 90 shape design variables are solved numerical results demonstrate a substantial performance improvement over conventional methods

optimized nonuniform rational b spline geometrical representation for aerodynamic design of wings the geometric representation and parameterization used in an aerodynamic wing design process determines the number of design variables and influences the smoothness of the wing representation in an attempt to reduce the number of design variables while preserving good smoothness properties the present research investigates the performance of an optimized nonuniform rational b spline nurbs geometrical representation for the aerodynamic design of wings as a first step an approach is described whereby optimal spatial positions and weights of a fixed number of nurbs control points is determined using a quasi newton optimization algorithm to approximate a general airfoil section the resulting optimized nurbs representation significantly reduces the number of design variables needed to define accurately a wing section while ensuring good smoothness properties in a second step the nurbs control point positions and weights are used as design variables in an aerodynamic optimization problem this methodology results in a rapid and robust design process as illustrated by examples of aerodynamic optimization for two and three dimensional cases

goal oriented model constrained optimization for reduction of large scale systems optimization oriented reduced order models should target a particular output functional span an applicable range of dynamic and parametric inputs and respect the underlying governing equations of the system to achieve this goal we present an approach for determining a projection basis that uses a goal oriented model constrained optimization framework the mathematical framework permits consideration of general dynamical systems with general parametric variations and is applicable to both linear and nonlinear systems results for a simple linear model problem of the two dimensional heat equation demonstrate the ability of the goal oriented approach to target a particular output functional of interest application of the methodology to a more challenging example of a subsonic blade row governed by the unsteady euler flow equations shows a significant advantage of the new method over the proper orthogonal decomposition

multigrid and upwind viscous flow solver on three dimensional overlapped and embedded grids a computationally efficient method is presented for solving the three dimensional governing equations of the viscous compressible flows about complex configurations with geometrically nonsimilar components the physical domain is decomposed into regions for which the grid generation is relatively simple and virtually without significant restrictions the navier stokes equations are solved by an implicit upwind finite volume scheme the convergence is accelerated by a multigrid algorithm despite the holes created in the computational domain by the overlapped grids which are completely or partially embedded within one another the block inversions and the diagonalized scalar inversions of the coefficient matrices are modified to allow the existence of such holes the method is tested through two demonstrative csises the solution for a supersonic flow past a blunt nose cylinder at a high angle of attack is obtained using a c o grid embedded in a global cartesian grid this solution is successfully compared with the one obtained using a single c o grid and the experimental data then supersonic interference flows past an ogive nose cylinder in the close proximity of a flat plate are solved using overlapped and topologically nonsimilar but simple grids

inverse identification of thermal parameters using reduced basis method a novel computational method is presented to inversely identify heat convection constants for complex engineering systems a reduced basis approach is developed as a forward solver for heat transfer analysis in order to significantly reduce the computational complexity in each forward analysis which is crucial for the inverse analysis of complex systems an intergeneration projection genetic algorithm ip ga is introduced as the inverse procedure to speed up the process of finding the desired global minimum of the fitness function of error that leads to the parameters to be identified as an example identification of the heat convection constants of a typical microelectronic package are performed using the present method and the performance is examined comparing with other inverse identification methods it is found that the reduced basis method combined with the ip ga significantly outperforms the conventional methods the proposed inverse identification method is efficient enough even for online analysis of inverse problems due to both the use of the reduced basis approach and the present inverse procedure

sensitivity analysis of unsteady aerodynamic loads in cascades a method for computing the effect perturbations in the shape of airfoils in a cascade have on the steady and unsteady flow through the cascade is presented first the full potential equation is used to describe the behavior of the nonlinear steady flow and the small disturbance unsteady flow through the cascade the steady flow and small disturbance unsteady flow versions of the full potential equation are then discretized on a computational grid of quadrilateral cells using a variational finite element technique the resulting discretized equations describing the nonlinear steady flow are solved using newton iteration with lower upper decomposition at each iteration similarly the discretized unsteady small disturbance equations which are linear are solved using a single lower upper decomposition next a sensitivity analysis is performed to determine the effect small changes in cascade and airfoil geometry have on the steady and unsteady flowfields the sensitivity analysis makes use of the nominal steady and unsteady flow lower upper decompositions so that no additional matrices need to be factored hence the present method is computationally very efficient

an approximately factored incremental strategy for calculating consistent discrete aerodynamic sensitivity derivatives in this study involving advanced fluid flow codes an incremental iterative formulation also known as the delta or correction form together with the well known spatially split approximate factorization algorithm is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis for smaller 2d problems a direct method can be applied to solve these linear equations in either the standard or the incremental form in which case the two are equivalent iterative methods are needed for larger 2d and future 3d applications however because direct methods require much more computer memory than is currently available iterative methods for solving these equations in the standard form are generally unsatisfactory due to a lack of diagonal dominance and perhaps ill conditioning of the coefficient matrix this problem can be overcome when these equations are cast in the incremental form these and other benefits are discussed herein the methodology is successfully implemented and tested in 2d using an upwind cell centered finite volume formulation applied to the thin layer navier stokes equations results are presented for two sample airfoil problems 1 subsonic low reynolds number laminar flow and 2 transonic high reynolds number turbulent flow

brief paper stabilization analysis of a generalized nonlinear axially moving string by boundary velocity feedback this paper addresses vibration suppression of an axially moving nonlinear string subject to boundary control at either the downstream or the upstream end the equation of motion and the boundary conditions are derived from hamilton s principle using the exact expression of the strain to describe the geometrical nonlinearity due to the finite transverse deformation we can approximate this model by various simpler models found in the literature we show that the oscillations of the moving string can be stabilized exponentially via linear negative velocity feedback acting at one end of the string our proofs rely on lyapunov s direct method using a carefully constructed energy functional

a point interpolation method with least square strain field pim lss for solution bounds and ultra accurate solutions using triangular mesh abstract a point interpolation method with least square strain field pim lss is developed for solid mechanics problems using triangular background mesh in the pim lss pim shape functions are used for displacement field construction that may or may not be compatible and a least square fitting technique is adopted to construct the strain field a strain constructed galerkin sc galerkin weak formulation is then proposed for establishing discretized pim lss models that have a number of special properties we proved theoretically 1 the pim lss provides a softening effect to the fem model and a stiffing effect to the node based smoothed point interpolation method ns pim model 2 the exact solution is bounded from both by pim lss solutions with strain field of zero order fitting and that with higher order fitting 3 there exists a preferred order of fitting for the strain field such that ultra accurate one order higher accuracy solution can be obtained using the pim lss these theorems and properties have been confirmed in numerical examples

reduced basis approximation and a posteriori error estimation for a boltzmann model abstract we present a reduced basis approximation and associated rigorous a posteriori output flow rate error bound for a simple linearized bgk boltzmann model for flow in a channel we consider two parameters the knudsen number and the accommodation coefficient the reduced basis approximation is built upon and the reduced basis error is measured relative to a truth mapped weighted spectral discretization of a stabilized petrov galerkin weak formulation we exploit the affine nature of the parametric dependence to provide an offline online computational procedure that decouples the spectral and reduced basis quantities the computational complexity of the online stage in which given a new parameter value we evaluate the reduced basis flow rate prediction and associated error bound depends only on the typically very small dimension of the reduced basis space n and not on the typically very large dimension of the truth spectral approximation n we demonstrate that the reduced basis approximation converges very rapidly with n and that the error estimator effectivities remain bounded albeit somewhat large in the online stage the reduced basis approximation achieves a certifiable relative accuracy of 10 2 with respect to the truth spectral result at only 1 100th the computational effort the method is appropriate in the many query and real time e g parameter estimation contexts in which there is a premium on reduced marginal cost and a tolerance for significant offline pre processing effort

approximation method for configuration optimization of trusses an efficient method for truss configuration optimization is presented elastic trusses are designed for minimum weight by varying the areas of the members and the location of the joints constraints on member stresses and euler buckling are imposed and multiple loading conditions are considered the method presented here utilizes an approximate structural analysis based on first order taylor series expansions of the member forces the force approximation succeeds in reducing the degree of coupling between the sizing and geometry design variables and thereby increases the accuracy of the approximation a numerical optimizer uses information from the approximate structural analysis as it minimizes the weight of the truss

flaw detection in sandwich plates based on time harmonic response using genetic algorithm an inverse identification technique is proposed to assess the presence location size and degree of flaw in the core layer of sandwich plates the time harmonic response of the sandwich plates is used as the input for inverse analysis the responses of the plates in forward analysis are predicted using finite element method fem based on mindlin plate theory the flaw is characterized by a set of parameters the genetic algorithm ga is applied to search the parameters to improve the efficiency of ga in searching for the true solution a two stage searching method is proposed numerical examples are given to illustrate the proposed technique

response surface techniques for diffuser shape optimization the design of incompressible diffusers for maximum pressure recovery is used to demonstrate the utility of response surface approximations for design optimization of eow devices two examples involving two and eve design variables are treated with the diffuser wall shapes described by polynomials and b splines in both cases monotonicity conditions drastically reduce the design space in this irregularly shaped space a pool of designs is selected by a d optimality criterion and analyzed by a e nite volume computational euid dynamics cfd code quadratic polynomial response surfaces are then e tted to the pressure recovery coefe cients to improve the prediction accuracy uncertain regressor terms and possible outlier design points are excluded based on statistical tests a standard optimization algorithm is used to e nd the optimal diffuser design from the response surface approximations the optimum diffusers exhibit minimal e ow separation and yield similar wall shapes for the two parameterizations a main asset of the response surface optimization approach lies in the smoothing of noisy response functions therefore theissueofnumericalnoiseincfd results basedon theuseof two different analysis codes is addressed