an upwinding embedded boundary method for maxwell s equations in media with material interfaces 2d case we propose a new upwinding embedded boundary method to solve time dependent maxwell s equations in media with material interfaces a global second order finite difference method is obtained by combining central difference schemes away from the interfaces and upwinding technique with jump conditions near the interfaces the proposed finite difference method allows time step based on a uniform mesh independent of the locations and shapes of the interfaces moreover the scheme is simple to implement in multidimensional cases numerical tests of wave equations with various types of material interfaces and electromagnetic scattering of 2d cylinders confirm the stability uniform accuracy and ease of implementation of the method

f murtagh 2005 correspondence analysis and data coding with java and r 230 pp us 76 00 isbn 1584885289

a pseudospectral method for time domain computation of electromagnetic scattering by bodies of revolution we present a multidomain pseudospectral method for the accurate and efficient time domain computation of scattering by body of revolution bor perfectly electrically conducting objects in the bor formulation of the maxwell equations the azimuthal dependence of the fields is accounted for analytically through a fourier series the numerical scheme in the r z plane is developed in general curvilinear coordinates and the method of characteristics is applied for patching field values in the individual subdomains to obtain the global solution a modified matched layer method is used for terminating the computational domain and special attention is given to proper treatment of the coordinate singularity in the scattered field formulation and correct time domain boundary conditions along edges numerical results for monochromatic plane wave scattering by smooth and nonsmooth axis symmetric objects including spheres cone spheres and finite cylinders is compared with results from the literature illustrating the accuracy and computational efficiency associated with the use of properly constructed spectral methods to emphasize the versatility of the presented framework we compute plane wave scattering by a missile and find satisfactory agreement with method of moment mom computations

difference approximations for the second order wave equation difference approximations are derived for the second order wave equation in one and two space dimensions without first writing it as a first order system both the dirichlet and the neumann problems are treated for the one dimensional case relations between the boundary error and the interior phase error are derived for a fully second order accurate discretization as well as a scheme that is fourth order accurate in the interior and second order accurate at the boundary general two dimensional domains are considered for the dirichlet problem where the domain is embedded in a cartesian grid and the boundary conditions are approximated by interpolation a stable conservative scheme is derived where the time step is determined only by the interior discretization formula discretization cells cut by the boundary are treated implicitly but the resulting scheme becomes explicit because the implicit dependence only is pointwise numerical examples are provided to verify the stability and accuracy of the proposed method

a high order accurate parallel solver for maxwell s equations on overlapping grids a scheme for the solution of the time dependent maxwell s equations on composite overlapping grids is described the method uses high order accurate approximations in space and time for maxwell s equations written as a second order vector wave equation high order accurate symmetric difference approximations to the generalized laplace operator are constructed for curvilinear component grids the modified equation approach is used to develop high order accurate approximations that use only three time levels and have the same time stepping restriction as the second order scheme discrete boundary conditions for perfect electrical conductors and for material interfaces are developed and analyzed the implementation is optimized for component grids that are cartesian resulting in a fast and efficient method the solver runs on parallel machines with each component grid distributed across one or more processors numerical results in two and three dimensions are presented for the fourth order accurate version of the method these results demonstrate the accuracy and efficiency of the approach

perturbation theory for anisotropic dielectric interfaces and application to subpixel smoothing of discretized numerical methods we derive a correct first order perturbation theory in electromagnetism for cases where an interface between two anisotropic dielectric materials is slightly shifted most previous perturbative methods give incorrect results for this case even to lowest order because of the complicated discontinuous boundary conditions on the electric field at such an interface our final expression is simply a surface integral over the material interface of the continuous field components from the unperturbed structure the derivation is based on a localized coordinate transformation technique which avoids both the problem of field discontinuities and the challenge of constructing an explicit coordinate transformation by taking the limit in which the coordinate perturbation is infinitesimally localized around the boundary not only is our result potentially useful in evaluating boundary perturbations e g from fabrication imperfections in highly anisotropic media such as many metamaterials but it also has a direct application in numerical electromagnetism in particular we show how it leads to a subpixel smoothing scheme to ameliorate staircasing effects in discretized simulations of anisotropic media in such a way as to greatly reduce the numerical errors compared to other proposed smoothing schemes

conformal finite different time domain fdtd with overlapping grids it is shown how to use many overlapping conformal grids in the neighborhood of the scatterer while using a rectangular grid away from the scatterer for solving maxwell s equations the locally conformal grids allow better approximation of the boundary condition on the scattering object while the rectangular grid preserves the simplicity and accuracy of the regular finite difference time domain fdtd algorithm these grids overlap typically about three zones it is shown how to connect together the calculations done in different overlapping grids

an upwinding boundary condition capturing method for maxwell s equations in media with material interfaces by using ghost points on either side of the interfaces a global second order accurate upwinding boundary condition capturing method for time domain maxwell s equations in media with material interfaces is proposed the equations are discretized on a uniform cartesian grid and the interfaces are allowed to intersect the grid in an arbitrary fashion the method is then obtained by combining central finite difference schemes with applicable nodes being replaced by the ghost points and upwinding technique with jump conditions across the interfaces being captured in a manner that the upwind property is always satisfied the resulting discretization has the desirable property that the allowed time step size is independent of the locations and the shapes of the interfaces numerical examples are then given to demonstrate the second order accuracy as well as the stability of the method where it is used to study wave equations with various types of material interfaces including electromagnetic scattering of a plane incident wave by a dielectric circular cylinder

nodal high order methods on unstructured grids we present a convergent high order accurate scheme for the solution of linear conservation laws in geometrically complex domains as our main example we include a detailed development and analysis of a scheme for the time domain solution of maxwell s equations in a three dimensional domain the fully unstructured spatial discretization is made possible by the use of a high order nodal basis employing multivariate lagrange polynomials defined on the triangles and tetrahedra while the equations themselves are satisfied in a discontinuous galerkin form with the boundary conditions being enforced weakly through a penalty term accuracy stability and convergence of the semidiscrete approximation to maxwell s equations is established rigorously and bounds on the growth of the global divergence error are provided concerns related to efficient implementations are discussed in detail this sets the stage for the presentation of examples verifying the theoretical results and illustrating the versatility flexibility and robustness when solving two and three dimensional benchmark problems in computational electromagnetics pure scattering as well as penetration is discussed and high parallel performance of the scheme is demonstrated

a boundary difference method for electromagnetic scattering problems with perfect conductors and corners boundary integral equations bie are widely used in applied electromagnetics with the boundary element method bem typically employed for numerical solution the paper extends the recently proposed boundary difference method bdm an alternative to bem to electromagnetic scattering problems with perfect conductors and with corners bdm shares several key features and advantages of bem but avoids the singular kernels inherent in bie convergence rates of the method established via numerical experiments are in agreement with the theoretical predictions

spectral methods based on prolate spheroidal wave functions for hyperbolic pdes we examine the merits of using prolate spheroidal wave functions pswfs as basis functions when solving hyperbolic pdes using pseudospectral methods the relevant approximation theory is reviewed and some new approximation results in sobolev spaces are established an optimal choice of the band limit parameter for pswfs is derived for single mode functions our conclusion is that one might gain from using the pswfs over the traditional chebyshev or legendre methods in terms of accuracy and efficiency for marginally resolved broadband solutions

accuracy of staircase approximations in finite difference methods for wave propagation while a number of increasingly sophisticated numerical methods have been developed for time dependent problems in electromagnetics the yee scheme is still widely used in the applied fields mainly due to its simplicity and computational efficiency a fundamental drawback of the method is the use of staircase boundary approximations giving inconsistent results usually experience of numerical experiments provides guidance of the impact of these errors on the final simulation result in this paper we derive exact discrete solutions to the yee scheme close to the staircase approximated boundary enabling a detailed theoretical study of the amplitude phase and frequency errors created furthermore we show how evanescent waves of amplitude o 1 o 1 occur along the boundary these characterize the inconsistencies observed in electromagnetic simulations and the locality of the waves explain why in practice the yee scheme works as well as it does the analysis is supported by detailed proofs and numerical examples

finite difference time domain modeling of curved surfaces em scattering the finite difference time domain fdtd method is generalized to include the accurate modeling of curved surfaces this generalization the contour path cp method accurately models the illumination of bodies with curved surfaces yet retains the ability to model corners and edges cp modeling of two dimensional electromagnetic wave scattering from objects of various shapes and compositions is presented

a staggered fourth order accurate explicit finite difference scheme for the time domain maxwell s equations abstract we consider a model explicit fourth order staggered finite difference method for the hyperbolic maxwell s equations appropriate fourth order accurate extrapolation and one sided difference operators are derived in order to complete the scheme near metal boundaries and dielectric interfaces an eigenvalue analysis of the overall scheme provides a necessary but not sufficient stability condition and indicates long time stability numerical results verify both the stability analysis and the scheme s fourth order convergence rate over complex domains that include dielectric interfaces and perfectly conducting surfaces for a fixed error level we find the fourth order scheme is computationally cheaper in comparison to the yee scheme by more than an order of magnitude some open problems encountered in the application of such high order schemes are also discussed

fdtd algorithm in curvilinear coordinates em scattering the finite difference time domain fdtd algorithm for the solution of electromagnetic scattering problems is formulated in generalized coordinates in two dimensions and implemented in a code with the lowest order bayliss turkel radiation boundary condition expressed in cylindrical coordinates it is shown that for a perfect conductor such a formulation leads to a stable well posed algorithm and that in regions where the curvature of the coordinate lines is not great the dispersion and anisotropy effects are negligible such effects become more pronounced in regions of high curvature leading to unphysical phase shifts the magnitude of such shifts and the amount of wavefront distortion is studied via numerical experiments using a cylindrical mesh near field results are given for two canonical shapes for each polarization the circular cylinder and cylinders of square and rectangular cross sections these results are compared with those obtained by exact eigenfunction expansion techniques with method of moments mm solutions and with solutions obtained from an alternate fdtd approach in each case agreement is excellent the propagation of a plane wave through a polar space in the absence of a scatterer is also examined and it is shown that the fdtd algorithm is capable of tracking the incident wave closely

correspondence analysis of multivariate categorical data by weighted least squares summary a generalization of correspondence analysis to multivariate categorical data is proposed where all two way contingency tables of a set of categorical variables are simultaneously fitted by weighted least squares an alternating least squares algorithm is developed to perform the fitting this technique has a number of advantages over the usual generalization known as multiple correspondence analysis it is also an analogue of least squares factor analysis for categorical data

a new estimator of the uniqueness in factor analysis a closed form estimator of the uniqueness unique variance in factor analysis is proposed it has analytically desirable properties consistency asymptotic normality and scale invariance the estimation procedure is given through the application to the two sets of emmett s data and holzinger and swineford s data the new estimator is shown to lead to values rather close to the maximum likelihood estimator

consistent boundary conditions for the yee scheme a new set of consistent boundary conditions for yee scheme approximations of wave equations in two space dimensions are developed and analyzed we show how the classical staircase boundary conditions for hard reflections or in the electromagnetic case conducting surfaces in certain cases give o 1 errors the proposed conditions keep the structure of the yee scheme and are thus well suited for high performance computing the higher accuracy is achieved by modifying the coefficients in the difference stencils near the boundary this generalizes our earlier results with gustafsson and wahlund in one space dimension we study stability and convergence and we present numerical examples

noniterative estimation and the choice of the number of factors in exploratory factor analysis based on the usual factor analysis model this paper investigates the relationship between improper solutions and the number of factors and discusses the properties of the noniterative estimation method of ihara and kano in exploratory factor analysis the consistency of the ihara and kano estimator is shown to hold even for an overestimated number of factors which provides a theoretical basis for the rare occurrence of improper solutions and for a new method of choosing the number of factors the comparative study of their estimator and that based on maximum likelihood is carried out by a monte carlo experiment

the finite difference time domain fdtd and the finite volume time domain fvtd methods in solving maxwell s equations the finite difference time domain fdtd and its current generalizations have been demonstrated to be useful and powerful tools for the calculation of the radar cross section rcs of complicated objects the radiation of antennas in the presence of other structures and other applications the mathematical techniques for conformal fdtd have matured the primary impediments to its implementation are the complex geometries and material properties associated with the problem even under these circumstances fdtd is more flexible to implement because it is based on first principles instead of a clever mathematical trick this paper gives an account of some new results on conformal fdtd obtained by the authors and their associates at lockheed martin space company since 1988 the emphasis is on nonsmooth boundary condition simulation

error bounded schemes for time dependent hyperbolic problems in this paper we address the error growth in time for hyperbolic problems in first order form in bounded domains the energy method is used to study when an error growth or a fixed error bound is obtained it is shown that the choice of boundary procedure is a crucial point numerical experiments corroborate the theoretical findings

on flexural waves in cylindrically anisotropic elastic rods a rod theory is developed for long waves in an elastic circular cylinder with cylindrical anisotropy detailed results for flexural waves and cylindrical orthotropy are given the theory uses the method of frobenius in the radial direction so that the equation of motion is satisfied exactly then the equations arising from the lateral boundary condition are truncated properly leading to a rod theory

a new compact difference scheme for second derivative in non uniform grid expressed in self adjoint form a single parameter family of self adjoint compact difference sacd schemes is developed for discretizing the laplacian operator in self adjoint form developed implicit scheme is formally second order accurate with respect to truncation error with a free parameter a which helps control the numerical properties in the spectral plane the sacd scheme is analyzed in the spectral plane for its resolution properties for both periodic and non periodic problems using the matrix spectral analysis t k sengupta g ganeriwal s de analysis of central and upwind schemes j comput phys 192 2 2003 677 694 the major objective here is to identify the advantages of the new scheme over the traditional explicit second order cd2 scheme in discretizing the laplacian operator in self adjoint form this appears in navier stokes equation and in other transport equations and boundary value problems bvp expressed in orthogonal co ordinate systems either in physical or in transformed plane we also compare the developed method with the higher order compact schemes for non uniform grids to demonstrate the accuracy of sacd scheme we have tested it for i bi directional wave propagation problem given by the second order wave equation and ii an elliptic bvp as in the stommel ocean model for the stream function these examples help infer the properties of sacd scheme when solving different types of partial differential equations most importantly the effects of grid stretching and choice of value of the free parameter a are investigated here we also compare the present implicit compact method with explicit compact method known as the higher order compact hoc method also the practical applications of the sacd scheme are explored by solving the navier stokes equation for the cases of a a flow inside a lid driven cavity and b the receptivity and instability of an external adverse pressure gradient flow over a flat plate in the former unsteadiness of the flow is captured and in the latter the receptivity of the flow is studied in causing flow instability by triggering tollmien schlichting waves the new scheme shows a marked improvement over the explicit scheme for low reynolds number steady flow in lid driven cavity whereas for the flow in the same geometry at higher reynolds numbers efficacy of the scheme is established by showing the formation of a triangular vortex and secondary vortical structures presented scheme is perfectly capable of expressing the diffusion operator accurately as shown via the capturing of instability waves inside the shear layer

regular article comparison of kinetic theory and discrete element schemes for modelling granular couette flows discrete element based simulations of granular flow in a 2d velocity space are compared with a particle code that solves kinetic granular flow equations in two and three dimensions the binary collisions of the latter are governed by the same forces as those governing the discrete elements both methods are applied to a granular shear flow of equally sized discs and spheres the two dimensional implementation of the kinetic approach shows excellent agreement with the results of the discrete element simulations during change to a three dimensional velocity space the qualitative features of the flow are maintained however some flow properties change quantitatively

conformal fdtd methods to avoid time step reduction with and without cell enlargement during the last decades there have been considerable efforts to develop accurate and yet simple conformal methods for modelling curved boundaries within the finite difference time domain fdtd algorithm in an earlier publication we proposed the uniformly stable conformal usc approach as a general three dimensional extension of fdtd without the need to reduce the maximum stable time step the main idea of usc is the usage of virtually enlarged cells near to the boundary leading to an increased implementation effort in this paper we review the usc method and introduce a new simple and accurate conformal scheme which does not use such enlarged cells this simplified conformal sc scheme has the same number of operations and algorithmic logic as the standard staircase method and thus is easily realizable in existing fdtd codes like usc it leads to accurate results without time step reduction showing a nearly second order convergence in practice the method is verified and compared to other approaches by means of several numerical 2d and 3d examples

a high order accurate embedded boundary method for first order hyperbolic equations abstract a stable and high order accurate embedded boundary method for first order hyperbolic equations is derived where the grid boundaries and the physical boundaries do not coincide high order interpolation is used the boundary stencils are based on a summation by parts framework and the boundary conditions are imposed by the sat penalty method which guarantees linear stability for one dimensional problems second fourth and sixth order finite difference schemes are considered the resulting schemes are fully explicit accuracy and numerical stability of the proposed schemes are demonstrated for both linear and nonlinear hyperbolic systems in one and two spatial dimensions

pseudospectral vs finite difference methods for initial value problems with discontinuous coefficient an initial value problem with piecewise constant coefficients is considered the accuracies for both finite difference methods and the pseudospectral method are analyzed and a modification of the initial value problem is suggested the modified problem is shown to have the same temporal period as the original problem does and a second order accuracy is obtained for the pseudospectral method at integral multiples of the temporal period

convergent cartesian grid methods for maxwell s equations in complex geometries a convergent second order cartesian grid finite difference scheme for the solution of maxwell s equations is presented the scheme employs a staggered grid in space and represents the physical location of the material and metallic boundaries correctly hence eliminating problems caused by staircasing and contrary to the popular yee scheme enforces the correct jump conditions on the field components across material interfaces a detailed analysis of the accuracy of the new embedding scheme is presented confirming its second order global accuracy furthermore the scheme is proven to be a bounded error scheme and thus convergent conditions for fully discrete stability is furthermore established this enables the derivation of bounds for fully discrete stability with cfl restrictions being almost identical to those of the much simpler yee scheme the analysis exposes that the effects of staircasing as well as a lack of properly enforced jump conditions on the field components have significant consequences for the global accuracy it is among other things shown that for cases in which a field component is discontinuous along a grid line as happens at general two and three dimensional material interfaces the yee scheme may exhibit local divergence and loss of global convergence to validate the analysis several one and two dimensional test cases are presented showing an improvement of typically 1 to 2 orders of accuracy at little or no additional computational cost over the yee scheme which in most cases exhibits first order accuracy c 2001 academic press

an efficient algorithm for joint correspondence analysis joint correspondence analysis is a technique for constructing reduced dimensional representations of pairwise relationships among categorical variables the technique was proposed by greenacre as an alternative to multiple correspondence analysis joint correspondence analysis differs from multiple correspondence analysis in that it focuses solely on between variable relationships greenacre described one alternating least squares algorithm for conducting joint correspondence analysis another alternating least squares algorithm is described in this article the algorithm is guaranteed to converge and does so in fewer iterations than does the algorithm proposed by greenacre a modification of the algorithm for handling heywood cases is described the algorithm is illustrated on two data sets

a second order accurate embedded boundary method for the wave equation with dirichlet data the accuracy of cartesian embedded boundary methods for the second order wave equation in general two dimensional domains subject to dirichlet boundary conditions is analyzed based on the analysis we develop a numerical method where both the solution and its gradient are second order accurate we avoid the small cell stiffness problem without sacrificing the second order accuracy by adding a small artificial term to the dirichlet boundary condition long time stability of the method is obtained by adding a small fourth order dissipative term several numerical examples are provided to demonstrate the accuracy and stability of the method the method is also used to solve the two dimensional tm z problem for maxwell s equations posed as a second order wave equation for the electric field coupled to ordinary differential equations for the magnetic field

regular article spectral collocation time domain modeling of diffractive optical elements a spectral collocation multi domain scheme is developed for the accurate and efficient time domain solution of maxwell s equations within multi layered diffractive optical elements special attention is being paid to the modeling of out of plane waveguide couplers emphasis is given to the proper construction of high order schemes with the ability to handle very general problems of considerable geometric and material complexity central questions regarding efficient absorbing boundary conditions and time stepping issues are also addressed the efficacy of the overall scheme for the time domain modeling of electrically large and computationally challenging problems is illustrated by solving a number of plane as well as non plane waveguide problems

a fast higher order solver for scattering by penetrable bodies in three dimensions in this paper we introduce a new fast higher order solver for scattering by inhomogeneous media in three dimensions as in previously existing methods the low complexity of our integral equation method o nlogn operations for an n point discretization is obtained through extensive use of the fast fourier transform fft for the evaluation of convolutions however the present approach obtains significantly higher order accuracy than these previous approaches yielding at worst third order far field accuracy or substantially better for smooth scatterers even for discontinuous and complex refractive index distributions possibly containing severe geometric singularities such as corners and cusps the increased order of convergence of our method results from i a partition of unity decomposition of the green s function into a smooth part with unbounded support and a singular part with compact support and ii replacement of the possibly discontinuous scatterer by an appropriate fourier smoothed scatterer the resulting convolutions can then be computed with higher order accuracy by means of o nlogn ffts we present a parallel implementation of our approach and demonstrate the method s efficiency and accuracy through a variety of computational examples for a very large scatterer considered earlier in the literature with a volume of 3648 l 3 where l is the wavelength using the same number of points per wavelength and in computing times comparable to those required by the previous approach the present algorithm produces far field values whose errors are two orders of magnitude smaller than those reported previously

high order finite difference methods for wave propagation in discontinuous media high order finite difference approximations are derived for the second order wave equation with discontinuous coefficients on rectangular geometries the discontinuity is treated by splitting the domain at the discontinuities in a multi block fashion each sub domain is discretized with compact second derivative summation by parts operators and the blocks are patched together to a global domain using the projection method this guarantees a conservative strictly stable and high order accurate scheme the analysis is verified by numerical simulations in one and two spatial dimensions

high order unconditionally stable fc ad solvers for general smooth domains i basic elements we introduce a new methodology for the numerical solution of partial differential equations in general spatial domains our algorithms are based on the use of the well known alternating direction implicit adi approach in conjunction with a certain fourier continuation fc method for the resolution of the gibbs phenomenon unlike previous alternating direction methods of order higher than one which can only deliver unconditional stability for rectangular domains the present high order algorithms possess the desirable property of unconditional stability for general domains the computational time required by our algorithms to advance a solution by one time step in turn grows in an essentially linear manner with the number of spatial discretization points used in this paper we demonstrate the fc ad methodology through a variety of examples concerning the heat and laplace equations in two and three dimensional domains with smooth boundaries applications of the fc ad methodology to hyperbolic pdes together with a theoretical discussion of the method will be put forth in a subsequent contribution the numerical examples presented in this text demonstrate the unconditional stability and high order convergence of the proposed algorithms as well the very significant improvements they can provide in one of our examples we demonstrate a one thousand improvement factor over the computing times required by some of the most efficient alternative general domain solvers

a staggered upwind embedded boundary sueb method to eliminate the fdtd staircasing error in spite of its flexibility and second order accuracy in a homogeneous medium yee s finite difference time domain fdtd method suffers from serious degradation when treating material interfaces greatly reducing its accuracy in the presence of inhomogeneous media and perfect conductors indeed such so called staircasing approximation may lead to local zeroth order and global first order errors in this work an embedded fdtd scheme the staggered upwind embedded boundary sueb method is developed for the solution of oneand two dimensional maxwell s equations this simple embedded technique uses upwind conditions in the fdtd method to correctly represent the location and physical conditions of material and metallic boundaries hence eliminating problems caused by the staircasing approximation accuracy analysis has been made to show that the sueb method maintains a second order accuracy globally since the entire problem has been embedded into the simple staggered grid similar to that employed by the yee s scheme extra effort is only needed when treating the grid points close to the interfaces therefore little additional computational cost is needed over yee s scheme the sueb method has been validated by analytical solutions for plane wave normally incident to a planar boundary and for the tm wave propagation in the presence of a dielectric cylinder and a perfectly electrically conducting cylinder

a noniterative method of joint correspondence analysis correspondence analysis leads to a graphical representation of the associations between categories of the row and column variables of a contingency table greenacre s 1988 formulation of joint correspondence analysis is a multivariate extension which finds the optimal joint display of contingency tables between all pairs of variables in a set greenacre presented a discrepancy function and an alternating least squares algorithm for its minimization boik 1996 presented an alternative algorithm also of the alternating least squares type for minimizing the same discrepancy function in this paper a noniterative procedure not based on the minimization of any discrepancy function is described

higher order fourier approximation in scattering by two dimensional inhomogeneous media this paper provides a theoretical analysis of a higher order fft based integral equation method introduced recently ieee trans antennas and propagation 48 2000 pp 1862 1864 for the evaluation of transverse electric polarized electromagnetic scattering from a bounded penetrable inhomogeneity in two dimensional space roughly speaking this method is based on fourier smoothing of the integral operator and the refractive index n x here we prove that the solution of the resulting integral equation approximates the solution of the exact integral equation with higher order accuracy even when n x is a discontinuous function as suggested by the numerical experiments contained in the paper mentioned above in detail we relate the convergence rates of the computed interior and exterior fields to the regularity of the scatterer and we demonstrate with a few numerical examples that the predicted convergence rates are achieved in practice

difference approximations of the neumann problem for the second order wave equation stability theory and numerical experiments are presented for a finite difference method that directly discretizes the neumann problem for the second order wave equation complex geometries are discretized using a cartesian embedded boundary technique both second and third order accurate approximations of the boundary conditions are presented away from the boundary the basic second order method can be corrected to achieve fourth order spatial accuracy to integrate in time we present both a second order and a fourth order accurate explicit method the stability of the method is ensured by adding a small fourth order dissipation operator locally modified near the boundary to allow its application at all grid points inside the computational domain numerical experiments demonstrate the accuracy and long time stability of the proposed method

calculation of the sar induced in head tissues using a high order dgtd method and triangulated geometrical models the great majority of numerical calculations of the specific absorption rate sar induced in human tissues exposed to microwaves are performed using the finite difference time domain fdtd method and voxel based geometrical models the straightforward implementation of the method and its computational efficiency are among the main reasons for fdtd being currently the leading method for numerical assessment of human exposure to electromagnetic waves however the rather difficult departure from the commonly used cartesian grid and cell size limitations regarding the discretization of very detailed structures of human tissues are often recognized as the main weaknesses of the method in this application context in particular interfaces between tissues where sharp gradients of the electromagnetic field may occur are hardly modeled rigorously in these studies we present here an alternative numerical dosimetry methodology which is based on a high order discontinuous galerkin time domain dgtd method and adapted geometrical models constructed from unstructured triangulations of tissue interfaces and discuss its application to the calculation of the sar induced in head tissues

finite difference time domain dispersion reduction schemes the finite difference time domain fdtd although recognized as a flexible robust and simple to implement method for solving complex electromagnetic problems is subject to numerical dispersion errors in addition to the traditional ways for reducing dispersion i e increasing sampling rate and using higher order degrees of accuracy a number of schemes have been proposed recently in this work an unified methodology for deriving new difference schemes is presented it is based on certain modifications of the characteristic equation that accompanies any given discretized version of the wave equation the method is duly compared with existing schemes and verified numerically