numerical simulations for radiation hydrodynamics a finite difference scheme is proposed for two dimensional radiation hydrodynamical equations in the transport limit the scheme is of godunov type in which the set of time averaged flux needed in the scheme is calculated through riemann problems solved in the scheme flow signals are explicitly treated while radiation signals are implicitly treated flow fields and radiation fields are updated simultaneously an iterative approach is proposed to solve the set of nonlinear algebraic equations arising from the implicitness of the scheme the sweeping method used in the scheme significantly reduces the number of iterations or computer cpu time needed a new approach to further accelerate the convergence is proposed which further reduces the number of iterations needed by more than one order no matter how many cells radiation signals propagate in one time step only an extremely small number of iterations are needed in the scheme and each iteration costs only about 0 8 percent of computer cpu time which is needed for one time step of a second order accurate and fully explicit scheme two dimensional problems are treated through a dimensionally split technique therefore iterations for solving the set of algebraic equations are carried out only in each one dimensional sweep through numerical examples it is shown that the scheme keeps the principle advantages of godunov schemes for flow motion in the time scale of flow motion numerical results are the same as those obtained from a second order accurate and fully explicit scheme the acceleration of the convergence proposed in this paper may be directly applied to other hyperbolic systems

correction to d stability and delay independent stability of homogeneous cooperative systems dec 2010 2882 2885 we correct some errors in the statements and proofs presented in section v of the above mentioned manuscript

monotone nonlinear realisations of response maps abstractthe problem of realization of a monotone response map as a monotone initialized system on a finite dimensional euclidean state space is investigated the dynamical part of the system is described by a delta differential equation on an arbitrary time scale this incorporates continuous and discrete time systems the main result states necessary and sufficient conditions for existence of a monotone realization of a particular class the criterion is expressed in the language of skew differential global universes

d stability and delay independent stability of homogeneous cooperative systems we introduce a nonlinear definition of d stability extending the usual concept for positive linear time invariant systems we show that globally asymptotically stable cooperative systems homogeneous of any order with respect to arbitrary dilation maps are d stable we also prove a strong stability result for delayed cooperative homogeneous systems finally we show that both of these results also hold for planar cooperative systems without the restriction of homogeneity

extension of the perron frobenius theorem to homogeneous systems this paper deals with a particular class of positive systems the state components of a positive system are positive or zero for all positive times these systems are often encountered in applied areas such as chemical engineering or biology it is shown that for this particular class the first orthant contains an invariant ray in its interior an invariant ray generalizes the concept of an eigenvector of linear systems to nonlinear homogeneous systems then sufficient conditions for uniqueness of this ray are given the main result states that the vector field on an invariant ray determines the stability properties of the zero solution with respect to initial conditions in the first orthant the asymptotic behavior of the solutions is examined finally we compare our results to the perron frobenius theorem which gives a detailed picture of the dynamical behavior of positive linear systems

on an implicit eno scheme essentially non oscillatory eno schemes which have high order accuracy in regions where solutions are smooth and effectively capture shocks and discontinuities have been developed for numerical solution of hyperbolic equations these methods have traditionally been implemented using explicit euler or explicit runge kutta time marching schemes and consequently suffer from the courant friedrichs lewy cfl time step restriction this restriction is significant for steady state problems and for transient problems with fronts whose speed is slow compared to the propagation speed in the rest of the domain in this paper a novel implicit time marching implementation of the eno roe scheme is developed simulation results which demonstrate the benefits of this implicit implementation are presented

on the asymptotic behavior of a class of deterministic models of cooperating species in this paper the global behavior of solutions of a class of ordinary differential equations modeling n cooperating biological species is determined the class of systems includes the classical lot

remarks on excitability stability and sign of equilibria in cooperative systems the strict positivity of equilibria is known to be equivalent to asymptotic stability in excitable positive linear systems in contrast with intuition this property does not hold for nonlinear cooperative systems however weaker results are pointed out and proved to be effective in the analysis of several nonlinear cooperative systems

sign and stability of equilibria in quasi monotone positive nonlinear systems the paper deals with the problem of finding the extension of a well established connection between sign and stability of nontrivial equilibria in positive linear systems to the class of quasi monotone positive nonlinear systems the mathematical framework to provide the sufficient conditions guaranteeing such a relationship is the stability theory for nonlinear systems especially the comparison principles and the method of vector lyapunov functions as an illustration of our results we present an example of a double effect evaporator to study the sign stability property of its only equilibrium point

a conforming finite element method for the time dependent navier stokes equations we study a spatial discretization of the stokes problem in a domain of mathbb r 2 or mathbb r 3 by a finite element method the unknowns being the velocity and the pressure optimal error

fourier analysis of a robust multigrid method for convection diffusion equations we consider a two grid method for solving 2d convection diffusion problems the coarse grid correction is based on approximation of the schur complement as a preconditioner of the schur complement we use the exact schur complement of modified fine grid equations we assume constant coefficients and periodic boundary conditions and apply fourier analysis we prove an upper bound for the spectral radius of the two grid iteration matrix that is smaller than one and independent of the mesh size the convection diffusion ratio and the flow direction i e we have a strong robustness result numerical results illustrating the robustness of the corresponding multigrid w cycle are given

iterative implementation of an implicit explicit hybrid scheme for hydrodynamics iterative implementation of an implicit explicit hybrid scheme for solving the euler equations is described in this paper the scheme was proposed by fryxellet al j comput phys 63 283 1986 is of the godunov type in both explicit and implicit regimes is conservative and is accurate to second order in both space and time for all courant numbers only a single level of iterations is involved in the implementation which solves both the implicit relations arising from upstream centered differences for all wave families and the nonlinearity of the euler equations the number of iterations required to reach a converged solution may be significantly reduced by the introduction of the multicolors proposed in this paper only a small number of iterations are needed in the scheme for a simulation with large time steps the multicolors may also be applied to other linear and nonlinear wave equations for numerical solutions

efficient unstructured mesh generation by means of delaunay triangulation and bowyer watson algorithm this work is devoted to the description of an efficient unstructured mesh generation method entirely based on the delaunay triangulation the distinctive characteristic of the proposed method is that point positions and connections are computed simultaneously this result is achieved by taking advantage of the sequential way in which the bowyer watson algorithm computes the delaunay triangulation two methods are proposed which have great geometrical flexibility in that they allow us to treat domains of arbitrary shape and topology and to generate arbitrarily nonuniform meshes the methods are computationally efficient and are applicable both in two and three dimensions

weakly compressible high order i stable central difference schemes for incompressible viscous flows abstract in this paper we propose a weakly compressible model for numerical simulation of the incompressible viscous flows this model asymptotically approximates the incompressible navier stokes equations when the mach number tends to zero the main advantage of this model is that its numerical discretization avoids any poisson solver thus is very attractive for problems with complicated geometries this model is discretized by high order center differences in space and the so called i stable method for time the linear stability region of an i stable method contains part of the imaginary axis when solving a system of convection diffusion equations with a small viscosity the i stable method allows a very large cell reynolds number thus is particularly suitable for the simulation of fluid flows with large reynolds numbers numerical experiments illustrate the efficiency and robustness of this approach

neural network adaptive control for nonlinear nonnegative dynamical systems nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative these models are widespread in engineering and life sciences and typically involve the exchange of nonnegative quantities between subsystems or compartments wherein each compartment is assumed to be kinetically homogeneous in this paper we develop a full state feedback neural adaptive control framework for adaptive set point regulation of nonlinear uncertain nonnegative and compartmental systems the proposed framework is lyapunov based and guarantees ultimate boundedness of the error signals corresponding to the physical system states and the neural network weighting gains in addition the neural adaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space for nonnegative initial conditions

solution of the euler equations for two dimensional transonic flow by a multigrid method the assumption of potential o w implies that the o w is irrotational this is not strictly correct when shock waves are present an exact description of transonic inviscid o w requires the solution of the euler equations the numerical solution of the euler equations for steady transonic o ws is therefore a problem of great interest to the aeronautical community it also presents a testing challenge to applied mathematicians and numerical analysts

on the approximation of the unsteady navier stokes equations by finite element projection methods this paper provides an analysis of a fractional step projection method to compute incompressible viscous flows by means of finite element approximations the analysis is based on the idea that the appropriate functional setting for projection methods must accommodate two different spaces for representing the velocity fields calculated respectively in the viscous and the incompressible half steps of the method such a theoretical distinction leads to a finite element projection method with a poisson equation for the incremental pressure unknown and to a very practical implementation of the method with only the intermediate velocity appearing in the numerical algorithm error estimates in finite time are given an extension of the method to a problem with unconventional boundary conditions is also considered to illustrate the flexibility of the proposed method

multiblock hybrid grid finite volume method to solve flow in irregular geometries in this work a finite volume based finite element method is suitably developed for solving incompressible flow and heat transfer on collocated hybrid grid topologies the method is generally applicable to arbitrarily shaped elements and orientations and thus challenges the potential to unify many of the different grid topologies into a single formulation the key point in this formulation is the correct estimation of the convective and diffusive fluxes at the cell faces using a novel physical influence scheme this scheme remarkably enhances the achieved solution accuracy it is shown that the extended formulation is robust enough to treat any combination of multiblock meshes with dual element shape employments in this regard the solution domain is broken up into a number of different multiblock arrangements in which each block is filled with only one type of finite element shape the combined grid can decrease the computational time and memory requirements and increase the numerical accuracy the results of the extended formulation are validated against different benchmark and other solutions the current results are in excellent agreement with the other solutions without exhibiting any disturbances around the block boundaries

stability and positivity of equilibria for subhomogeneous cooperative systems building on recent work on homogeneous cooperative systems we extend results concerning stability of such systems to subhomogeneous systems we also consider subhomogeneous cooperative systems with constant input and relate the global asymptotic stability of the unforced system to the existence and stability of positive equilibria for the system with input

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

finite element approximation of the nonstationary navier stokes problem i regularity of solutions and second order error estimates for spatial discretization this is the first part of a work dealing with the rigorous error analysis of finite element solutions of the nonstationary navier stokes equations second order error estimates are proven for spatial discretization using conforming or nonconforming elements the results indicate a fluid like behavior of the approximations even in the case of large data so long as the solution remains regular the analysis is based on sharp a priori estimates for the solution particularly reflecting its behavior as t to 0 and as t to infty it is shown that the regularity customarily assumed in the error analysis for corresponding parabolic problems cannot be realistically assumed in the case of the navier stokes equations as it depends on nonlocal compatibility conditions for the data the results which are presented here are independent of such compatibility conditions which cannot be verified in practice

grid independent convergence of the multigrid method for first order equations the multigrid method for numerical solution of systems of first order partial differential equations is analyzed the smoothing iterations are of polynomial type and are used on all grids under certain conditions the convergence of the iterations is independent of the grid size this is explained by the propagation of smooth error modes out through the boundary and the damping of oscillatory modes an upper bound is derived on the number of multigrid v cycles needed to solve a two dimensional scalar equation numerical experiments with a simple scalar equation and the euler equations confirm the theoretical results

spectral conditions for stability and stabilization of positive equilibria for a class of nonlinear cooperative systems nonlinear cooperative systems associated to vector fields that are concave or subhomogeneous describe well interconnected dynamics that are of key interest for communication biological economical and neural network applications for this class of positive systems we provide conditions that guarantee existence uniqueness and stability of strictly positive equilibria these conditions can be formulated directly in terms of the spectral radius of the jacobian of the system if control inputs are available then it is shown how to use state feedback to stabilize an equilibrium point in the interior of the positive orthant

asymptotic tracking for constrained monotone systems this note addresses tracking control of nonlinear discrete time monotone systems subject to input and state constraints forcing saturation on a previously designed controller may in general lead to destabilization or at least result in constraint violation and performance losses hereby it is shown that for a certain class of nonlinear monotone systems it is possible to design a static nonlinear output feedback which saturated among suitable state dependent bounds is able to guarantee constraint satisfaction and asymptotic tracking of piecewise constant references with a moderate online computational burden simulation experiments concerning the synthesis of a protein demonstrate the effectiveness of the proposed control strategy

steady viscous flow in a triangular cavity steady recirculating viscous flow inside an equilateral triangular cavity is generated by translating one side the navier stokes equations are solved numerically using finite differences on a transformed geometry alternative numerical approaches and associated numerical difficulties are also discussed the results show a primary eddy and a series of secondary eddies at the stagnant corner for high reynolds numbers the interior of the primary eddy has constant vorticity but its value cannot be predicted by the mean squared law

the glt class as a generalized fourier analysis and applications recently the class of generalized locally toeplitz glt sequences has been introduced as a generalization both of classical toeplitz sequences and of variable coefficient differential operators and for every sequence of the class it has been demonstrated that it is possible to give a rigorous description of the asymptotic spectrum in terms of a function the symbol that can be easily identified this generalizes the notion of a symbol for differential operators discrete and continuous or for toeplitz sequences for which it is identified through the fourier coefficients and is related to the classical fourier analysis the glt class has nice algebraic properties and indeed it has been proven that it is stable under linear combinations and products in this paper we prove that the considered class is closed under inversion as well when the sequence which is inverted shows a sparsely vanishing symbol sparsely vanishing symbol a symbol which vanishes at most in a set of zero lebesgue measure furthermore we show that the glt class virtually includes any finite difference or finite element discretization of pdes and based on this we demonstrate that our results on glt sequences can be used in a pde setting in various directions 1 as a generalized fourier analysis for the study of iterative and semi iterative methods when dealing with variable coefficients non rectangular domains non uniform gridding or triangulations 2 in order to provide a tool for the stability analysis of pde numerical schemes e g a necessary von neumann criterium for variable coefficient systems of pdes is obtained uniformly with respect to the boundary conditions 3 for a multigrid analysis of convergence and for providing spectral information on large preconditioned systems in the variable coefficient case etc the final part of the paper deals indeed with problems 1 3 and other possible directions in which the glt analysis can be conveniently employed

stability theory of difference approximations for multidimensional initial boundary value problems an attempt is made to generalize results for arbitrary multidimensional difference schemes severe obstacles are encountered however for dissipative difference schemes the problem may be resolved

observations on the stability properties of cooperative systems we extend two fundamental properties of positive linear time invariant lti systems to homogeneous cooperative systems specifically we demonstrate that such systems are d stable meaning that global asymptotic stability is preserved under diagonal scaling we also show that a delayed homogeneous cooperative system is globally asymptotically stable gas for all non negative delays if and only if the system is gas for zero delay

finite element solution of the unsteady navier stokes equations by a fractional step method abstract a finite element method is presented for the numerical simulation of time dependent incompressible viscous flows the method is based on a fractional step approach to the time integration of the navier stokes equations in which only the incompressibility condition is treated implicitly this leads to a computational scheme of extremely simple algorithmic structure that is particularly attractive for cost effective solutions of large scale problems numerical results indicate the versatility and effectiveness of the proposed method

calculation of incompressible viscous flows by an unconditionally stable projection fem this paper investigates the numerical performance of a finite element implementation of a new incremental fractional step method to compute steady and unsteady incompressible viscous flows under general boundary conditions and using unstructured meshes a variational framework is adopted which accommodates two different spaces for representing and approximating the velocity fields calculated respectively in the viscous and inviscid phases of the method but which leads to a very simple numerical scheme in terms of only one discrete velocity field an unconditionally stable semi implicit approximation of the nonlinear term is used to eliminate any time step restriction as far as the numerical stability is concerned numerical results for five test problems in two dimensions are reported to illustrate the flexibility of the proposed method

fourier analysis of iterative methods for elliptic boundary value problems his paper presents a fourier method for analyzing stationary iterative methods and preconditioners for discretized elliptic boundary value problems as in the von neumann stability analysis of hyperbolic and parabolic problems the approach is easier to apply reveals more details about convergence properties than about standard techniques and can be applied in a systematic way to a wide class of numerical methods although the analysis is applicable only to periodic problems the results essentially reproduce those of classical convergence and condition number analysis for problems with other boundary conditions such as the dirichlet problem in addition they give suggestive new evidence of the strengths and weaknesses of methods such as incomplete factorization preconditioners in the dirichlet case

convergence analysis of iterative methods by pseudodifference operators abstract the convergence of iterative methods to solve linear partial differential equations numerically is analyzed by the theory of pseudodifference operators approximate inverses are determined from the symbol of the iterative operator so that implicit and preconditioned methods are covered the behavior of the symbol for higher wave numbers describes the convergence rate for the corresponding error modes the results are applied to krylov subspace methods stationary iterations of gauss seidel type the multigrid algorithm and time stepping methods for flow problems

steady viscous flow in a triangular cavity by efficient numerical techniques abstract accurate and efficient calculations of the flow inside a triangular cavity are presented for high reynolds numbers the navier stokes equations expressed in a stream function and vorticity formulation are solved numerically using finite differences on a transformed geometry second order numerical boundary conditions are derived and newton s iteration is employed to solve the nonlinear system resulting from the finite difference discretization aside from solving the equilateral triangular cavity problem we have also been able to compute numerical solutions for scalene triangular cavity problems our coarse mesh results for the equilateral triangular cavity problem are compared with finer mesh results in the literature and the agreement is good

brief paper global stabilization of a class of partially known nonnegative systems in this paper we deal with the problem of global output feedback stabilization of a class of n dimensional nonlinear nonnegative systems possessing a one dimensional analytically unknown part that is also a measured output we first propose our main result an output feedback control procedure taking advantage of measurements of the uncertain part able to globally stabilize the system toward an adjustable equilibrium point in the positive orthant though quite general this result is based on hypotheses that might be difficult to check in practice then in a second step through a theorem on a class of nonnegative systems linking the existence of a positive equilibrium to its global asymptotic stability we propose other hypotheses for our main result to hold these new hypotheses are more restrictive but much simpler to check an illustrative example highlights both the potentially complex open loop dynamics of the considered systems and the interesting characteristics of the control procedure

a second order iterative implicit explicit hybrid scheme for hyperbolic systems of conservation laws an iterative implicit explicit hybrid scheme is proposed for hyperbolic systems of conservation laws each wave in a system may be implicitly or explicitly or partially implicitly and partially explicitly treated depending on its associated courant number in each numerical cell and the scheme is able to smoothly switch between implicit and explicit calculations the scheme is of godunov type in both explicit and implicit regimes is in a strict conservation form and is accurate to second order in both space and time for all courant numbers the computer code for the scheme is easy to vectorize multicolors proposed in this paper may reduce the number of iterations required to reach a converged solution by several orders for a large time step the feature of the scheme is shown through numerical examples

rigorous quantitative analysis of multigrid i constant coefficients two level cycle with l 2 norm exact numerical convergence factors for any multigrid cycle can be predicted by local mode fourier analysis for general linear elliptic partial differential equation pde systems with piecewise smooth coefficients in general domains discretized by uniform grids it is proved that in the limit of small meshsizes these predicted factors are indeed obtained provided the cycle is supplemented with a proper processing at and near the boundaries that processing it is proved costs negligible extra computer work apart from mode analysis a coarse grid approximation cga condition is introduced which is both necessary and sufficient for the multigrid algorithm to work properly the present part studies the l 2 convergence in one cycle for equations with constant coefficients in the sequel brandt rigorous quantitative analysis of multigrid ii extensions and practical implications manuscript extensions are discussed to many cycles asymptotic convergence to more levels with arbitrary cycle ty

stability properties of equilibria of classes of cooperative systems this note deals with the constant control problem for homogeneous cooperative and irreducible systems these systems serve as models for positive systems a necessary and sufficient condition for global asymptotic stability of the zero solution of this class of systems is known adding a constant control allows to shift the equilibrium point from zero to a point in the first orthant we prove that for every nontrivial nonnegative control vector a unique nontrivial equilibrium point is achieved which is globally asymptotically stable if the zero solution of the uncontrolled system is globally asymptotically stable in addition a converse result is provided finally a stability result for a particular class of kolmogorov systems is established we compare our main results to those in the literature

multigrid calculation of steady viscous flow in a triangular cavity lid driven recirculating flow in a triangular cavity is simulated at different reynolds numbers using a multigrid solution procedure for the navier stokes equations discretized on triangular grids the discretization uses a control volume methodology with linear internodal variation of the flow variables the use of the multigrid technique provides rapid and grid independent rates of convergence richardson extrapolation is used to obtain accurate representations of the flow field for all reported reynolds numbers the most significant feature of the flow is the occurrence of a sequence of eddies of rapidly decreasing intensity towards the stationary lower corner of the cavity streamtraces of the eddies contours of vorticity and plots of the centerline velocity and pressure are presented the solution at low reynolds numbers is compared with the analytical results of moffat

fourier analysis of multigrid methods for general systems of pdes most iteration methods for solving boundary value problems can be viewed as approximations of a time dependent differential equation in this paper we show that the multigrid method has the effect of increasing the timestep for the smooth part of the solution leading back to an increase of the convergence rate for the nonsmooth part the convergence is an effect of damping fourier analysis is used to find the relation between the convergence rate for multigrid methods and singlegrid methods the analysis is performed for general partial differential equations and an arbitrary number of grids the difference in the behavior of the iterations between firstand second order equations is discussed the theoretical results are confirmed in simple numerical experiments

improved implicit residual smoothing for steady state computations of first order hyperbolic systems improved implicit residual smoothing for steady state computations of first order hyperbolic systems

finite element approximation of the nonstationary navier stokes problem part ii stability of solutions and error estimates uniform in time in this paper assumptions about the stability of a solution are introduced in the numerical analysis of the nonstationary navier stokes problem for the purpose of extending local a priori error estimates and local a posteriori error estimates globally in time