grid generation techniques in computational fluid dynamics revue des differentes methodes on montre que les regions tridimensionnelles sont mieux traitees par fragmentation du champ en sous regions avec generation de grilles dans chaque sous region interet des grilles adaptatives couplees a des solutions physiques

alternating direction adaptive grid generation an alternating direction method has been developed to adaptively resolve numerical solutions to physical problems by moving the points of a coordinate grid with the solution or with the salient quantities derived from it a surface grid is defined over the grid on the physical region grid movement is computed on this abstractly defined solution surface with the use of pointwise weights and is then projected back to determine new locations in the physical region the weights cause clustering relative to the uniform conditions of surface arc length and are formed with magnitudes of quantities that are used for point attraction when the salient quantities have been used to form the surface the gradients are implicitly revolved and surface curvature becomes the primary remaining quantity in each coordinate direction the magnitude of normal curvature is used with arbitrary weights a movement cycle generally consists of a sweep through the coordinate curves in a given direction on a curve by curve basis and then in alternating directions to do the same thing until all directions have been covered

robust state estimation for singularly perturbed systems abstractthis paper deals with the design of interval observers for singularly perturbed linear systems the full order system is first decoupled into slow and fast subsystems then using the cooperativity theory an interval observer is designed for the slow and fast subsystems assuming that the measurement noise and the disturbances are bounded and the singular perturbed parameter is uncertain this decoupling leads to two observers that estimate the lower and upper bounds for the feasible state domain a numerical example shows the efficiency of the proposed technique

a moving finite element method with error estimation and refinement for one dimensional time dependent partial differential equations we discuss a moving finite element method for solving vector systems of time dependent partial differential equations in one space dimension the mesh is moved so as to equidistribute the spatial component of the discretization error in h 1 we present a method of estimating this error by using p hierarchic finite elements the error estimate is also used in an adaptive mesh refinement procedure to give an algorithm that combines mesh movement and refinement we discretize the partial differential equations in space using a galerkin procedure with piecewise linear elements to approximate the solution and quadratic elements to estimate the error a system of ordinary differential equations for mesh velocities are used to control element motions we use existing software for stiff ordinary differential equations for the temporal integration of the solution the error estimate and the mesh motion computational results using a code based on our method are presented for several examples

interval estimation for lpv systems applying high order sliding mode techniques in this paper the problem of design of interval observers for linear parameter varying lpv systems containing non detectable or non strongly observable parts is addressed firstly a high order sliding mode hosm method is applied to the strongly observable subsystem obtained by an appropriate change of coordinates to estimate the state and its derivative secondly this information is used to decrease the level of uncertainty in the rest of the system which leads to improvement of accuracy of the set membership estimates generated by an interval observer moreover it is shown that hosm techniques allows us to relax the applicability conditions of standard interval observer design methods the efficiency of the proposed approach is demonstrated through simulation examples

coupled boundary interval observer for lpv systems subject to uncertainties in input output and parameters abstract the topic of this publication is the design of interval observers for lpv systems under consideration of parameter input and output uncertainties that are described by bounded intervals in the course of the design also time varying bounds of the parameter intervals are considered representing the case when parameters are measured with an unknown but bounded measurement error in this case an existing approach is extended to handle these parameter uncertainties the effectiveness of the approach is demonstrated by two numerical examples

brief paper interval observer design for consistency checks of nonlinear continuous time systems this paper deals with fault detection for nonlinear continuous time systems a procedure based on interval analysis is proposed to build a guaranteed qlpv quasi linear parameter varying approximation of the nonlinear model the interval qlpv approximation makes it possible to derive two point observers which estimate respectively the lower and the upper bound of the state vector using cooperativity theory a set guaranteed to contain the actual value of the residual is then designed the modelling uncertainties and measurement errors are taken into account at the design stage the proposed methodology is illustrated through numerical simulations

solution adaptive grid strategies based on point redistribution solution adaptive grid strategies based on the redistribution of a fixed number of points are described in this paper the redistribution is performed using weight functions that vary based on significant flow features the weight functions are evaluated using an equidistribution principle in this paper emphasis is placed on the development of weight functions applicable to compressible flows exhibiting large scale separated vortical flows vortex vortex and vortex surface interactions separated shear layers and multiple shocks of diaerent intensities algebraic elliptic and parabolic methods of grid generation have been utilized for structured grid redistribution additionally a point movement scheme is presented for generalized structured unstructured hybrid grid adaptation computer aided geometry design cagd techniques are combined with redistribution schemes to maintain the fidelity of solid boundaries in particular solid boundaries are represented using non uniform rational b splines nurbs a grid generation software system parallel multiblock adaptive grid generation pmag using an elliptic redistribution scheme is also described with emphasis placed on the parallel implementation for multiblock structured grids with unstructured blocking topologies and on interpolation issues computational examples demonstrating the influence of diaerent weight functions and grid redistribution strategies are presented 2000 elsevier science s a all rights reserved

generalized petrov galerkin methods for the numerical solution of burgers equation generalized petrov galerkin methods are applied in two different ways for the numerical solution of burgers equation in the first place it is used to produce upwinding in the way described by mitchell and griffiths 9 10 the main objective of this paper is in the second place to use it as a moving finite element method in particular it is shown that the methods of miller and co workers4 6 and herbst et al 7 8 can be incorporated in the more general approach presented in this paper several choices for the test functions are discussed and numerical results are given

fast generation of three dimensional computational boundary conforming periodic grids of c type a fast computer program grid3c has been developed to generate multilevel three dimensional c type periodic boundary conforming grids for the calculation of realistic turbomachinery and propeller flow fields the technique is based on two analytic functions that conformally map a cascade of semi infinite slits to a cascade of doubly infinite strips on different riemann sheets up to four consecutively refined three dimensional grids can be automatically generated and permanently stored on four different computer tapes grid nonorthogonality is introduced by a separate coordinate shearing and stretching performed in each of three coordinate directions the grids can be easily clustered closer to the blade surface the trailing and leading edges and the hub or shroud regions by changing appropriate input parameters hub and duct or outer free boundary can have different axisymmetric shapes a vortex sheet of arbitrary thickness emanating smoothly from the blade trailing edge is generated automatically by grid3c blade cross sectional shape chord length twist angle sweep angle and dihedral angle can vary in an arbitrary smooth fashion in the spanwise direction input coordinates must be cartesian while the output grid coordinates can be cartesian or cylindrical

a variational form of the winslow grid generator a structured grid generator based on a new approximation of dirichlet s functional is developed an unconstrained minimization process guarantees that all quadrilateral grid cells are convex at each iteration numerical results are presented in comparison with those for the original form of the winslow method a generalization to the case of adaptive grids based on harmonic maps between surfaces is considered

mesh independent spectra in the moving finite element equations we derive the moving finite element mfe equations for the solution of a scalar evolutionary equation in d space dimensions d geqq 1 and introduce the elementwise approach to mfe this approa

general curvilinear coordinate systems the basic ideas of the construction and use of numerically generated boundary fitted coordinate systems for the numerical solution of partial differential equations are discussed with such coordinate systems all computation can be done on a fixed square grid in the rectangular transformed region regardless of the shape or movement of the physical boundaries a number of different types of configurations for the transformed region and the basic transformation relations from a cartesian system to a general curvilinear system are given the material of this paper is applicable to all types of coordinate system generation

boundary fitted coordinate systems for numerical solution of partial differential equations a review a comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given some general mathematical framework and error analysis common to such coordinate systems is also included the general categories of generating systems are those based on conformal mapping orthogonal systems nearly orthogonal systems systems produced as the solution of elliptic and hyperbolic partial differential equations and systems generated algebraically by interpolation among the boundaries also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation dynamically adaptive coordinate systems coupled with the physical solution and time dependent systems that follow moving boundaries are treated references reporting experience using such coordinate systems are reviewed as well as those covering the system development

three dimensional adaptive grid method a three dimensional solution adaptive grid scheme is described which is suitable for complex fluid flows this method using tension and torsion spring analogies was previously developed and successfully applied for two dimensional flows in the present work a collection of three dimensional flow fields are used to demonstrate the feasibility and versatility of this concept to include an added dimension flow fields considered include 1 supersonic flow past an aerodynamic afterbody with a propulsive jet at incidence to the free stream 2 supersonic flow past a blunt fin mounted on a solid wall and 3 supersonic flow over a bump in addition to generating three dimensional solution adapted grids the method can also be used effectively as an initial grid generator the utility of the method lies in 1 optimum distribution of discrete grid points 2 improvement of accuracy 3 improved computational efficiency 4 minimization of data base sizes and 5 simplified three dimensional grid generation

design of interval observer for a class of uncertain unobservable nonlinear systems this paper investigates the interval observer design for a class of nonlinear continuous systems which can be represented as a superposition of a uniformly observable nominal subsystem with a lipschitz nonlinear perturbation it is shown in this case there exists an interval observer for the system that estimates the set of admissible values for the state consistent with the output measurements an illustrative example of the observer application is given with simulation results

a moving petrov galerkin method for transport equations a time dependent transport equation is solved numerically by using a petrov galerkin technique on a time dependent grid a piecewise linear trial solution and piecewise hermite cubic test functions are used the same method is also applied to a time independent problem in which case it automatically generates a grid in a way which bears some resemblance to certain existing grid generation techniques several numerical examples are given

sensitivity based methods for convergence acceleration of iterative algorithms abstract a new method to accelerate the convergence of iterative schemes for the numerical integration of systems of partial differential equations has been developed the basic idea is that the residual at a grid point depends on the values of the solution vector at the neighboring grid points used in the local discretization approximation thus the new acceleration method is based on the sensitivity of the future residual to the change in the solution vector at the neighboring grid points with the objective to minimize the future residual the result is a set of optimum iterative relaxation parameters for the entire flow field or for each individual grid line the method is easy to implement in the existing codes we have applied it to a finite difference code for two dimensional incompressible navier stokes equations test cases involve laminar and turbulent flows with severe grid clustering and flow separation the results are compared with those of a basic explicit runge kutta rk time stepping iterative algorithm and with the implicit residual smoothing 1rs and the distributed minimal residual dmr acceleration techniques the new acceleration scheme is shown to be superior to these methods especially on highly clustered grids

interval estimation for continuous time switched linear systems this paper deals with the design of interval observers for switched linear systems sls a class of hybrid systems under the assumption that the disturbances and the measurement noise are bounded upper and lower bounds for the state are calculated new conditions of cooperativity in discrete time instants are firstly proposed then some techniques for interval estimation are developed in continuous time it is shown that it is possible to calculate the observer gains making the estimation error dynamics cooperative and stable via some change of coordinates under arbitrary switching sequences the performances of the developed techniques are illustrated through numerical examples

structured mesh adaption space accuracy and interpolation methods abstract in this paper we review the main stages of the construction of a variational method to optimize and to adapt two and three dimensional structured grids the formalism and the notation presented enable a constructive and comprehensive description of the adaption process the major part of this paper is devoted to the study of various interpolation methods which are used for the correct space localization of the adaption for cell center cell vertex recovery and for overlapping grids interpolation in particular the behavior of the linear interpolation least square minimization and taylor series expansion methods are investigated several examples of the methods described and the combination of adaption and interpolation are presented showing their possibilities

adaptive gridding for finite difference solutions to heat and mass transfer problems abstract the authors purpose in writing this paper is to review some of their recent work in the calculation of optimal meshes for the solution of parabolic and elliptic partial differential equations pde they first explain our strategies for the adaptive placement of mesh points in addition they make some speculation as to promising avenues for future research in mesh adaptation finally they discuss examples of the application of adaptive gridding to problems of heat and mass transfer they draw these examples from our work in combustion modeling in obtaining numerical solutions of pdes the spatial derivatives are often approximated by discrete representations on a mesh network the accuracy of any numerical solution depends in an important way on the relationship of the location of the mesh points to changes in the dependent variables the authors objective is to investigate finite difference methods in which the mesh networks adapt themselves dynamically to obtain accurate solutions such methods represent an important advance in overcoming a major shortcoming of traditional fixed mesh methods which are often unable to resolve accurately steep fronts or sharp peaks

a vectorized finite volume adaptive grid algorithm for navier stokes calculations an adaptive grid finite volume method has been used to solve the navier stokes equations for complete forebody and afterbody flowfields around blunt bodies the code which is applicable for axisymmetric or two dimensional flows allows the mesh to adjust during the computation to provide a closer spacing of mesh points in regions of high gradients thus minimizing the number of required computational points the solution technique is explicit utilizing a maximum time step advancement at each grid point to accelerate convergence to the steady state the code has been fully vectorized for efficient solution on the cyber 203 computer a very flexible rezoning routine is used to concentrate mesh points anywhere in the field either by a user defined weighting function or by allowing high gradient regions to adjust the grid the grid adjustment routine is implicit in nature and represents a very small portion of the total computational cost currently the code runs in approximately 1 6 x 10 5 seconds per grid point per iteration

adaptive zoning for singular problems in two dimensions abstract winslow s method for the automatic generation of computation meshes is extended to adaptively vary the zone sizes and orthogonality of grid lines in the resulting mesh through simple analysis and numerical examples the adaptive mesh is shown to give significant increases in accuracy in the computation of singular problems

acceleration of iterative algorithms on highly clustered grids a family of new methods has been developed to accelerate the convergence rate of iterative algorithms for obtaining a steady state solution as an asymptotic limit of an unsteady second order partial differential equation or a system of such equations it was assumed that a central differencing has been used for spatial discretization the new acceleration methods are based on the sensitivity of the future residual at every grid point to the change in the solution vector components at the neighboring grid points used in the local discretization approximation the acceleration parameters introduced in the methods have been optimized with the objective to minimize the future global residual the new sensitivity based methods have been applied to finite difference codes for twoand three dimensional laminar incompressible flow navier stokes equations two dimensional turbulent incompressible flow navier stokes equations and two dimensional compressible flow euler equations the new sensitivity based acceleration methods demonstrated superior performance in all test cases that involved severe grid clustering and grid nonorthogonality and included laminar and turbulent flows with closed and open flow separation

interval observer design for continuous time switched systems under known switching and unknown inputs this paper deals with unknown input estimation for switched linear systems in an unknown but bounded error ubbe framework based on a known switching signal and under the fulfilment of the relati

optimum acceleration factors for iterative solution of linear and nonlinear differential systems abstract a new acceleration concept for iterative schemes is described the concept is based on elementary variational calculus and can be readily implemented in the iterative solution of a wide variety of linear and nonlinear differential systems the method is not limited to finite difference finite element or finite volume discretization schemes but only to schemes that are inherently iterative most importantly the method is exact in the sense that optimal relaxation acceleration factors can be analytically determined for a class of commonly encountered systems possessing simple nonlinearity for systems exhibiting complex nonlinearity the method can be applied in a semi exact but highly accurate fashion using truncated taylor series without any modification this acceleration method can be directly applied to existing iterative schemes using either orthogonal or completely arbitrary non orthogonal computational grids since the formulation of the method is dependent only on the governing differential system the described method belongs to the general class of minimal residual techniques but can be applied to nonlinear systems

linear variational methods and adaptive grids abstract the construction of two and three dimensional computational grids using linear variational methods is analyzed the generating equations include aspect ratios to prevent grid folding and stretching transformations to distribute grid points control functions for adaptive grids can also be included in all cases the grid points are determined by solving a diagonally dominant linear system of equations

interval estimation for continuous time lpv switched systems this paper deals with interval state estimation for continuous time linear parameter varying lpv switched systems with measured polytopic parameter dependence assuming a known switching signal

interactive method of variational grid generation abstract in the paper the elliptic variational grid generation technique based on methods of optimal control for distributed systems is presented the interactive nature of the method consists in adaptive changing of the golas of correction steps in the process of grid generation the corrections concern orthogonality and uniformity of the mesh

an unknown input interval observer for lpv systems under l2 gain and l gain criteria abstract this paper investigates the design of an unknown input interval observer for linear parameter varying systems the proposed method provides a solution to the decoupling conditions under l 2 gain and l gain performance level it is shown that the design of the unknown input interval observer parameters can be formulated as a sdp problem the major advantages with regard to other solutions is that first it does not require the explicit knowledge of a time varying state transformation for the estimation error dynamics to satisfy the meztler property rather it is shown how such a property can be formulated as a part of the sdp optimization process second decoupling and l 2 l constraints are formulated on the thickness of the interval length in spite of half the interval length the proposed methodology is illustrated on a numerical academic example

design of positive linear observers for positive linear systems via coordinate transformations and positive realizations two new approaches to designing positive linear observers for positive linear systems are proposed the first one employs a coordinates transformation and the second relies on the theory of positive realization these approaches allow one to enlarge the class of positive systems that admit positive linear observers new results on compartmental systems are also presented

moving finite elements i we present new and general numerical methods for dealing with problems whose solutions develop sharp transition layers or near shocks these methods allow many nodes automatically to concentrate in the critical regions and move with them for clarity of exposition we concentrate on the space of piecewise linear functions with movable nodes with burgers equation as our test equation but the generalization to much more general spaces and equations including even certain previous moving vorticity blobs of the first author and s doss for the navier stokes equations becomes clear in this paper we present the theoretical and computational details of our scheme along with computational trial runs for burgers equation showing that the nodes do concentrate sharply and move with the shocks as desired the conclusiveness of these preliminary numerical trials is marred somewhat by the fact that we never successfully debugged a newton s method for our implicit stiff ode solver and were thus limited to ver

brief paper near optimal interval observers bundle for uncertain bioreactors in this paper we design an interval observer for the estimation of unmeasured variables of uncertain bioreactors the observer is based on a bounded error observer as proposed in lemesle v gouze j l 2005 hybrid bounded error observers for uncertain bioreactor models bioprocess and biosystems engineering 27 311 318 that makes use of a loose approximation of the bacterial kinetics we first show how to generate guaranteed upper and lower bounds on the state provided that known intervals for the initial condition and the uncertainties are available these so called framers depend on a tuning gain they can be run in parallel and the envelope provides the best estimate an optimality criterion is introduced leading to the definition of an optimal observer we show that this criterion provides directly a gain set containing the best framers the method is applied to the estimation of the total biomass of an industrial wastewater treatment plant demonstrating its efficiency

a two dimensional mesh moving technique for time dependent partial differential equations abstract we discuss an adaptive mesh moving technique that can be used with a finite difference or finite element scheme to solve initial boundary value problems for systems of partial differential equations in two space dimensions and time the mesh moving technique is based on an algebraic node movement function determined from the geometry and propagation of regions having significant discretization error indicators our procedure is designed to be flexible so that it can be used with many existing finite difference and finite element methods to test the mesh moving algorithm we implemented it in a system code with an initial mesh generator and a maccormack finite difference scheme on quadrilateral cells for hyperbolic vector systems of conservation laws results are presented for several computational examples the moving mesch scheme reduces dispersive errors near shocks and wave fronts and thereby reduces grid requirements necessary to compute accurate solutions while increasing computational efficiency

a simple adaptive technique for nonlinear wave problems abstract a method for the numerical integration of the nonlinear schrodinger equation is derived which uses variable time steps and a moving spatial grid the benefits of adaptation are clearly demonstrated in the numerical experiments reported the simple technique employed to move the nodes can be applied with little coding effort to general one dimensional systems of pdes

a quasi elliptic transformation for moving boundary problems with large anisotropic deformations we have developed a quasi elliptic set of equations for generating a discretization mesh that optimally conforms to an entire domain that undergoes large deformations in primarily one direction we have applied this method to the axisymmetric problem of the transient displacement of a viscous liquid by a high pressure gas the liquid initially fills completely a tube the diameter of which may be constant or change smoothly suddenly or periodically along its finite length key ingredients for the success of the proposed transformation are limiting the orthogonality requirements on the mesh and employing an improved node distribution function along the deforming boundary the retained orthogonal term along with the penalty method for the imposition of the boundary conditions overcome the inherent restrictions of a conformal transformation producing meshes of high quality this term also eliminates the discontinuous slopes of the coordinate lines that are normal to the free surface these usually arise due to the harmonic transformation around highly deforming surfaces the mathematical anisotropy in the mesh generating equations directly corresponds to the physical one when the initially straight and normal to the axis of symmetry air fluid interface at the tube entrance develops mostly along the axial direction generating a long open bubble moreover the generalized node distribution imposes an optimal discretization of the bubble surface itself combining this scheme with the mixed finite element method produces a powerful tool with extended robustness and accuracy in order to reduce the computational cost the resulting set of equations is solved with a non linear gauss seidel technique and a variable time step specific applications of the proposed scheme are presented

signed zeros of gaussian vector fields density correlation functions and curvature we calculate correlation functions of the signed density of zeros of gaussian distributed vector fields we are able to express correlation functions of arbitrary order through the curvature tensor of a certain abstract riemann cartan or riemannian manifold as an application we discuss one and two point functions the zeros of a two dimensional gaussian vector field model the distribution of topological defects in the high temperature phase of two dimensional systems with orientational degrees of freedom such as superfluid films thin superconductors and liquid crystals

interval observer design for continuous time linear parameter varying systems abstract this paper studies interval observer design for linear parameter varying systems subject to uncertainties in parameters input and output based on a general assumption that these uncertainties are unknown but bounded by known intervals a novel interval observer is presented to estimate the bounds of state to attenuate the effect of uncertainties and obtain tight state intervals a novel l norm based design method is proposed numerical simulations are conducted to demonstrate the performance of the proposed method

application of a variational method for generating adaptive grids the application of variational methods for generating adaptive grids is not as straightforward as one is led to believe proper scaling suitable weight functions and appropriate clustering on boundaries must be employed to obtain a satisfactory grid this work which is based on the framework developed by brackbill and saltzman provides simple methods for determining scaling and investigates possible options for selecting the weight function and clustering points on the boundaries the concepts developed here are applied to two two dimensional problems a model problem based on burger s equation which contains two length scales and transonic flow past airfoils using the euler equations

simple time and space adaptation in one dimensional evolutionary partial differential equations a simple technique for time and space adaptation in one dimensional evolutionary partial differential equations suggested by sanz serna and christie 1 is tested it is found that the equidistribution of hu xi greatly improves on the equidistribution of arc length used by those authors the time step control is found to perform poorly in the integration of rough solutions and the reasons for this behaviour are analysed

the use of solution adaptive grids in solving partial differential equations the grid point distribution used in solving a partial differential equation using a numerical method has a substantial influence on the quality of the solution an adaptive grid which adjusts as the solution changes provides the best results when the number of grid points available for use during the calculation is fixed basic concepts used in generating and applying adaptive grids are reviewed in this paper and examples illustrating applications of these concepts are presented

an exact handling of the gradient for overcoming persistent problems in nonlinear observer design via convex optimization techniques abstract this paper proposes a comprehensive solution to persistent problems faced by nonlinear observer design via convex optimization techniques namely the construction of an exact error model and the handling of unmeasurable premises instead of using the differential mean value theorem it is shown that the error system is always exactly amenable via algebraic rearrangements to an explicit matrix polynomial form of the gradient where the error signal appears factorized at the rightmost side thus allowing lyapunov based derivation of conditions in the form of linear matrix inequalities or sum of squares an effective exploitation of the nonlinear characteristics of the observer while naturally decoupling available and non available signals is achieved via exact takagi sugeno tensor product models or polynomial rewriting of the error system not the plant generalizations such as h disturbance rejection or decay rate are straightforward in contrast with recent approaches the output is not required to be linear nor the systems involved to be affine in control illustrative examples are provided that overcome recent approaches on the subject

review of some adaptive node movement techniques in finite element and finite difference solutions of partial differential equations abstract this article summarizes the results of a literature search for adaptive numerical methods of solving partial differential equations the methods discussed involve the adaptive movement of nodes so as to obtain a low level of solution truncation error while minimizing the number of nodes used in the calculation such methods are applicable to the solution of nonstationary flow problems that contain moving regions of rapid change in the flow variables surrounded by regions of relatively smooth variation flows with shock waves contact surfaces slip streams phase change interfaces and boundary layers can be modelled with great precision by these methods it will be shown that significant economies of execution can be attained if nodes are moved so that they remain concentrated in regions of rapid variation of the flow variables

a simplified adaptive mesh technique derived from the moving finite element method an adaptive mesh technique is derived as a constrained minimization of the functional used in the moving finite element mfe method the result is a matrix equation for mesh velocities alone i e a pure adaptive mesh prescription the method retains many attractive features of mfe including the ability to independently control mesh motion through penalty terms

applications and generalizations of variational methods for generating adaptive meshes abstract generating computation meshes for irregular regions have been of interest to a lot of people in many areas of research for a long time one technique that has met with sucess over the long run has been to generate methods using an elliptic equation or a system of elliptic equations the technique in its simplest form uses a system of laplace equations which are solved by direct or iterative methods as people gained more experience with this method source terms were added to the laplace equations to gain additional control of the mesh in variable coefficients of the derivatives were added for further flexibility in this paper the authors work with a method that systematically generates a set of elliptic equations without having to explicitly perturb a set of laplace equations with source terms and variable coefficients this technique uses the variational methods often associated with elliptic equations following this introduction they briefly discuss the variational formulation in two dimensional cartesian geometry then the formulation will be generalized to three dimensions next several three dimensional test problems will be shown after displaying these three dimensional test results the author wil the exhibit an application of the mesh generation technique in two dimensions this application involves generating an adaptive mesh for a supersonic flow past a step in a wind tunnel author

generalized nonlinear minimal residual gnlmr method for iterative algorithms abstract most iterative methods for solving steady state problems can be shown to be equivalent to solving time dependent problems of either parabolic or hyperbolic type the relaxation factor used in accelerating an iterative method to obtain the converged solution plays the same role as the time step size used in advancing the transient solution to the steady state solution for a time dependent problem with this transformation one can expose the mechanism of the acceleration schemes in the presented study this time dependent approach together with the single iteration multi step algorithm are applied to generalize the nonlinear minimal residual nlmr method for iterative solutions of linear and nonlinear problems most importantly both theoretical studies and numerical experiments confirm the monotone convergence behavior of the generalized nlmr method with the multi step algorithm it is found that both the rate and the smoothness of convergence of the nlmr method can be improved even further several interesting problems that originated from this method are also discussed

the direct variational grid generation method extended to curves the direct variational grid generation method is extended to weighted grids on smooth curves in r 3 by introducing a new weighted chord functional the new functional is positive definite at a global minimum but not everywhere convex lack of convexity appears to a significant obstacle in extending the direct variational approach to surface grid generation

stable interval observers in bbc for linear systems with time varying input bounds this technical note deals with the design of stable interval observers and estimators for continuous time linear dynamic systems under uncertain initial states and uncertain inputs enclosed within time varying zonotopic bounds no monotony assumption such as cooperativity is required in the vector field the interval observer stability directly derives from the stability of the observer state matrix where any poles real or complex single or multiple are handled in the same way

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

interval observers for linear time invariant systems with disturbances it is shown that for any time invariant exponentially stable linear system with additive disturbances time varying exponentially stable interval observers can be constructed the technique of construction relies on the jordan canonical form that any real matrix admits and on time varying changes of coordinates for elementary jordan blocks which lead to cooperative linear systems the approach is applied to detectable linear systems

design of interval observers and controls for pdes using finite element approximations synthesis of interval state estimators is investigated for the systems described by a class of parabolic partial differential equations pdes first a finite element approximation of a pde is constructed and the design of an interval observer for the derived ordinary differential equation is given second the interval inclusion of the state function of the pde is calculated using the error estimates of the finite element approximation finally the obtained interval estimates are used to design a dynamic output stabilizing control the results are illustrated by numerical experiments with an academic example and the black scholes model of financial market

parameter estimation in variational grid generation two approaches to numerical variational grid generation use a linear combination of three variational problems to control the properties of the grid previously the parameters in the linear combination were determined by experimentation good estimates for these parameters can be obtained from simple model problems

adaptive mesh techniques for fronts in star formation abstract we present an implicit adaptive grid finite difference technique specifically designed to locate and track arbitrary fronts interfaces and structures in a radiation hydro flow the adaptive mesh is constructed in such a way that the average change of the flow variables per grid zone is the same throughout the entire grid a local grid refinement of up to a factor of 10 6 compared to an equidistant mesh has been obtained on a machine with 14 decimal digits per word crucial to this type of approach is the use of a stiffness operator which prevents tangling of the mesh the elliptic equation for the grid motion is solved implicitly coupled with the equations for the flow variables per timestep very steep and narrow flow features can travel many times their own width in true space however with respect to the adaptive mesh the motion of such flow features is always less than one zone thus the courant friedrichs lewy 1 cfl condition s accuracy limitation is always fulfilled although its stability criterion does not pose any timestep limitations for our implicit numerical method in fact the choice of timesteps is based purely on physical and accuracy considerations typical applications run on courant numbers ranging from 0 1 to 10 12 the performance of this numerical scheme is demonstrated on a planar 1 d shocktube and the formation of a one solar mass protostar in spherical symmetry

fast iterative algorithms based on optimized explicit time stepping abstract the generalized nonlinear minimal residual gnlmr method is shown to consistently accelerate and stabilize iterative algorithms for solving nonlinear problems by using the optimized explicit multistepping the examples presented in this paper illustrate the beneficial effects of the optimized multistep algorithm on the computational efficiency and the convergence rate as applied to several nonlinear problems in fluid dynamics the significant reduction in computing time when using the multiple optimized acceleration factors is only negligibly weighed down by the computation costs due to the requirements for additional computer storage

achieving finite element mesh quality via optimization of the jacobian matrix norm and associated quantities part i a framework for surface mesh optimization structured mesh quality optimization methods are extended to optimization of unstructured triangular quadrilateral and mixed finite element meshes n ew interpretations of well known nodally bssed objective functions are made possible using matrices and matrix norms the matrix perspective also suggests several new objective functions particularly significant is the interpretation of the oddy metric and the smoothness objective functions in terms of the condition number of the metric tensor and jacobian matrix respectively objective functions are grouped according to dimensionality to form weighted combinations a simple unconstrained local optimum is computed using a modiiied n ewton iteration the optimization approach was implemented in the cubit mesh generation code and tested on several problems results were compared against several standard element based quaiity measures to demonstrate that good mesh quality can be achieved with nodally based objective functions

design of reduced order interval observers for lti systems with bounded time varying disturbances a parametric approach this paper investigates the design problem of reduced order interval observers for linear time invariant systems with bounded time varying disturbances although there are many excellent design met

interval state estimation for a class of nonlinear systems the goal of this technical note is to design interval observers for a class of nonlinear continuous time systems the first part of this work shows that it is usually possible to design an interval observer for linear systems by means of linear time invariant changes of coordinates even if the system is not cooperative this result is extended to a class of nonlinear systems using partial exact linearisations the proposed observers guarantee to enclose the set of system states that is consistent with the model the disturbances and the measurement noise moreover it is only assumed that the measurement noise and the disturbances are bounded without any additional information such as stationarity uncorrelation or type of distribution the proposed observer is illustrated through numerical simulations

interval state observer for nonlinear time varying systems this paper is devoted to the design of interval observers for linear time varying ltv systems and a class of nonlinear time varying systems in the output canonical form an interval observer design is feasible if it is possible to calculate the observer gains making the estimation error dynamics cooperative and stable it is shown that under some mild conditions the cooperativity of an ltv system can be ensured by a static linear transformation of coordinates the efficiency of the proposed approach is demonstrated through numerical simulations

generation of computational grids using optimization a method for generation of computational grids using principles of nonlinear programming optimization is described grids are generated so that certain discrete measures of grid smoothness and orthogonality are max imized using a fast iterative optimization procedure the method can also be used to improve an existing grid ir respective of the method used for its generation if the original grid contains regions of overlap nonpositive jacobian this method is capable of unraveling the grid and making it useful for computations the iterative op timization procedure is efficient due to the use of a conjugate direction method with exact line searching examples are given of the application of this technique to two and three dimensional computational grids the extension of the method to generate solution adaptive grids is discussed n the past few years there has been a great deal of interest in the development of computational grid generation techniques1 for discretizing complex regions for the numerical solution of partial differential equations the commonly used grid generation methods have achieved a high degree of sophistication and ease of use however for complex con figurations the existing methods do not always produce ac ceptable grids for computations grid quality deterioration is especially apparent in three dimensional grid generation methods and when two dimensional grids are combined to form a three dimensio nal grid 2 3 in addition to grid quality problems many methods suffer from computational ineffi ciency for these reasons the authors have perceived a need for a grid generatio n method that could be used to improve the quality of a given computational grid in addition the method should be capable of serving as a stand alone grid generation procedure independent of other techniques the basic concept behind this grid generation method is to assume from the outset that the grid to be generated or op timized consists of straight line segments joining the nodal grid points this is in contrast to methods that solve elliptic parabolic or hyperbolic partial differential equations or use conformal mapping these methods are based on con tinuous not discrete coordinate transformations and therefore suffer from discretization errors for any grid con sisting of a finite number of grid points the grid generation technique described herein formulates discrete measures of grid smoothness and orthogonality at each grid point and therefore does not suffer from truncation errors on coarse grids these measures of grid quality are then minimized us ing a conjugate direction procedure with exact line searching the resulting grids are optimal with respect to the particular smoothness and orthogonality measures chosen and there are many possible choices for their exact forms the next section describes the formulation of the method followed by some typical results of using this method to im prove existing grids or generate new grids finally exten sions of the method for generating solution adaptive grids are discussed and other areas of possible future research are pointed out analysis the formulation of the method will be illustrated for two dimensional grids the details of the method for the three dimensional case are given in the appendix we will discuss the grid generation method by first noting similarities with the saltzman brackbill4 variational grid generation method in the variational method two func tionals are introduced that provide measures of grid smoothness

coordinate system control adaptive meshes the discussion of the formulation and properties of the adaptive mesh algorithm is as complete as space permits as should be clear from the discussion adaptive gridding is most useful for singular perturbation problems where localized regions with large gradients develop spontaneously often choosing the correct weight function is not trivial and sometimes it is appropriate to cause the mesh to respond to structure in several dependent variables simultaneously

an easy design for interval observers this paper deals with the problem of interval estimation the proposed approach is based on the use of successive derivatives in continuous time or forward measurements in discrete time in an alg

interval observers for continuous time lpv systems with l 1 l 2 performance an approach to interval observer design for linear parameter varying lpv systems is proposed it is assumed that the vector of scheduling parameters in lpv models is not available for measurement two different interval observers are constructed for nonnegative systems and for a generic case stability conditions are expressed in terms of matrix inequalities which can be solved with respect to the observer gains using standard numerical solvers applying l 1 l 2 framework the robustness and estimation accuracy with respect to model uncertainty are analyzed the efficiency of interval estimation for lpv models is demonstrated through numerical experiments for a microfluidic system and an academic example

on the elliptic mesh generation in domains containing multiple inclusions and undergoing large deformations we present an improved method to generate a sequence of structured meshes even when the physical domain contains deforming inclusions this method belongs to the class of arbitrary lagrangian eulerian ale methods for solving moving boundary problems its tools are either a separate mappings of the domain boundaries and enforcing the node distribution on lines emanating from singular points or b domain decomposition and separate mappings of each subdomain using suitable coordinate systems the latter is shown to be more versatile and general in both cases a set of elliptic equations is used to generate the grid extending in this way the method advanced by dimakopoulos and tsamopoulos y dimakopoulos j a tsamopoulos a quasi elliptic transformation for moving boundary problems with large anisotropic deformations j comput phys 192 2003 494 522 we shall present examples where this earlier method and all other mesh generating methods which are based on a conformal mapping or solving a quasi elliptic set of pdes fail to produce an acceptable mesh and accurate solutions in such geometries furthermore in contrast to other methods appropriate boundary conditions and constraints such as orthogonality of specific mesh lines and prespecified node distributions on them can be easily implemented along a specific part of the domain or its boundary hence no attractive terms at specific corners or singular points are needed to increase the mesh resolution around the moving interfaces while keeping low the memory requirements and the computational time a local mesh refinement technique has been incorporated as well the method is demonstrated in two challenging examples where no remeshing is required in spite of the large domain deformations in the first one the transient growth of two bubbles embedded in a viscoelastic filament undergoing stretching in the axial direction is examined while in the second one the linear and non linear dynamics of two bubbles in a viscous medium are determined in an acoustic field the large elasticity of the filament in the first case or the large inertia in the second case coupled with the externally induced large deformations of the liquid domain requires the accurate calculation which is achieved by the method we propose herein the governing equations are solved using the finite element galerkin method with appropriate modifications to solve the hyperbolic constitutive equation of a viscoelastic fluid these are coupled with an implicit euler method for time integration or with arnoldi s algorithm for normal mode analysis

interval observer for a class of uncertain nonlinear singular systems this paper investigates the problem of observer design for a general class of linear singular time delay systems in which the time delays are involved in the state the output and the known input if there exists the involvement of the delay could be multiple which however is rarely studied in the literature sufficient conditions are proposed which guarantee the existence of a luenberger like observer for the general system

stability and l 1 l1 to l 1 l1 performance analysis of uncertain impulsive linear positive systems with applications to the interval observation of impulsive and switched systems with constant delays abstractsolutions to the interval observation problem for delayed impulsive and switched systems with l1 performance are provided the approach is based on first obtaining stability and l1 l1 to l1

the moving finite element method applications to general partial differential equations with multiple large gradients abstract the moving finite element mfe method has been reduced to practice in the automatic solution program dyla for general systems of transient partial differential equations pdes in 1 d several test examples are presented which illustrate the unique node movement and systematic control features which are intrinsic in the mfe method computational dilemmas of numerical diffusion gibbs overshooting and undershooting zone tangling and grid remap or re connection aliasing which occur frequently in conventional pde methods are essentially eliminated in the mfe method arbitrarily large gradients or shocks can be solved with extremely high resolution and accuracy for non coincident or even counterdirected propagating wavefronts boundary layers of arbitrarily small dimensions are solved with high accuracy simultaneously with the large scale structures in reactive and non reactive fluid calculations the mfe method requires a small fraction of the grid nodes which are used in conventional pde solution methods because the nodes migrate continuously and systematically to those positions where they are most needed in order to yield accurate pde solutions on entire problem domains courant friedrichs lewy time step limits are exceeded by wide margins by factors of two to several thousand finally the extension of the mfe method to 2 d is briefly discussed

a theory of phase singularities for image representation and its applications to object tracking and image matching this paper studies phase singularities pss for image representation we show that pss calculated with laguerre gauss filters contain important information and provide a useful tool for image analysis pss are invariant to image translation and rotation we introduce several invariant features to characterize the core structures around pss and analyze the stability of pss to noise addition and scale change we also study the characteristics of pss in a scale space which lead to a method to select key scales along phase singularity curves we demonstrate two applications of pss object tracking and image matching in object tracking we use the iterative closest point algorithm to determine the correspondences of pss between two adjacent frames the use of pss allows us to precisely determine the motions of tracked objects in image matching we combine pss and scale invariant feature transform sift descriptor to deal with the variations between two images and examine the proposed method on a benchmark database the results indicate that our method can find more correct matching pairs with higher repeatability rates than some well known methods

technical communique nonlinear bounded error state estimation of continuous time systems this paper presents a first study on the application of interval analysis and consistency techniques to state estimation of continuous time systems described by nonlinear ordinary differential equations the approach is presented in a bounded error context and the resulting methodology is illustrated by an example

saddles singularities and extrema in random phase fields four simple topological rules are derived that constrain the arrangement of critical points saddles singularities and extrema in a random phase field these rules relate the signs of the singularities to the nature of the extrema maxima or minima and the topology of the saddles once the latter is fixed only a single degree of freedom remains and if for example some extremum is chosen to be a maximum this choice automatically determines the nature of all other extrema and the signs of all singularities thus even in a random wave field there are extensive topologically mandated correlations between all critical points higher order gradient fields derived from the phase are considered and the rules and their induced correlations are shown to apply also to these fields other aspects of the phase field are discussed and it is shown for example that the number of saddles very nearly but not necessarily exactly equals the number of singularities plus the number of extrema and that during the evolution of the wave field large numbers of different specific features must appear simultaneously