phase error control for fd td methods of second and fourth order accuracy for fd td methods used to solve maxwell s equations we determine the spatial resolution of the discretized domain in terms of the total computation time and the desired phase error it is shown that the spatial step should vary as spl delta x spl sim g e sub spl phi t sub c sup 1 s in order to maintain a prescribed phase error level e sub spl phi throughout the computation time t sub c where s 2 or 4 is the spatial order of accuracy of the scheme and g is a geometric factor significantly we show that the rule of thumb of using 10 20 points per wavelength to determine the spatial cell size for the standard scheme is not optimal our results are verified by numerical simulations in two dimensions with the yee 1966 scheme and a new fourth order accurate fd td scheme

z transform theory and the fdtd method in implementing the finite difference time domain fdtd method on materials which are dispersive or nonlinear the relationship between the flux density and the electric field can be the most complicated part of the problem because the fdtd method is a sampled time domain method this relationship can be can be looked upon as a digital filtering problem the z transform is typically used in digital filtering and signal processing problems the paper illustrates the use of the z transform in implementing the fdtd method where complicated dispersive or nonlinear materials are involved

an analysis of new and existing fdtd methods for isotropic cold plasma and a method for improving their accuracy over the past few years a number of different finite difference time domain fdtd methods for modeling electromagnetic propagation in an isotropic cold plasma have been published we have analyzed the accuracy and stability of these methods to determine which method provides the greatest accuracy for a given computation time for completeness two new fdtd methods for cold plasma one of which is based on the concept of exponential fitting are introduced and evaluated along with the existing methods we also introduce the concept of cutoff modification which can be easily applied to most of the fdtd methods and which we show can improve the accuracy of these methods with no additional computational cost von neumann s stability analysis is used to evaluate the stability of the various methods and their accuracy is determined from a straightforward time and space harmonic analysis of the dispersion and dissipation errors results of numerical experiments to verify the accuracy analysis are presented it is found that for low loss plasma the piecewise linear recursive convolution method plrc method is the most accurate but the method of young see radio sci vol 29 p 1513 22 1994 can use less memory and is nearly as accurate in this low loss plasma regime cutoff modification can significantly reduce the error near cutoff at the expense of slightly greater error at lower frequencies for strongly collisional plasmas the plrc method also provides the most accurate solution

periodic moving averages of random variables with regularly varying tails in this paper we establish the basic asymptotic theory for periodic moving averages of i i d random variables with regularly varying tails the moving average coefficients are allowed to vary according to the season a simple reformulation yields the corresponding results for moving averages of random vectors our main result is that when the underlying random variables have finite variance but infinite fourth moment the sample autocorrelations are asymptotically stable it is well known in this case that sample autocorrelations in the classical stationary moving average model are asymptotically normal

time domain finite difference and finite element methods for maxwell equations in complex media extensions of finite difference time domain fdtd and finite element time domain fetd algorithms are reviewed for solving transient maxwell equations in complex media also provided are a few representative examples to illustrate the modeling capabilities of fdtd and fetd for complex media the term complex media refers here to media with dispersive bi anisotropic inhomogeneous and or nonlinear properties present in the constitutive tensors

a scalable fully implicit compressible euler solver for mesoscale nonhydrostatic simulation of atmospheric flows a fully implicit solver is developed for the mesoscale nonhydrostatic simulation of atmospheric flows governed by the compressible euler equations to spatially discretize the euler equations on a height based terrain following mesh we apply a cell centered finite volume scheme in which an advection upstream splitting ausm up method with a piecewise linear reconstruction is employed to achieve second order accuracy for the low mach flow a second order explicit first step single diagonal coefficient diagonally implicit runge kutta esdirk method with adaptive time stepping is applied to stabilize physically insignificant fast waves and accurately integrate the euler equations in time the nonlinear system arising at each time step is solved by using a jacobian free newton krylov schwarz nks algorithm to accelerate the convergence and improve the robustness we employ a class of additive schwarz preconditioners in which the subdomain jacobian matrix is constructed using a first order spatial discretization several test cases are used to validate the correctness of the scheme and examine the performance of the solver large scale results on a supercomputer with up to 18 432 processor cores are provided to show the parallel performance of the proposed method

finite volume transport on various cubed sphere grids the performance of a multidimensional finite volume transport scheme is evaluated on the cubed sphere geometry advection tests with prescribed winds are used to evaluate a variety of cubed sphere projections and grid modifications including the gnomonic and conformal mappings as well as two numerically generated grids by an elliptic solver and spring dynamics we explore the impact of grid non orthogonality on advection tests over the corner singularities of the cubed sphere grids using some variations of the transport scheme including the piecewise parabolic method with alternative monotonicity constraints the advection tests revealed comparable or better accuracy to those of the original latitudinal longitudinal grid implementation it is found that slight deviations from orthogonality on the modified cubed sphere quasi orthogonal grids do not negatively impact the accuracy in fact the more uniform version of the quasi orthogonal cubed sphere grids provided better overall accuracy than the most orthogonal and therefore much less uniform conformal grid it is also shown that a simple non orthogonal extension to the transport equation enables the use of the highly non orthogonal and computationally more efficient gnomonic grid with acceptable accuracy

a generalized recursive convolution method for time domain propagation in porous media an efficient numerical method referred to as the auxiliary differential equation ade method is proposed to compute convolutions between relaxation functions and acoustic variables arising in sound propagation equations in porous media for this purpose the relaxation functions are approximated in the frequency domain by rational functions the time variation of the convolution is thus governed by first order differential equations which can be straightforwardly solved the accuracy of the method is first investigated and compared to that of recursive convolution methods it is shown that while recursive convolution methods are first or second order accurate in time the ade method does not introduce any additional error the ade method is then applied for outdoor sound propagation using the equations proposed by wilson et al in the ground 2007 appl acoust 68 173 200 a first one dimensional case is performed showing that only five poles are necessary to accurately approximate the relaxation functions for typical applications finally the ade method is used to compute sound propagation in a three dimensional geometry over an absorbing ground results obtained with wilson s equations are compared to those obtained with zwikker and kosten s equations and with an impedance surface for different flow resistivities

a parallel well balanced finite volume method for shallow water equations with topography on the cubed sphere a finite volume scheme for the global shallow water model on the cubed sphere mesh is proposed and studied in this paper the new cell centered scheme is based on osher s riemann solver together with a high order spatial reconstruction on each patch interface of the cubed sphere only one layer of ghost cells is needed in the scheme and the numerical flux is calculated symmetrically across the interface to ensure the numerical conservation of total mass the discretization of the topographic term in the equation is properly modified in a well balanced manner to suppress spurious oscillations when the bottom topography is non smooth numerical results for several test cases including a steady state nonlinear geostrophic flow and a zonal flow over an isolated mountain are provided to show the flexibility of the scheme some parallel implementation details as well as some performance results on a parallel supercomputer with more than one thousand processor cores are also provided

a simplified lax wendroff correction for staggered grid fdtd modeling of electromagnetic wave propagation in frequency dependent media the lax wendroff correction is an elegant method for increasing the accuracy and computational efficiency of finite difference time domain fdtd solutions of hyperbolic problems however the conventional approach leads to implicit solutions for staggered grid fdtd approximations of maxwell s equations with frequency dependent constitutive parameters to overcome this problem we propose an approximation that only retains the purely acoustic i e lossless terms of the lax wendroff correction this modified lax wendroff correction is applied to an o 2 4 accurate staggered grid fdtd approximation of maxwell s equations in the radar frequency range 10 mhz 10 ghz the resulting pseudo o 4 4 scheme is explicit and computationally efficient and exhibits all the major numerical characteristics of an o 4 4 accurate fdtd scheme even for strongly attenuating and dispersive media the numerical properties of our approach are constrained by classical numerical dispersion and von neumann routh stability

a general method for fdtd modeling of wave propagation in arbitrary frequency dispersive media a general formulation is presented for finite difference time domain fdtd modeling of wave propagation in arbitrary frequency dispersive media two algorithmic approaches are outlined for incorporating dispersion into the fdtd time stepping equations the first employs a frequency dependent complex permittivity denoted form 1 and the second employs a frequency dependent complex conductivity denoted form 2 a pade representation is used in z transform space to represent the frequency dependent permittivity form 1 or conductivity form 2 this is a generalization over several previous methods employing either debye lorentz or drude models the coefficients of the pade model may be obtained through an optimization process leading directly to a finite difference representation of the dispersion relation without introducing discretization error stability criteria for the dispersive fdtd algorithms are given we show that several previously developed dispersive fdtd algorithms can be cast as special cases of our more general framework simulation results are presented for a one dimensional 1 d air muscle example considered previously in the literature and a three dimensional 3 d radiation problem in dispersive lossy soil using measured soil data

locally implicit discontinuous galerkin time domain method for electromagnetic wave propagation in dispersive media applied to numerical dosimetry in biological tissues we are concerned here with the numerical simulation of electromagnetic wave propagation in biological media because of their water content these media are dispersive i e their electromagnetic material characteristics depend of the frequency in the time domain this translates in a time dependency of these parameters that can be taken into account through and additional auxiliary differential equation for e g the electric polarization which is coupled to the system of maxwell s equations from the application point of view the problems at hand most often involve irregularly shaped structures corresponding to biological tissues modeling realistically the interfaces between tissues is particularly important if one is interested in evaluating accurately the impact of field discontinuities at these interfaces in this paper we propose and study a locally implicit discon tinuous galerkin time domain method formulated on an unstructured tetrahedral mesh for solving the resulting system of differential equations in the case of debye type media three dimensional numerical simulations are presented concerning the exposure of head tissues to a localized source radiation 1 introduction this article is concerned with the numerical simulation of electromagnetic wave propagation in dispersive media these are materials in which either or both of the electromagnetic material parameters e and are functions of frequency note that the conductivity may also be a function of frequency but its effect can be rolled into the complex permittivity in reality all materials have frequency dependent e and but many materials can be approximated as frequency independent over a frequency band of interest simplifying their analysis and simulation here we will focus on the much more common case of frequency dependent permittivity a lot of practical electromagnetic wave propagation problems involve such propagation media such as those involving the interaction of an electromagnetic wave with biological tissues the numerical modeling of the propagation of electromagnetic waves through human tissues is at the heart of many biomedical applications such as the microwave imaging of cancer tumors or the treatment of the latter by hy perthermia for example microwave imaging for breast cancer detection is expected to be safe for the patient and has the potential to detect very small cancerous tumors in the breast 3 14 24 beside the definition of microwave based hyperthermia as an immunotherapy strategy for cancer can also be cited 2 11 the electroporation technique can also be an application which consists of applying nanopulses to the tissues enabling only intracellular membranes to be affected and then opening the route to therapeutic strategies such as electrochemotherapy or gene transfer 21 30 25 26 28 because for all these biomedical applications experimental modeling is almost impossible computer simulation is the approach of choice for understanding the underlying

piecewise linear recursive convolution for dispersive media using fdtd electromagnetic propagation through linear dispersive media can be analyzed using the finite difference time domain fdtd method by employing the recursive convolution rc approach to evaluate the discrete time convolution of the electric field and the dielectric susceptibility function the rc approach results in a fast and computationally efficient algorithm however the accuracy achieved is not generally as good as that obtained with other methods a new piecewise linear recursive convolution plrc method is described here that has greatly improved accuracy over the original rc approach but retains its speed and efficiency advantages

a standard test set for numerical approximations to the shallow water equations in spherical geometry a suite of seven test cases is proposed for the evaluation of numerical methods intended for the solution of the shallow water equations in spherical geometry the shallow water equations exhibit the major difficulties associated with the horizontal dynamical aspects of atmospheric modeling on the spherical earth these cases are designed for use in the evaluation of numerical methods proposed for climate modeling and to identify the potential trade offs which must always be made in numerical modeling before a proposed scheme is applied to a full baroclinic atmospheric model it must perform well on these problems in comparison with other currently accepted numerical methods the cases are presented in order of complexity they consist of advection across the poles steady state geostrophically balanced flow of both global and local scales forced nonlinear advection of an isolated low zonal flow impinging on an isolated mountain rossby haurwitz waves and observed atmospheric states one of the cases is also identified as a computer performance algorithm efficiency benchmark for assessing the performance of algorithms adapted to massively parallel computers

parameter estimation for infinite variance fractional arima consider the fractional arima time series with innovations that have infinite variance this is a finite parameter model which exhibits both long range dependence long memory and high variability we prove the consistency of an estimator of the unknown parameters which is based on the periodogram and derive its asymptotic distribution this shows that the results of mikosch gadrich kluppelberg and adler for arma time series remain valid for fractional arima with long range dependence we also extend the limit theorem for sample autocovariances of infinite variance moving averages developed in davis and resnick to moving averages whose coefficients are not absolutely summable

a perfectly matched layer for fluid solid problems application to ocean acoustics simulations with solid ocean bottoms a time domain legendre spectral element method is described for full wave simulation of ocean acoustics models i e coupled fluid solid problems in unbounded or semi infinite domains taking into account shear wave propagation in the ocean bottom the technique can accommodate range dependent and depth dependent wave speed and density as well as steep ocean floor topography for truncation of the infinite domain to efficiently absorb outgoing waves a fluid solid complex frequency shifted unsplit perfectly matched layer is introduced based on the complex coordinate stretching technique the complex stretching is rigorously taken into account in the derivation of the fluid solid matching condition inside the absorbing layer which has never been done before in the time domain two implementations are designed a convolutional formulation and an auxiliary differential equation formulation because the latter allows for implementation of high order time schemes leading to reduced numerical dispersion and dissipation a topic of importance in particular in long range ocean acoustics simulations the method is validated for a two dimensional fluid solid pekeris waveguide and for a three dimensional seamount model which shows that the technique is accurate and numerically long time stable compared with widely used paraxial absorbing boundary conditions the perfectly matched layer is significantly more efficient at absorbing both body waves and interface waves

a fast time domain integral equation based scheme for analyzing scattering from dispersive objects a fast integral equation based scheme for analyzing transient scattering from inhomogeneous dispersive bodies is presented a time domain integral equation in terms of the electric flux inside the body is constructed by invoking the volume equivalence principle i e by equating the sum of the incident electric field and that radiated by equivalent volume polarization currents to the total electric field the proposed algorithm for solving this time domain integral equation incorporates a recursive convolution scheme that updates the polarization current from knowledge of the electric flux to reduce the computational cost and memory requirement of the resulting marching on in time scheme it is augmented with the plane wave time domain algorithm numerical results that validate the proposed approach and demonstrate its accuracy are presented

error analysis of finite element methods for 3 d maxwell s equations in dispersive media we consider the time dependent maxwell s equations in dispersive media on a bounded three dimensional domain a semi discrete standard finite element method and a semi discrete mixed finite element method are developed and error estimates are provided we believe this is the first finite element error analysis carried out for maxwell s equations in dispersive media

a general framework for the finite difference time domain simulation of real metals we present an efficient framework for the finite difference time domain simulation of real metals the complex permittivity function of a metal is fitted to experimental data in the frequency domain using a non linear least squares algorithm a memory efficient finite difference time domain fdtd scheme is presented for the simulation of the dispersive behavior of a metal in the frequency domain the stability limit for the proposed scheme is determined and compared to the courant limit excellent agreement between our fdtd formulation and the analytical solution for reflections from a thin metal sheet is found

superconvergence analysis for maxwell s equations in dispersive media in this paper we consider the time dependent maxwell s equations in dispersive media on a bounded three dimensional domain global superconvergence is obtained for semi discrete mixed finite element methods for three most popular dispersive media models the isotropic cold plasma the one pole debye medium and the two pole lorentz medium global superconvergence for a standard finite element method is also presented to our best knowledge this is the first superconvergence analysis obtained for maxwell s equations when dispersive media are involved

generalized analysis of stability and numerical dispersion in the discrete convolution fdtd method a simple technique is described for determining the stability and numerical dispersion of finite difference time domain fdtd calculations that are linear second order in space and time and include dispersion by the discrete convolution method the technique is applicable to anisotropic materials numerical examples demonstrate the accuracy of the technique for several anisotropic and or dispersive materials

modelling of wave propagation in wire media using spatially dispersive finite difference time domain method numerical aspects the finite difference time domain fdtd method is applied for modelling of wire media as artificial dielectrics both frequency dispersion and spatial dispersion effects in wire media are taken into account using the auxiliary differential equation method according to the authors knowledge this is the first time when the spatial dispersion effect is considered in the fdtd modelling the stability of developed spatially dispersive fdtd formulations is analyzed through the use of von neumann method combined with the routh hurwitz criterion the results show that the conventional stability courant limit is preserved using standard discretization scheme for wire media modelling flat sub wavelength lenses formed by wire media are chosen for validation of proposed spatially dispersive fdtd formulation results of the simulations demonstrate excellent sub wavelength imaging capability of the wire medium slabs the size of the simulation domain is significantly reduced using the modified perfectly matched layer mpml which can be placed in close vicinity of the wire medium it is demonstrated that the reflections from the mpml wire medium interface are less than 70 db that lead to dramatic improvement of convergence compared to conventional simulations

the cubed sphere a new gridding technique for the solution of partial differential equations in spherical geometry is presented the method is based on a decomposition of the sphere into six identical regions obtained by projecting the sides of a circumscribed cube onto a spherical surface by choosing the coordinate lines on each region to be arcs of great circles one obtains six coordinate systems which are free of any singularity and define the same metric taking full advantage of the symmetry properties of the decomposition a variation of the composite mesh finite difference method can be applied to couple the six grids and obtain with a high degree of efficiency very accurate numerical solutions of partial differential equations on the sphere the advantages of this new technique over both spectral and uniform longitude latitude grid point methods are discussed in the context of applications on serial and parallel architectures we present results of two test cases for numerical approximations to the shallow water equations in spherical geometry the linear advection of a cosine bell and the nonlinear evolution of a rossby haurwitz wave performance analysis for this latter case indicates that the new method can provide with substantial savings in execution times numerical solutions which are as accurate as those obtainable with the spectral transform method

limit theory for the sample covariance and correlation functions of moving averages abstract document describes a moving average process which have regularly varying tail probabilities with index alpha 0 the limit distribution of the sample covariance function is derived in the case that the process has a finite variance but an infinite variance but an infinite fourth moment furthermore in the infinite variance case 0 alpha 2 the sample correlation function is shown to converge in distribution to the ratio of two independent stable random variables with indices alpha and alpha 2 respectively this result immediately gives the limit distribution for the least squares estimates of the parameters in an autoregressive process author

corrected impulse invariance method in z transform theory for frequency dependent fdtd methods the classical impulse invariance method in z transform theory is found to be incorrect and inaccurate when the impulse response is discontinuous at initial time t 0 such inaccuracy results in higher numerical errors if it is used to develop the update equations for frequency dependent finite difference time domain fdtd methods in this paper thorough discussions of corrected impulse invariance method in the realm of z transform theory for dispersive media are presented the correction is shown to be necessary for dispersive media which exhibit discontinuity at t 0 in the time domain susceptibility function a corrected z transform table is provided to facilitate the conversion from frequency to z domain with the aid of the table various formulations of frequency dependent fdtd update equations using both corrected and classical impulse invariance methods are carried out conveniently detailed performance measures such as numerical permittivity leading error term dispersion relation normalized phase and attenuation errors as well as memory storage requirements are included along with some extensive numerical comparisons

a flexible inner outer preconditioned gmres algorithm a variant of the gmres algorithm is presented that allows changes in the preconditioning at every step there are many possible applications of the new algorithm some of which are briefly discussed in particular a result of the flexibility of the new variant is that any iterative method can be used as a preconditioner for example the standard gmres algorithm itself can be used as a preconditioner as can cgnr or cgne the conjugate gradient method applied to the normal equations however the more appealing utilization of the method is in conjunction with relaxation techniques possibly multilevel techniques the possibility of changing preconditioners may be exploited to develop efficient iterative methods and to enhance robustness a few numerical experiments are reported to illustrate this fact

estimation of sparse jacobian matrices and graph coloring blems given a mapping with a sparse jacobian matrix the problem of minimizing the number of function evaluations needed to estimate the jacobian matrix by differences is investigated this problem can be attacked as a graph coloring problem and this approach leads to very efficient algorithms the behavior of these algorithms is studied and in particular it is proved that two of the algorithms are optimal for band graphs numerical evidence is presented which indicates that these two algorithms are nearly optimal on practical problems

a wave propagation method for hyperbolic systems on the sphere presented in this work is an explicit finite volume method for solving general hyperbolic systems on the surface of a sphere applications where such systems arise include passive tracer advection in the atmosphere shallow water models of the ocean and atmosphere and shallow water magnetohydrodynamic models of the solar tachocline the method is based on the curved manifold wave propagation algorithm of rossmanith bale and leveque a wave propagation algorithm for hyperbolic systems on curved manifolds j comput phys 199 2004 631 662 which makes use of parallel transport to approximate geometric source terms and orthonormal riemann solvers to carry out characteristic decompositions this approach employs tvd wave limiters which allows the method to be accurate for both smooth solutions and solutions in which large gradients or discontinuities can occur in the form of material interfaces or shock waves the numerical grid used in this work is the cubed sphere grid of ronchi iacono and paolucci the cubed sphere a new method for the solution of partial differential equations in spherical geometry j comput phys 124 1996 93 114 which covers the sphere with nearly uniform resolution using six identical grid patches with grid lines lying on great circles boundary conditions across grid patches are applied either through direct copying from neighboring grid cells in the case of scalar equations or 1d interpolation along great circles in the case of more complicated systems the resulting numerical method is applied to several test problems for the advection equation the shallow water equations and the shallow water magnetohydrodynamic smhd equations for the smhd equations we make use of an unstaggered constrained transport method to maintain a discrete divergence free magnetic field

a fully implicit method for lattice boltzmann equations existing approaches for solving the lattice boltzmann equations with finite difference methods are explicit and semi implicit both have certain stability constraints on the time step size in this work a fully implicit second order finite difference scheme is developed we focus on a parallel highly scalable newton krylov ras algorithm for the solution of a large sparse nonlinear system of equations arising at each time step here ras is a restricted additive schwarz preconditioner based on a first order spatial discretization we show numerically that by using the fully implicit method the time step size is no longer constrained by the cfl condition and the newton krylov ras algorithm is scalable on a supercomputer with more than ten thousand processors moreover to calculate the steady state solution we investigate an adaptive time stepping strategy the total compute time required by the implicit method with adaptive time stepping is much smaller than that of an explicit method for several t

efficient implementation of tam and auriault s time domain impedance boundary condition a new and efficient time domain implementation is proposed for the impedance model originally introduced by tam and auriault tam c k w and auriault l time domain impedance boundary conditions for computational aeroacoustics aiaa journal vol 34 no 5 may 1996 pp 917 923 in the frequency domain the pressure can be calculated from the product of the impedance with the normal velocity in the time domain a convolution is needed which may become a costly operation present solutions for this problem involve either a full convolution and storage of a time history of data or a translation of the frequency domain models to time domain formulations involving time derivatives the former approach is very costly in terms of memory and cpu time the latter makes the implementation discretization specific and vulnerable to stability issues a new formulation based on recursive convolution results in an efficient implementation that stores only one accumulator which can be updated at each time step with minimal addition and multiplication it allows for the exact representation of the impedance at a given frequency the formulation is validated by a comparison with the measurement data from the nasa langley grazing flow impedance tube the simulations are performed by introducing a plane wave at a single frequency in the tube and this is done for six frequencies and five different mean flow speeds

limit theory for moving averages of random variables with regularly varying tail probabilities let z k infty k infty be iid where the z k s have regularly varying tail probabilities under mild conditions on a real sequence c j j geq 0 the stationary process x n sum infty j 0 c jz n j n geq 1 exists a point process based on x n converges weakly and from this a host of weak limit results for functionals of x n ensue we study sums extremes excedences and first passages as well as behavior of sample covariance functions

high order accurate fdtd schemes for dispersive maxwell s equations in second order form using recursive convolutions abstract we propose a novel finite difference time domain fdtd scheme for the solution of maxwell s equations in which linear dispersive effects are present the method uses high order accurate approximations in space and time for the dispersive maxwell s equations written as a second order vector wave equation with a time history convolution term the modified equation approach is combined with the recursive convolution rc method to develop high order approximations accurate to any desired order in space and time high order accurate centered approximations of the physical maxwell interface conditions are derived for the dispersive setting in order to fully restore accuracy at discontinuous material interfaces second and fourth order accurate versions of the scheme are presented and implemented in two spatial dimensions for the case of the drude linear dispersion model the stability of these schemes is analyzed finally our approach is also amenable to curvilinear numerical grids if used with an appropriate generalized laplace operator

an fdtd algorithm with perfectly matched layers for general dispersive media a three dimensional 3 d finite difference time domain fdtd algorithm with perfectly matched layer pml absorbing boundary condition abc is presented for general inhomogeneous dispersive conductive media the modified time domain maxwell s equations for dispersive media are expressed in terms of coordinate stretching variables we extend the recursive convolution rc and piecewise linear recursive convolution plrc approaches to arbitrary dispersive media in a more general form the algorithm is tested for homogeneous and inhomogeneous media with three typical kinds of dispersive media i e lorentz medium unmagnetized plasma and debye medium excellent agreement between the fdtd results and analytical solutions is obtained for all testing cases with both rc and plrc approaches we demonstrate the applications of the algorithm with several examples in subsurface radar detection of mine like objects cylinders and spheres buried in a dispersive half space and the mapping of a curved interface because of their generality the algorithm and computer program can be used to model biological materials artificial dielectrics optical materials and other dispersive media

full wave modeling of therapeutic ultrasound efficient time domain implementation of the frequency power law attenuation for the simulation of therapeutic ultrasound applications a method including frequency dependent attenuation effects directly in the time domain is highly desirable this paper describes an efficient numerical time domain implementation of the power law attenuation model presented by szabo szabo j acoust soc am 96 491 500 1994 simulations of therapeutic ultrasound applications are feasible in conjunction with a previously presented finite differences time domain fdtd algorithm for nonlinear ultrasound propagation ginter et al j acoust soc am 111 2049 2059 2002 szabo implemented the empirical frequency power law attenuation using a causal convolutional operator directly in the time domain equation though a variety of time domain models has been published in recent years no efficient numerical implementation has been presented so far for frequency power law attenuation models solving a convolutional integral with standard time domain techniques requires enormous computational ef

integral based exponential time differencing algorithms for general dispersive media and the cfs pml two efficient integral based exponential time differencing etd algorithms for general dispersive media in the finite difference time domain fdtd are introduced the first employs a linear approximation for the field over an integral time step in the integrand denoted algorithm i and the second employs a taylor series for approximating the field over the integral time step denoted algorithm ii compared with the auxiliary differential equation ade method and the piecewise linear recursive convolution plrc method the proposed algorithms have the same second order accuracy but can lead to a substantial saving in both the memory space and cpu time consumption to complete the scheme for the open region problems a novel integral based etd implementation of the complex frequency shifted perfectly matched layer cfs pml is proposed compared with the well known recursive convolution implementation of the cfs pml cpml this new implementation can lead to a substantial saving in the cpu time and a significant improvement of around 20 db in the absorbing performance and through the integral based etd algorithm a much simpler interpretation of the cpml is presented

vorticity and entropy boundary conditions for acoustical finite difference time domain simulations in this paper a time domain numerical model for describing the presence of vorticity and entropy boundary layers is introduced the boundary model can be inserted in acoustic time domain models such as the finite difference time domain fdtd model for studying the acoustic behavior of high quality resonator structures the main focus in deriving the model is on numerical efficiency boundary layer theory is reviewed to obtain a three dimensional formulation of its influence on fdtd equations that must be applied in boundary discretization cells the dependence that is encountered is approximated in time domain in such a way that no numerical convolution is required although this approximation is rather inaccurate it is sufficient for most applications and introduces almost no extra computational effort several numerical examples illustrate the applicability of the model

frequency dispersive materials for 3 d hybrid solvers in time domain the recursive convolution method to treat linear dispersive materials in the finite difference time domain fdtd is here generalized to an explicit finite volume solver and an implicit finite element solver both solvers are interfaced to fdtd resulting in two hybrid solvers the stability of the solvers is analyzed and the accuracy is demonstrated in several scattering cases where a plane wave illuminates a sphere with complex permittivity excellent agreement with the analytical mie series solution is obtained for materials of debye and lorentz type as well as for a material consisting of two lorentz poles

convergence analysis of some algorithms for solving nonsmooth equations this paper presents convergence analysis of some algorithms for solving systems of nonlinear equations defined by locally lipschitzian functions for the directional derivative based and the generalized jacobian based newton methods both the iterates and the corresponding function values are locally superlinearly convergent globally a limiting point of the iterate sequence generated by the damped directional derivative based newton method is a zero of the system if and only if the iterate sequence converges to this point and the stepsize eventually becomes one provided that the system is strongly bd regular and semismooth at this point in this case the convergence is superlinear a general attraction theorem is presented which can be applied to two algorithms proposed by han pang and rangaraj a hybrid method which is both globally convergent in the sense of finding a stationary point of the norm function of the system and locally quadratically convergent is also presented

parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed sphere high resolution and scalable parallel algorithms for the shallow water equations on the sphere are very important for modeling the global climate in this paper we introduce and study some highly scalable multilevel domain decomposition methods for the fully implicit solution of the nonlinear shallow water equations discretized with a second order well balanced finite volume method on the cubed sphere with the fully implicit approach the time step size is no longer limited by the stability condition and with the multilevel preconditioners good scalabilities are obtained on computers with a large number of processors the investigation focuses on the use of semismooth inexact newton method for the case with nonsmooth topography and the use of two and three level overlapping schwarz methods with different order of discretizations for the preconditioning of the jacobian systems we test the proposed algorithm for several benchmark cases and show numerically that this approach converges well with smooth and nonsmooth bottom topography and scales perfectly in terms of the strong scalability and reasonably well in terms of the weak scalability on machines with thousands and tens of thousands of processors

a fully implicit domain decomposition algorithm for shallow water equations on the cubed sphere popular approaches for solving shallow water equations swes for climate modeling are explicit and semiimplicit methods and both have certain constraints on the time step size in this paper we propose and study a fully implicit method which imposes no limit on the time step size but requires the solution of a large sparse nonlinear system of equations at every time step the focus of the paper is a parallel fully coupled newton krylov ras algorithm with a jacobian matrix explicitly calculated on a weakly nonmatching cubed sphere mesh here ras is a restricted additive schwarz method we show numerically that with such a preconditioned nonlinearly implicit method the time step size is no longer constrained by the cfl condition and we report superlinear speedup of the algorithm on machines with thousands of processors for problems with smooth and nonsmooth solutions

analysis of a time domain finite element method for 3 d maxwell s equations in dispersive media abstract we consider the time dependent maxwell s equations in dispersive media on a bounded domain in three dimensional space a fully discrete finite element scheme is developed to approximate the electric field equation derived from the maxwell s equations optimal energy norm error estimates are proved for nedelec curl conforming edge elements this is the first finite element error analysis for maxwell s equations in dispersive media

stable non gaussian random processes stochastic models with infinite variance stable random variables on the real line multivariate stable distributions stable stochastic integrals dependence structures of multivariate stable distributions non linear regression complex stable stochastic integrals and harmonizable processes self similar processes chentsov random fields introduction to sample path properties boundedness continuity and oscillations measurability integrability and absolute continuity boundedness and continuity via metric entropy integral representation historical notes and extensions

superconvergence analysis of nonconforming mixed finite element methods for time dependent maxwell s equations in isotropic cold plasma media in this paper based on our previous work of asymptotic expansion an initial effort of global superconvergence analysis of time domain maxwell s equations in isotropic cold plasma media is obtained for semi discrete mixed finite element scheme during this procedure superclose analysis of the interpolation of the smoothing solution and the solution of mixed finite element method is obtained for the first time by the post processing operators superconvergence phenomena can be found to our best knowledge this is the first global superconvergence analysis presented by nonconforming mixed finite element methods when isotropic cold plasma media is involved

anisotropic medium pml for vector fetd with modified basis functions a novel anisotropic medium perfectly matched layer pml implementation is presented for boundary truncation in the three dimensional vector finite element time domain fetd method this approach utilizes a complex set of vector test and basis functions in the pml region that recover the usual basis functions in the non pml region numerical examples show that the proposed pml fetd approach has small reflection errors and no observed late time instabilities for simulations involving up to 10 sup 6 time steps

an unsplit convolutional perfectly matched layer improved at grazing incidence for seismic wave propagation in poroelastic media the perfectly matched layer pml absorbing technique has become popular in numerical modeling in elastic or poroelastic media because of its efficiency in absorbing waves at nongrazing incidence however after numerical discretization at grazing incidence large spurious oscillations are sent back from the pml into the main domain the pml then becomes less efficient when sources are located close to the edge of the truncated physical domain under study for thin slices or for receivers located at a large offset we develop a pml improved at grazing incidence for the poroelastic wave equation based on an unsplit convolutional formulation of the equation as a first order system in velocity and stress we show its efficiency for both nondissipative and dissipative biot porous models based on a fourth order staggered finite difference method used in a thin mesh slice the results obtained are improved significantly compared with those obtained with the classical pml

extension of the adi fdtd method to debye media this paper describes an extension of the alternating direction implicit finite difference time domain adi fdtd method to analyze problems involving debye media

an efficient physics based preconditioner for the fully implicit solution of small scale thermally driven atmospheric flows in atmospheric flow situations typical of a small scale atmospheric thermal a separation of time scales exists between the fast sound wave time scale and the advective time scale atmospheric models have been designed to take advantage of this disparity of time scales with numerical approaches such as the semi implicit or split explicit approach being used to efficiently step over the fast sound waves some of these numerical approaches are first order in time to improve accuracy over these methods a fully implicit and nonlinearly consistent inc flow solver has been developed for the navier stokes equation set in our inc method the equation set is solved by use of the jacobian free newton krylov jfnk method an efficient preconditioner has been developed which uses the semi implicit method to solve the governing equations being that this preconditioner was designed to attack the fastest waves in the system and not other features in the implicit system such as advection or turbulent diffusion the preconditioning technique is labeled as a physics based preconditioner a variety of linear solvers including ssor krylov methods and or multigrid approaches are used to approximately invert the pressure matrix in the semi implicit algorithm a suite of simulations will be conducted utilizing different linear solvers for the simple problem of the bouyant rise of a warm bubble the problem will also document the ability of the inc approach to achieve second order in time accuracy

the spectral element method for the shallow water equations on the sphere the spectral element method is implemented for the shallow water equations in spherical geometry and its performance is compared with other models this is the first step in evaluating the suitability of spectral elements for climate modeling the potential advantages and disadvantages of spectral elements over more conventional models used for climate studies are discussed the method requires that the sphere be tiled with rectangles for which we make use of the gnomonic projection to map the sphere onto the cube to measure the performance of the method relative to other models results are presented from a standard suite of shallow water test cases for the sphere these results confirm the spectral accuracy of the method

dispersion analysis of finite difference and discontinuous galerkin schemes for maxwell s equations in linear lorentz media abstract in this paper we consider maxwell s equations in linear dispersive media described by a single pole lorentz model for electronic polarization we study two classes of commonly used spatial discretizations finite difference methods fd with arbitrary even order accuracy in space and high spatial order discontinuous galerkin dg finite element methods both types of spatial discretizations are coupled with second order semi implicit leap frog and implicit trapezoidal temporal schemes by performing detailed dispersion analysis for the semi discrete and fully discrete schemes we obtain rigorous quantification of the dispersion error for lorentz dispersive dielectrics in particular comparisons of dispersion error can be made taking into account the model parameters and mesh sizes in the design of the two types of schemes this work is a continuation of our previous research on energy stable numerical schemes for nonlinear dispersive optical media 6 7 the results for the numerical dispersion analysis of the reduced linear model considered in the present paper can guide us in the optimal choice of discretization parameters for the more complicated and nonlinear models the numerical dispersion analysis of the fully discrete fd and dg schemes for the dispersive maxwell model considered in this paper clearly indicate the dependence of the numerical dispersion errors on spatial and temporal discretizations their order of accuracy mesh discretization parameters and model parameters the results obtained here cannot be arrived at by considering discretizations of maxwell s equations in free space in particular our results contrast the advantages and disadvantages of using high order fd or dg schemes and leap frog or trapezoidal time integrators over different frequency ranges using a variety of measures of numerical dispersion errors finally we highlight the limitations of the second order accurate temporal discretizations considered

spectral transform solutions to the shallow water test set abstract solutions to the test case suite proposed by williamson et al j comput phys 102 211 1992 for the shallow water equations in spherical geometry are presented the solutions have been generated using a conventional spectral transform technique combined with a semi implicit time differencing scheme for several of the test cases closed form solutions do not exist for these cases high resolution numerical integrations of the spectral transform model are used to provide reference solutions against which alternative numerical schemes and lower resolution spectral transform solutions can be evaluated the sensitivity of the high resolution numerical solutions associated with temporal truncation spatial truncation and internal dissipation are quantified in order to help bound their uncertainty in almost all of the test cases the spectral transform method proves to be a highly accurate solution technique this is particularly the case at resolutions typically associated with atmospheric general circulation models used to simulate the atmosphere s climate the most serious deficiency of the spectral transform method in the context of the test cases is the introduction of spurious minima and maxima into the solution caused by gibbs phenomenon when sharp gradients exist although this behavior is not necessarily a problem for accurately simulating fluid flow it can become a serious problem for atmospheric general circulation models if the spurious wave structures result in nonphysical states such as negative water vapor mixing ratio

upwind schemes and boundary conditions with applications to euler equations in general geometries abstract a unified treatment of several upwind shock capturing algorithms is presented each algorithm has a riemann initial value problem as its basis the treatment of boundaries involves solving the associated riemann initial boundary value problem the first author s algorithm applied to multidimensional euler equations in general geometries is then presented its worth is verified by various calculations which include mach 8 supersonic flow past a circular cylinder

an fdtd formulation for dispersive media using a current density a novel finite difference time domain fdtd formulation for dispersive media called the je convolution jec method is derived using the convolution relationship between the current density j and the electric field e the high accuracy of the jec method is confirmed by computing the reflection and transmission coefficients for a nonmagnetized plasma slab in one dimension it is found that the new method has an accuracy comparable to the auxiliary differential equation ade while having the same computational efficiency as the less accurate recursive convolution rc method numerical simulations also show that the jec method exhibits significantly higher accuracy than the rc method in modeling wave attenuation inside the plasma

parameter estimation for arma models with infinite variance innovations abstract we consider a standard arma process of the form phi b xt theta b zt where the innovations zt belong to the domain of attraction of a stable law so that neither the zt nor the xt have a finite variance our aim is to estimate the coefficients of phi and theta since maximum likelihood estimation is not a viable possibility due to the unknown form of the marginal density of the innovation sequence we adopt the so called whittle estimator based on the sample periodogram of the x sequence despite the fact that the periodogram does not a priori seem like a logical object to study in this non l situation we show that our estimators are consistent obtain their asymptotic distributions and show that they converge to the true values faster than in the usual l2 case

operator splitting methods for maxwell s equations in dispersive media with orientational polarization we present two operator splitting schemes for the numerical simulation of maxwell s equations in dispersive media of debye type that exhibit orientational polarization the maxwell debye model the splitting schemes separate the mechanisms of wave propagation and polarization to create simpler sub steps that are easier to implement in addition dimensional splitting is used to propagate waves in different axial directions we present a sequential operator splitting scheme and its symmetrized version for the maxwell debye system in two dimensions the splitting schemes are discretized using implicit finite difference methods that lead to unconditionally stable schemes we prove that the fully discretized sequential scheme is a first order time perturbation and the symmetrized scheme is a second order time perturbation of the crank nicolson scheme for discretizing the maxwell debye model numerical examples are presented that illustrate our theoretical results

perfectly matched layer media with cfs for an unconditionally stable adi fdtd method a perfectly matched layer pml medium with complex frequency shifted cfs constitutive parameters is introduced for the three dimensional alternating direction implicit adi formulation of the finite difference time domain fdtd method the absorbing boundary is implemented using the convolutional pml cpml approach it is demonstrated that the resulting adi cpml scheme is unconditionally stable the effectiveness of the absorbing medium as a function of the time step is also demonstrated the proposed method has the advantage that it allows the application of the adi method to low frequency analysis

solution of 3d time domain electromagnetic problems using optimal subspace projection abstracttime domain problems for controlled source electromagnetic exploration require accurate discretization of the solution for multiple spacial and temporal scales therefore forward simulation using conventional computational methods becomes computationally expensive even without accounting for induced polarization ip effects these effects create another complication caused by the presence of a convolution integral in the time domain maxwell system we suggested a novel fast and robust algorithm to solve the 3d time domain electromagnetic em problems that can be considered as a generalization of the spectral lanczos decomposition method the new method also allowed us to incorporate the ip effects without significant cost increase the discretized large scale maxwell system was projected onto a small subspace consisting of the laplace domain solutions the so called parameter dependent krylov subspace for an optimally chosen set of laplace parameters the projected system preserved stabilit

fdtd for nth order dispersive media previously a method for applying the finite difference time domain fdtd method to dispersive media with complex permittivity described by a function with a single first order pole was presented this method involved the recursive evaluation of a discrete convolution and was therefore relatively efficient in this work the recursive convolution approach is extended to media with dispersions described by multiple second order poles the significant change from the first order implementation is that the single backstore variable for each second order pole is complex the approach is demonstrated for a pulsed plane wave incident on a medium with a complex permittivity described by two second order poles and excellent agreement is obtained with the exact solution

stability and phase error analysis of fd td in dispersive dielectrics four fd td extensions for the modeling of pulse propagation in debye or lorentz dispersive media are analyzed through studying the stability and phase error properties of the coupled difference equations corresponding to maxwell s equations and to the equations for the dispersion for good overall accuracy the author shows that all schemes should be run at their courant stability limit and that the timestep should finely resolve the medium timescales particularly for debye schemes it should be at least spl delta t 10 sup spl minus 3 spl tau while for lorentz schemes it should be spl delta t 10 sup spl minus 2 spl tau where spl tau is a typical medium relaxation time a numerical experiment with a debye medium confirms this the author has determined that two of the discretizations for debye media are totally equivalent in the lorentz medium case the author establishes that the method that uses the polarization differential equation to model dispersion is stable for all wavenumbers and that the method using the local in time constitutive relation is weakly unstable for modes with wavenumber k such that k spl delta x spl pi 2

finite difference modeling of electromagnetic wave propagation in dispersive and attenuating media realistic modeling of electromagnetic wave propagation in the radar frequency band requires a full solution of maxwell s equations as well as an adequate description of the material properties we present a finite difference time domain fdtd solution of maxwell s equations that allows accounting for the frequency dependence of the dielectric permittivity and electrical conductivity typical of many near surface materials this algorithm is second order accurate in time and fourth order accurate in space conditionally stable and computationally only marginally more expensive than its standard equivalent without frequency dependent material properties empirical rules on spatial wavefield sampling are derived through systematic investigations of the influence of various parameter combinations on the numerical dispersion curves since this algorithm intrinsically models energy absorption efficient absorbing boundaries are implemented by surrounding the computational domain by a thin 2 dominant waveleng

a high order accurate scheme for maxwell s equations with a generalized dispersive material model abstract a high order accurate scheme for solving the time domain maxwell s equations with a generalized dispersive material model is described the equations for the electric field are solved in second order form and a general dispersion model is treated with the addition of one or more polarization vectors which obey a set of auxiliary differential equations ade numerical methods are developed for both second order and fourth order accuracy in space and time the equations are discretized using finite differences and advanced in time with a single stage three level space time scheme which remains stable up to the usual explicit cfl restriction as proven using mode analysis because the equations are treated in their second order form there is no need for grid staggering and instead a collocated grid is used composite overlapping grids are used to treat complex geometries with boundary conforming grids and a high order upwind dissipation is added to ensure robust and stable approximations on overlapping grids numerical results in two and three space dimensions confirm the accuracy and stability of the new schemes

globally convergent newton methods for nonsmooth equations this paper presents some globally convergent descent methods for solving systems of nonlinear equations defined by locally lipschitzian functions these methods resemble the well known family of damped newton and gauss newton methods for solving systems of smooth equations they generalize some recent newton like methods for solving b differentiable equations which arise from various mathematical programs

a novel piecewise linear recursive convolution approach for dispersive media using the finite difference time domain method two novel methods for implementing recursively the convolution between the electric field and a time dependent electric susceptibility function in the finite difference time domain fdtd method are presented both resulting algorithms are straightforward to implement and employ an inclusive susceptibility function which holds as special cases the lorentz debye and drude media relaxations the accuracy of the new proposed algorithms is found to be systematically improved when compared to existing standard piecewise linear recursive convolution plrc approaches it is conjectured that the reason for this improvement is that the new proposed algorithms do not make any assumptions about the time variation of the polarization density in each time interval no finite difference or semi implicit schemes are used for the calculation of the polarization density the only assumption that these two new methods make is that the first time derivative of the electric field is constant within each fdtd time interval

an efficient time domain perfectly matched layers formulation for elastodynamics on spherical domains summary many practical applications require the analysis of elastic wave propagation in a homogeneous isotropic media in an unbounded domain one widely used approach for truncating the infinite domain is the so called method of perfectly matched layers pmls most existing pml formulations are developed for finite difference methods based on the first order velocity stress form of the elasticity equations and they are not straight forward to implement using standard finite element methods fems on unstructured meshes some of the problems with these formulations include the application of boundary conditions in half space problems and in the treatment of edges and or corners for time domain problems several pml formulations which do work with fems have been proposed although most of them still have some of these problems and or they require a large number of auxiliary nodal history memory variables in this work we develop a new pml formulation for time domain elastodynamics on a spherical domain which reduces to a two dimensional formulation under the assumption of axisymmetry our formulation is well suited for implementation using fems where it requires lower memory than existing formulations and it allows for natural application of boundary conditions we solve example problems on two dimensional and three dimensional domains using a high order discontinuous galerkin dg discretization on unstructured meshes and explicit time stepping we also study an approach for stabilization of the discrete equations and we show several practical applications for quality factor predictions of micromechanical resonators along with verifying the accuracy and versatility of our formulation copyright 2014 john wiley sons ltd

shallow water model on cubed sphere by multi moment finite volume method a global numerical model for shallow water flows on the cubed sphere grid is proposed in this paper the model is constructed by using the constrained interpolation profile multi moment finite volume method cip mm fvm two kinds of moments i e the point value pv and the volume integrated average via are defined and independently updated in the present model by different numerical formulations the lax friedrichs upwind splitting is used to update the pv moment in terms of a derivative riemann problem and a finite volume formulation derived by integrating the governing equations over each mesh element is used to predict the via moment the cubed sphere grid is applied to get around the polar singularity and to obtain uniform grid spacing for a spherical geometry highly localized reconstruction in cip mm fvm is well suited for the cubed sphere grid especially in dealing with the discontinuity in the coordinates between different patches the mass conservation is completely achieved over the whole globe the numerical model has been verified by williamson s standard test set for shallow water equation model on sphere the results reveal that the present model is competitive to most existing ones

an efficient finite element time domain formulation for the elastic second order wave equation a non split complex frequency shifted convolutional pml the perfectly matched layer pml technique has demonstrated very high efficiency as absorbing boundary condition for the elastic wave equation recast as a first order system in velocity and stress in attenuating non grazing bulk and surface waves this paper develops a novel convolutional pml formulation based on the second order wave equation with displacements as the only unknowns to annihilate spurious reflections from near grazing waves the derived variational form allows for the use of e g finite element and the spectral element methods as spatial discretization schemes a recursive convolution update scheme of second order accuracy is employed such that highly stable effective time integration with the newmark beta implicit and explicit with mass lumping method is achieved the implementation requires minor modifications of existing displacement based finite element software and the stability and efficiency of the proposed formulation is verified by relevant two dimensional benchmarks that accommodate bulk and surface waves copyright 2011 john wiley sons ltd

the sample autocorrelations of heavy tailed processes with applications to arch we study the sample acvf and acf of a general stationary sequence under a weak mixing condition and in the case that the marginal distributions are regularly varying this includes linear and bilinear processes with regularly varying noise and arch processes their squares and absolute values we show that the distributional limits of the sample acf can be random provided that the variance of the marginal distribution is infinite and the process is nonlinear this is in contrast to infinite variance linear processes if the process has a finite second but infinite fourth moment then the sample acp is consistent with scaling rates that grow at a slower rate than the standard root n consequently asymptotic confidence bands are wider than those constructed in the classical theory we demonstrate the theory in full detail far an arch 1 process

the cumulant theory of cyclostationary time series i foundation the problem of characterizing the sine wave components in the output of a polynomial nonlinear system with a cyclostationary random time series input is investigated the concept of a pure nth order sine wave is introduced and it is shown that pure nth order sine wave strengths in the output time series are given by scaled fourier coefficients of the polyperiodic temporal cumulant of the input time series the higher order moments and cumulants of narrowband spectral components of time series are defined and then idealized to the case of infinitesimal bandwidth such spectral moments and cumulants are shown to be characterized by the fourier transforms of the temporal moments and cumulants of the time series it is established that the temporal and spectral cumulants have certain mathematical and practical advantages over their moment counterparts to put the contributions of the paper in perspective a uniquely comprehensive historical survey that traces the development of the ideas of temporal and spectral cumulants from their inception is provided

a nonsmooth version of newton s method newton s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized jacobian instead of the derivative this extension includes the b derivative version of newton s method as a special case convergence theorems are proved under the condition of semismoothness it is shown that the gradient function of the augmented lagrangian forc2 nonlinear programming is semismooth thus the extended newton s method can be used in the augmented lagrangian method for solving nonlinear programs

choosing the forcing terms in an inexact newton method an inexact newton method is a generalization of newton s method for solving f x 0 f mathbb r n to mathbb r n in which at the kth iteration the step s k from the current approximate solution x k is required to satisfy a condition f x k f x k s k leqslant eta k f x k for a forcing term eta k in 0 1 in typical applications the choice of the forcing terms is critical to the efficiency of the method and can affect robustness as well promising choices of the forcing terms are given their local convergence properties are analyzed and their practical performance is shown on a representative set of test problems

propagation in linear dispersive media finite difference time domain methodologies finite difference time domain fdtd methodologies are presented for electromagnetic wave propagation in two different kinds of linear dispersive media an nth order lorentz and an mth order debye medium the temporal discretization is accomplished by invoking the central difference approximation for the temporal derivatives that appear in the first order differential equations from this the final equations are temporally advanced using the classical leapfrog method one dimensional scattering from a dielectric slab is chosen for a test case provided that the maximum operating frequency times the time step is small and that the wave is adequately resolved in space as shown in the error analysis the agreement between the computed and exact solutions will be excellent the attached data which are associated with the four pole lorentz dielectric and the five pole debye medium verify this assertion