non uniform grid accelerated local global boundary condition ng lgbc for acoustic scattering a global absorbing boundary condition utilizing accelerated integration scheme based on the non uniform grid ng approach is hybridized with a local boundary condition producing an accurate and efficient mesh truncation scheme for finite method analysis of open region acoustic scattering problems the method affords arbitrarily shaped in particular non convex boundaries that conform to essentially concave obstacles of dimensions large compared with the wavelength

solving high order uncertain differential equations via runge kutta method high order uncertain differential equations are used to model differentiable uncertain systems with high order differentials and how to solve the high order uncertain differential equations is a core issue in practice this paper aims at proposing a numerical method to solve the high order uncertain differential equations based on the runge kutta recursion formula which is of high precision degree a procedure is designed and some numerical experiments are performed to illustrate the effectiveness and efficiency of the runge kutta method in addition this paper also presents a numerical method to calculate the expected value of a function of the solution

stability analysis of the green s function method gfm used as an abc for arbitrarily shaped boundaries the time domain discrete green s function of the external region beyond a given boundary has been recently introduced as a discretized version of the impedance condition it is incorporated within the framework of the finite difference time domain fdtd as a quasi local single layer boundary condition termed the green s function method gfm the stability characteristics of this method are provided the analysis is based on the general representation of the method in matrix form whose eigenvalues are investigated this formulation helps detect and remove possible instabilities of the algorithm a demonstration of the ability of the gfm absorbing boundary condition abc to deal with re entrant corner problems is given

stability of queueing networks and scheduling policies we develop a programmatic procedure for establishing the stability of queueing networks and scheduling policies the method uses linear or nonlinear programming to determine what is an appropriate quadratic functional to use as a lyapunov function if the underlying system is markovian our method establishes not only positive recurrence and the existence of a steady state probability distribution but also the geometric convergence of an exponential moment we illustrate this method on several example problems

multilayered discrete green s functions based on mixed potential finite difference formulation an approach to calculating discrete green s functions dgfs in multilayered media is proposed based on the finite difference scheme of time domainmixed potential equations the calculated dgfs have very high accuracy in comparison to the direct fdtd solution furthermore the steady state values of the dgfs are properly estimated in terms of the scalar potential ensuring stability out of the truncating window these dgfs are applicable to the analysis of antennas with multilayered planar structures in such analysis the proposed method has the advantage of the method of moments in that the computations are performed only on the antenna regardless of the white space around it moreover the broadband frequency characteristic of the antenna is achieved with a single simulation run such as in the fdtdmethod the theoretical results have been verified by the experimental results on a wideband coplanar waveguide cpw fed monopole antenna

the use of time domain diakoptics in time discrete models of fields the principles of diakoptics are extended to time domain solutions and the technique is applied to the solution of fields by introducing space approximating polynomials since transmission line networks provide time discrete models suitable for exact numerical analysis the topic is approached by tearing these transmission line models and then showing how reconnection is made in the time domain

closed form fdtd compatible green s function based on combinatorics abstract the advantages of the finite difference time domain fdtd method are often hampered by the need to model large white spaces between and around scattering objects in the continuous realm these large spaces are customarily bridged by the usage of integral operators that transform the sources to any observation point using an appropriate green s function a companion procedure for the discretized world can be realized in principle by straightforward sampling of the continuous green s function however such a procedure does not track the fdtd algorithm and hence yields different results alternatively an fdtd compatible discrete green s function is derived in this work with the yee discretized maxwell s equations as first principles the derivation involves a process of counting many combinations of paths in the spatial temporal grid leading to recursive combinatorial expressions that are solved in closed form numerical implementations of the resultant green s function in short pulse propagation problems produce results validated by conventional fdtd computations the advantages of efficient computations over large distances in particular with regard to short pulses are thus demonstrated

a fast time domain finite element boundary integral method for electromagnetic analysis a time domain finite element boundary integral fe bi method is presented for analyzing electromagnetic em scattering from two dimensional 2 d inhomogeneous objects the scheme s finite element component expands transverse fields in terms of a pair of orthogonal vector basis functions and is coupled to its boundary integral component in such a way that the resultant finite element mass matrix is diagonal and more importantly the method delivers solutions that are free of spurious modes the boundary integrals are computed using the multilevel plane wave time domain algorithm to enable the simulation of large scale scattering phenomena numerical results demonstrate the capabilities and accuracy of the proposed hybrid scheme

uncertain wave equation with infinite half boundary wave equation is a type of second order and hyperbolic partial differential equation it is a commonly used tool to model many kinds of wave propagations such as sound wave electromagnetic wave water wave and string vibration propagations similarly uncertain wave equation is a type of uncertain partial equation driven by liu process which is widely used to model the wave propagation with uncertain noise such as vibrating string in uncertain environment the existing literature has studied uncertain wave equation with infinite boundary since infinite boundary is a much ideal condition this paper aims at studying the uncertain wave equation with infinite half boundary

on the functional central limit theorem and the law of the iterated logarithm for markov processes let xt t 0 be an ergodic stationary markov process on a state space s if is its infinitesimal generator on l2 s dm where m is the invariant probability measure then it is shown that for all f in the range of hat a n 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 int limits 0 nt f x s text ds text t underline underline 0 converges in distribution to the wiener measure with zero drift and variance parameter 2 2 f g 2 g g where g is some element in the domain of such that g f theorem 2 1 positivity of 2 is proved for nonconstant f under fairly general conditions and the range of is shown to be dense in 1 a functional law of the iterated logarithm is proved when the 2 th moment of f in the range of is finite for some 0 theorem 2 7 a under the additional condition of convergence in norm of the transition probability p t x d y to m dy as t for each x the above results hold when the process starts away from equilibrium theorems 2 6 2 7 b applications to diffusions are discussed in some detail

stochastic approximations and adaptive control of a discrete time single server network with random routing this paper considers a discrete time system composed of k infinite capacity queues that compete for the use of a single server customers arrive in independent and identically distributed i i d batches and are served according to a server allocation policy upon completing service customers either leave the system or are routed instantaneously to another queue according to some random mechanism as an alternative to simply randomized strategies a policy based on a stochastic approximation algorithm is proposed to drive a long run average cost to a given value the underlying motivation can be traced back to implementation issues associated with constrained optimal strategies a version of the ordinary differential equation ode method as given by metivier and priouret is developed for proving almost sure convergence of this algorithm this is done by exploiting the recurrence structure of the system under nonidling policies a probabilistic representation of solutions to an associated poisson equatio

theoremes de convergence presque sure pour une classe d algorithmes stochastiques a pas decroissant the paper studies the pathwise asymptotic behaviour of stochastic algorithms of the following general form theta n 1 theta n gamma n 1 f theta n y n 1 the hypotheses allowing discontinuities on the adaptation termf the process y n n 0 is a markov chain controlled by n for each fixed the markov chain y n n 0 is essentially of positive recurrent type

source decomposition as a diakoptic boundary condition in fdtd with reflecting external regions the diakoptic approach is utilized for the creation of boundary conditions for the truncation of the fdtd computational grid in the presence of reflecting external media the interfaces between the regions can be of arbitrary shape and are in close proximity to the scatterers in both regions surface green s functions over these interfaces serve to characterize the external domain from a viewpoint of the computational domain previously used field definitions of such green s functions that can be viewed as analogs of parameters in microwave networks have involved effective hard boundaries at the interfaces these boundaries however can cause artificial interactions with physical reflecting bodies in the external domain to eliminate this phenomenon the green s functions are now defined in terms of outgoing and incoming wave constituents rather than fields this distinction between the aforementioned constituents is made by viewing them as originating from sources within and outside the computational domain the green s function based boundary conditions are demonstrated to operate successfully in the two dimensional case resolving the aforementioned resonance issues efficiently and accurately

accuracy of the discrete green s function formulation of the fdtd method this paper reports an evaluation of the accuracy of the discrete green s function dgf formulation of the finite difference time domain fdtd method recently the closed form expression for the dgf and its efficient numerical implementation were presented which facilitates applications of the dgf in fdtd simulations of radiation and scattering problems so far the accuracy of the dgf formulation of the fdtd method has been rather marginally treated in the literature moreover although windowing has been reported as an efficient method of dgf waveform truncation and a remedy for stability issues the accuracy and usability of this technique have not yet been fully evaluated in this paper previously unrevealed accuracy limitations of the dgf formulation of the fdtd method are demonstrated in several numerical tests specifically the truncation errors are compared for the most frequently applied windowing functions with the best performance shown for the hann s window

a liapounov bound for solutions of the poisson equation in this paper we consider psi irreducible markov processes evolving in discrete or continuous time on a general state space we develop a liapounov function criterion that permits one to obtain explicit bounds on the solution to the poisson equation and in particular obtain conditions under which the solution is square integrable these results are applied to obtain sufficient conditions that guarantee the validity of a functional central limit theorem for the markov process as a second consequence of the bounds obtained a perturbation theory for markov processes is developed which gives conditions under which both the solution to the poisson equation and the invariant probability for the process are continuous functions of its transition kernel the techniques are illustrated with applications to queueing theory and autoregressive processes

the time domain discrete green s function method gfm characterizing the fdtd grid boundary for a given fdtd simulation space with an arbitrarily shaped boundary and an arbitrary exterior region most existing absorbing boundary conditions become inapplicable a green s function method gfm is presented which accommodates arbitrarily shaped boundaries in close proximity to a scattering object and an arbitrary composition in the exterior of the simulation space central to this method is the numerical precomputation of a green s function tailored to each problem which represents the effects of the boundary and the external region this function becomes the kernel for a single layer absorbing boundary operator it is formulated in a manner which naturally incorporates numerically induced effects such as the numerical dispersion associated with the fdtd scheme the green s function is an exact absorber in the discretized space this property should be contrasted with other methods which are initially designed for the continuum and are subsequently discretized thereby incurring inherent errors in the discrete space which cannot be eliminated unless the continuum limit is recovered in terms of accuracy the gfm results have been shown to be of a similar quality to the pml and decidedly superior to the mur 1981 condition the properties of the gfm are substantiated by a number of numerical examples in one two and three dimensions

least squares estimation in uncertain differential equations uncertain differential equations are a type of differential equations driven by liu processes how to estimate the parameters in an uncertain differential equation based on the observed data is a crucial problem in the real applications of these equations by means of the least squares estimation this article proposes a principle of minimum noise as an approach to the problem following this principle the estimates of the parameters in some special types of uncertain differential equations are derived which are represented as functions of the observed data in addition some numerical experiments are performed to illustrate the principle

a novel hybridization of higher order finite element and boundary integral methods for electromagnetic scattering and radiation problems a novel hybridization of the finite element fe and boundary integral methods is presented for an efficient and accurate numerical analysis of electromagnetic scattering and radiation problems the proposed method derives an adaptive numerical absorbing boundary condition abc for the finite element solution based on boundary integral equations unlike the standard finite element boundary integral approach the proposed method is free of interior resonance and produces a purely sparse system matrix which can be solved very efficiently unlike the traditional finite element absorbing boundary condition approach the proposed method uses an arbitrarily shaped truncation boundary placed very close to the scatterer radiator to minimize the computational domain and more importantly the method produces a solution that converges to the true solution of the problem to demonstrate its great potential the proposed method is implemented using higher order curvilinear vector elements a mixed functional is designed to yield both electric and magnetic fields on an integration surface without numerical differentiation to be used in the calculation of the adaptive abc the required evaluation of boundary integrals is carried out using the multilevel fast multipole algorithm which greatly reduces both the memory requirement and cpu time the finite element equations are solved efficiently using the multifrontal algorithm a mathematical analysis is conducted to study the convergence of the method finally a number of numerical examples are given to illustrate its accuracy and efficiency

linear quadratic uncertain differential game with application to resource extraction problem uncertain differential game investigates interactive decision making of players over time and the system dynamics is described by an uncertain differential equation this paper goes further to study the two player zero sum uncertain differential game in order to guarantee the saddle point nash equilibrium a max min theorem is provided furthermore when the system dynamics is described by a linear uncertain differential equation and the performance index function is quadratic the existence of saddle point nash equilibrium is obtained via the solvability of a corresponding riccati equation finally a resource extraction problem is analyzed by using the theory proposed in this paper

a multidimensional z transform evaluation of the discrete finite difference time domain green s function analytical expressions for frequency and time domain discrete green s functions are developed below rather than discretizing the continuous green s functions directly we derive the discrete green s functions from first principles i e the difference equations this is done with the purpose of obtaining discrete integral operators that would replicate results obtained via the finite difference time domain fdtd method the main effort is directed at inversions of multidimensional frequency domain expressions in the z transform domain the green s functions obtained in this way coincide with time domain developments presented earlier both in the form of direct numerical computations and via combinatorics and the catalan triangle the z transform methodology resulting from this development provides an orderly manner for deriving expressions for multidimensional discrete integral operators that can be hybridized with fdtd based differential operators in a self consistent manner