root mean square measure of nonlinear effects to the transient response of thin wires a root mean square rms measure of effect of nonlinear loading on the transient response of thin wires is proposed the transient behavior of nonlinearly loaded wires is analyzed directly in the time domain the problem is formulated via the space time hallen integral equation the equation is solved by the space time galerkin bubnov boundary element procedure numerical results for the transient response of a thin wire computed by a time domain code based on this method are compared with results obtained from a frequency domain code some illustrative numerical results for the spatial distribution of the rms values of time varying currents are also presented

fdtd calculation of radiation patterns impedance and gain for a monopole antenna on a conducting box the ability of the finite difference time domain fdtd method to calculate radiation patterns input impedance and gain for a monopole antenna on a conducting box is demonstrated results are given for the bare box and with the box coated with a dielectric layer radiation patterns are compared with measurements and with the method of moments for the bare box radiation patterns for the dielectric covered box and all impedance and gain results are compared with measurements only good agreement is obtained in all cases the fdtd approach includes a dielectric covering quite easily while this would be quite difficult for a method of moments approach the fdtd method requires similar computer time as the method of moments for a single frequency result but produces wide bandwidth impedance and gain results with much less computer time

a solution to certain polynomial equations with applications to nonlinear fitting we present a combinatorial method for solving a certain system of polynomial equations of vandermonde type in 2n variables by reducing it to the problem of solving two special linear systems of size n and rooting a single univariate polynomial of degree n over c all solutions can be found with fixed precision using up to polylogarithmic factors o n 2 bitwise operations in the worst case furthermore if the data is well conditioned then this can be reduced to o n bit operations up to polylogarithmic factors as an application we show how this can be used to fit data to a complex exponential sum with n terms in the same nearly optimal time

coupled simulation of transient heat flow and electric currents in thin wires application to bond wires in microelectronic chip packaging abstract this work addresses the simulation of heat flow and electric currents in thin wires an important application is the use of bond wires in microelectronic chip packaging the heat distribution is modeled by an electrothermal coupled problem which poses numerical challenges due to the presence of different geometric scales the necessity of very fine grids is relaxed by solving and embedding a 1d sub problem along the wire into the surrounding 3d geometry the arising singularities are described using de rham currents it is shown that the problem is related to fluid flow in porous 3d media with 1d fractures c d angelo siam journal of numerical analysis 50 1 pp 194 215 2012 a careful formulation of the 1d 3d coupling condition is essential to obtain a stable scheme that yields a physical solution elliptic model problems are used to investigate the numerical errors and the corresponding convergence rates additionally the transient electrothermal simulation of a simplified microelectronic chip package as used in industrial applications is presented

subcell modeling of frequency dependent thin layers in the fdtd method a subcell modeling technique for frequency dependent thin layers in finite difference time domain method is introduced the proposed method is based on the application of the integral form of the maxwell ampere equation and the solution of a set of auxiliary equations to advance the field components it has the ability to handle one or several frequency dependent thin layers embedded in a frequency dependent medium without solving high order differential equations to validate our proposed method we compare the obtained results with analytical solutions and with numerical references in both time domain and frequency domain

fdtd local grid with material traverse often a finite difference time domain fdtd calculation requires a relatively higher mesh resolution in only small subvolumes of the total mesh space by locally applying finer grids local grids to these volumes the necessary resolution can be obtained computation time and memory requirements may be far less than for an fdtd space with the smaller mesh resolution throughout in many situations it is important that these local grids function when materials traverse the main grid local grid mg lg boundary surfaces since the volumes that require local grids may not be isolated in a homogeneous medium a local grid method which allows dielectric and or conducting materials to traverse the boundaries is developed three different fdtd problems that utilize the local grid method are used as validation tests results are compared with uniform mesh fdtd solutions

a novel 3 d cpfdtd scheme for modeling grid nonconformally aligned transmitter structures in this paper a novel three dimensional 3 d subcell algorithm for modeling metallic objects which are nonconformally oriented within the finite difference time domain fdtd grid is proposed the generally applicable algorithm is based on the contour path cp technique and enables in combination with an enhanced nonconformally aligned source model a more accurate spatial representation of antenna structures than the common staircase approach to evaluate the performance of the new algorithm the simulation results are compared with the classical staircase approach for dipole antennas as well as for a generic phone significant improvements were achieved for all antenna parameters from the near and far field i e feedpoint impedance radiation pattern and field distributions

fdtd model of electrically thick frequency dispersive coatings on metals and semiconductors based on surface impedance boundary conditions a new finite difference time domain fdtd model for conductors coated with electrically thick frequency dispersive coatings is developed the model is based on first order impedance boundary conditions as the most important original feature of the model the frequency dependence of the material parameters of the coating is very general dispersive coatings of lorentz debye or drude type with multiple pole pairs and a fixed electrical conductivity can be modeled with the proposed technique another new property of the model is the use of rational approximation in a way that enables accurate approximation of the impedance function in a wide range corresponding to several thickness resonances of the coating the conductor losses in the metal backing that are neglected in many earlier models are accounted for in the proposed model the model is formulated for planar interfaces in the general three dimensional situation for the yee algorithm and verified against analytical reference results with numerical examples in one dimensional and two dimensional problems

a parallel finite volume runge kutta algorithm for electromagnetic scattering a 3d explicit finite volume algorithm has been developed to simulate scattering from complex geometries on parallel computers using structured body conformal curvilinear grids most simulations for practical 3d geometries require a large number of grid points for adequate spatial resolution making them suitable to parallel computation the simulations have been carried out using a multi block zonal approach in the message passing paradigm on the sp 2 each zone is placed on a separate processor and inter processor communication is carried out using the message passing library interface mpl mpi integration of maxwell s equations is performed using the four stage runge kutta time integration method on a dual grid this method of integrating on a staggered grid gives enhanced dissipative and dispersive characteristics a scattered field formulation has been used and the liao boundary condition is used at the outer nonreflecting boundary the far zone transformation has also been implemented efficiently using specialized mpl functions to evaluate the far zone scattering results results show extremely good comparisons for scattering from the sphere and the ogive with the exact solution and standard fdtd type algorithms comparisons for nonaxisymmetric targets like the nasa almond with experimental data has also been found to be extremely good

a finite difference time domain near zone to far zone transformation electromagnetic scattering an efficient time domain near zone to far zone transformation for fdtd finite difference time domain computations is presented the approach is to keep a running accumulation of the far zone time domain vector potentials due to the tangential electric and magnetic fields on a closed surface surrounding the scatterer at each time step at the end of the computation these vector potentials are converted to time domain far zone fields many far zone bistatic directions can be included efficiently during one fdtd computational run frequency domain results can be obtained via fast fourier transform wideband results for scattering from a perfectly conducting plate were obtained from a single fdtd computation transformed to the frequency domain and compared with moment method results this approach is significantly more efficient than computing many fdtd results using sinusoidally varying excitation if a wide frequency band is of interest coupled with recent advances in computing fdtd results for frequency dependent materials wideband results for far zone scattering from targets including frequency dependent materials can be obtained efficiently

an equivalent feed model for the fdtd analysis of antennas driven through a ground plane by coaxial lines for the finite difference time domain fdtd analysis of antennas excited by coaxial lines an equivalent model of the antenna feed is presented here under the quasi static approximation the coaxial aperture is simply represented as the equivalent magnetic frill current and the equivalent load circuit including the effects of the coaxial line it leads us to a simple modification of the standard fdtd update equation at the aperture without any additional cell modeling of the line the validity of the proposed model is confirmed by comparing of the fdtd results and the measured data

near and far field calculations in fdtd simulations using kirchhoff surface integral representation kirchhoff s surface integral representation ksir is used to calculate the near and far fields from the finite difference time domain fdtd simulation the ksir is very simple to implement and its distinct advantage is that the calculation of any of the six field components depends on the value of the same field component over a closed surface this avoids interpolation errors when using the popular yee scheme for fdtd in addition to its efficiency and simplicity of implementation the ksir leads to highly accurate near fields that reduce absorbing boundary condition abc errors

a hybrid numerical method for three dimensional spatially developing free shear flows abstract a new algorithm has been developed and implemented for solving the three dimensional incompressible navier stokes equations on a domain that is infinite in the vertical y direction mapped spectral method is used in y a classical fourier method is used in z and high order compact finite differencing is used in x a projection method is discussed that ensures exact conservation of mass and satisfaction of the boundary conditions at infinity the new aspects of these schemes are described test cases to validate the code are presented and results for two and three dimensional mixing layers are given

a fourier hermite pseudospectral method for penetrative convection a fourier hermite pseudospectral method is developed to study numerically the three dimensional penetrative convection problem under the boussinesq approximation an s shaped temperature profile in the absence of motion is prescribed in the vertical direction all variables are expanded in terms of fourier hermite basis functions the hermite functions are scaled to adjust the length of the computational domain in the vertical a semi implicit scheme is used for time marching with the third order adam bashforth and crank nicholson scheme for the nonlinear and linear terms respectively an implementation of the numerical method on a parallel computer is also described numerical simulation results of resolution 643are presented for low to moderate rayleigh numbers with a prandtl number of unity the highly stable outer regions are seen to act as effective lids and all penetrative flow are contained within the computational box variances heat fluxes and their budgets are reported for several rayleigh numbers to demonstrate the efficacy of the numerical method

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

stagnation point von karman coefficient on the basis of various direct numerical simulations dns of turbulent channel flows the following picture is proposed i at a distance y from either wall the taylor microscale lambda is proportional to the average distance l s between stagnation points of the fluctuating velocity field i e lambda y b 1 l s y with b 1 constant for delta nu y or approximately equal to delta where the wall unit delta nu is defined as the ratio of kinematic viscosity nu to skin friction velocity u tau and delta is the channel s half width ii the number density n s of stagnation points varies with height according to n s c s delta nu 3 y 1 where y identical with y delta nu and c s is constant in the range delta nu y or approximately equal to delta iii in that same range the kinetic energy dissipation rate per unit mass equals 2 3 e u tau 3 kappa s y where e is the total kinetic energy per unit mass normalized by u tau 2 and kappa s b 1 2 c s is the stagnation point von karman coefficient iv in the limit of exceedingly large reynolds numbers re tau identical with delta delta nu large enough for the reynolds stress uv to equal u tau 2 in the range delta nu y delta and assuming that production of turbulent kinetic energy balances dissipation locally in that range and limit the mean velocity u normalized by u tau obeys d dy u approximately equal to 2 3 e kappa s y in that same range v it follows that the von karman coefficient kappa is a meaningful and well defined coefficient and the log law holds in turbulent channel pipe flows only if e is independent of y and re tau in that range in which case kappa approximately kappa s vi in support of d dy u approximately equal to 2 3 e kappa s y dns data of turbulent channel flows which include the highest currently available values of re tau are best fitted by e approximately equal to 2 3 b 4 y 2 15 and d dy u approximately equal to b 4 kappa s y 1 2 15 with b4 independent of y in delta nu y delta if the significant departure from uv approximately equal to u tau 2 at these re tau values is taken into account

the treatment of thin wires in the fdtd method using a weighted residuals approach in this contribution the problem of accurately representing thin wires within the finite difference time domain fdtd mesh is addressed by means of a method based on the weighted residual wr interpretation of the fdtd algorithm results for wire dipoles and wire transmission lines obtained using the proposed method are presented and compared to those obtained using existing techniques it is shown that the proposed method yields results which are more accurate and are less dependent on the choice of cell size than other approaches and in addition lends itself well to being extended for more complicated structures details of the calculation of the update equations are given

the eigenvalues of hermite and rational spectral differentiation matrices we derive expressions for the eigenvalues of spectral differentiation matrices for unbounded domains in particular we consider galerkin and collocation methods based on hermite functions as well as rational functions a fourier series combined with a cotangent mapping we show that i first derivative matrices have purely imaginary eigenvalues and second derivative matrices have real and negative eigenvalues ii for the hermite method the eigenvalues are determined by the roots of the hermite polynomials and for the rational method they are determined by the laguerre polynomials and iii the hermite method has attractive stability properties in the sense of small condition numbers and spectral radii

a note on the convergence of godunov type methods for shock reflection problems abstract this paper identifies a new pathology that can be found for numerical simulations of nonlinear conservation law systems many of the difficulties already identified in the literature rarefaction shocks carbuncle phenomena slowly moving shocks wall heating etc can be traced to insufficient numerical dissipation and the current case is no different however the details of the case we study here are somewhat unique in that the solution which is found by the numerics can fail to have a derivative anywhere in the post shock region

spectral methods for the navier stokes equations with one infinite and two periodic directions abstract two numerical methods were designed to solve the time dependent three dimensional incompressible navier stokes equations in boundary layers method a semi infinite domain and mixing layers or wakes method b fully infinite domain their originality lies in the use of rapidly decaying spectral basis functions to approximate the vertical dependence of the solutions combined with one method a or two method b slowly decaying extra functions for each wave vector that exactly represent the irrotational component of the solution at large distances both methods eliminate the pressure term as part of the formulation thus avoiding fractional step time integration they yield rapid convergence and are free of spurious modes in the orr sommerfeld spectra they are also efficient although the operation count is of order n 2 n is the number of modes in the infinite direction these methods have been used for extensive direct numerical simulations of transition and turbulence a new time integration scheme with low storage requirements and good stability properties is also described

energy based comparison between the fourier galerkin method and the finite element method abstract the fourier galerkin method in short ffth has gained popularity in numerical homogenisation because it can treat problems with a huge number of degrees of freedom because the method incorporates the fast fourier transform fft in the linear solver it is believed to provide an improvement in computational and memory requirements compared to the conventional finite element method fem here we systematically compare these two methods using the energetic norm of local fields which has the clear physical interpretation as being the error in the homogenised properties this enables the comparison of memory and computational requirements at the same level of approximation accuracy we show that the methods effectiveness relies on the smoothness regularity of the solution and thus on the material coefficients thanks to its approximation properties fem outperforms ffth for problems with jumps in material coefficients while ambivalent results are observed for the case that the material coefficients vary continuously in space ffth profits from a good conditioning of the linear system independent of the number of degrees of freedom but generally needs more degrees of freedom to reach the same approximation accuracy more studies are needed for other fft based schemes non linear problems and dual problems which require special treatment in fem but not in ffth

finite difference time domain calculation of transients in antennas with nonlinear loads transient currents for an antenna with a nonlinear load are calculated using finite difference time domain fdtd methods the fdtd electric field across the nonlinear load which determines the voltage across the load is calculated by solving a nonlinear equation at each time step this allows the time step to be at the courant limit and is more efficient than reducing the time step size in all the fdtd cells to maintain stability in just the cell containing the nonlinear load the stability of this approach relative to a simpler approach of approximating the diode as a variable resistor is demonstrated as a validation of the method the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed and compared with calculated results obtained by another method the approach given here extends the applicability of the fdtd method to problems involving radiation and scattering from antennas including nonlinear loads

discrete orthogonal function expansions for non uniform grids using the fast fourier transform abstract discrete orthogonal function expansions are obtained for non uniformly spaced data by combined use of mapping functions and the fast fourier transform the result yields alias free differentiation and integration operators the method is applicable to periodic zero or zero derivative boundary conditions or combinations thereof truncation is required to avoid aliasing and or singularity but the truncation error is explicit quantitatively expressible and generally small this approach is demonstrated in an infinite physical domain with application to linear convection and diffusion the resulting errors are orders of magnitude smaller than those generated by standard finite difference methods difficulties arising from image fields are an important phenomena the method of differentiation as well as the boundary conditions imply artificial image fields a vortex pairing problem is presented which shows that image flows can totally alter the solution the new scheme avoids this undesirable effect by keeping image flows infinitely far away

time domain extrapolation to the far field based on fdtd calculations a scheme to extrapolate scattered fields calculated by the finite difference time domain fdtd method to the far zone is developed it could replace the usual extrapolation scheme for a single frequency in that it yields a spectrum with only one incident pulse the method comprises the following steps 1 using an incident pulse 2 performing an fdtd calculation and using the currently calculated data on s to extrapolate to the far field and 3 fourier transforming the far field time response to obtain the frequency domain response the approach seems to be more convenient in time domain calculations and more in agreement with the spirit of fdtd

asymptotic and numerical analysis for holland and simpson s thin wire formalism in the context of simulation of electromagnetic propagation the thin wire formalism of holland and simpson allows one to deal with scattering by perfectly conducting thin wires by coupling a standard fdtd method with a discrete 1d wave equation ruling the current inside the wires this method can be very accurate but it involves a fitting parameter that requires careful calibration we propose a consistency analysis and derive a formula for the calibration of this parameter in the case of a simplified 2d analogue of the method of holland and simpson our proof relies on the observation that this method is actually a hidden version of the singular function method well known in the context of elliptic equations in domains with a singular boundary

an improved thin wire representation for fdtd computations we have shown that finite difference time domain fdtd electromagnetic computations for a conductor system having a radius smaller than 0 15deltar or larger than 0 65 deltar deltar is the lateral side length of cells employed modeled using arbitrary radius wire representations proposed so far with a time increment determined from the upper limit of courant s stability condition result in numerical instability a primary factor causing this numerical instability is that the speed of waves propagating in the radial direction from the wire in the immediate vicinity of the wire exceeds the speed of light and therefore courant s condition is not satisfied there it is further shown that for these cases the arbitrary radius wire representation can be improved by modifying the material parameters for the axial field components closest to the wire as well as those for the radial electric and circulating magnetic field components the improved wire representation is effective in representing a wire whose radius ranges from 0 0001deltar to 0 9deltar

fdtd modeling of arrays and grids of lossy conductors based on impedance sheet conditions fast finite difference time domain fdtd modeling techniques for arrays of parallel wires and wire meshes are developed the analytical basis of the models lies in the use of impedance sheet conditions kontorovich conditions for dense wire arrays and grids connecting the tangential electric fields and the averaged currents in the plane of a wire array or grid the proposed methods allow us to avoid the direct discretization of the fields inside the wires greatly simplifying the modeling task the conductor losses in the wires are accounted for assuming a strong or weak skin effect the impedance sheet conditions are formulated in the time domain using the convolution integral which is evaluated recursively in fdtd numerical examples and comparisons with analytical results are provided to verify the proposed techniques

full wave analysis and wide band design of probe fed multilayered cylindrical rectangular microstrip antennas the input impedance and radiation pattern of the probe fed multilayered cylindrical rectangular microstrip antennas pmcmsa are analyzed by using a novel approach which combines the conformal finite difference time domain fdtd and gedney s unsplit version of the perfectly matched layer absorbing boundary condition method and the green s functions in cylindrically stratified media the near fields of such antennas and the current distributions on the patches are obtained by the conformal fdtd method numerically and then the modified spectral domain green s functions in arbitrary cylindrically stratified media are used to determine the radiation pattern the effect of the small radius of the probe on the performance of antennas is investigated through the thin wire algorithm in cylindrical coordinates a simple design scheme of the probe fed cylindrically stacked antennas is also proposed for increasing the impedance bandwidth

a generalization of the wiener rational basis functions on infinite intervals part i derivation and properties we formulate and derive a generalization of an orthogonal rational function basis for spectral expansions over the infinite or semi infinite interval the original functions first presented by wiener are a mapping and weighting of the fourier basis to the infinite interval by identifying the fourier series as a biorthogonal composition of jacobi polynomials functions we are able to define generalized fourier series which when appropriately mapped to the whole real line and weighted generalize wiener s basis functions it is known that the original wiener rational functions inherit sparse galerkin matrices for differentiation and can utilize the fast fourier transform fft for computation of the expansion coefficients we show that the generalized basis sets also have a sparse differentiation matrix and we discuss connection problems which are necessary theoretical developments for application of the fft

numerical method for incompressible vortical flows with two unbounded directions a new efficient and accurate method has been developed for computing unsteady incompressible viscous flows in a domain where two dimensions are unbounded the third dimension is periodic and the vorticity is rapidly decaying in the unbounded directions we use the term unbounded to mean doubly infinite no boundaries of any kind this is an extension of the methods described by others for flows with two periodic and one unbounded direction where the irrotational velocities outside the vortical domain are treated analytically the new method is shown to be both accurate and efficient the method presented here has finite but arbitrarily high order formal accuracy and incurs substantial additional cost for a given mesh however this increased cost is more than offset by the reduction in the number of mesh points required for a given accuracy the result is that for accurate computations the present method can be orders of magnitude more efficient than others currently in use this paper presents the method discusses implementation issues validates its accuracy and presents sample calculations

generation of fdtd subcell equations by means of reduced order modeling adapted finite difference time domain fdtd update equations exist for a number of objects that are smaller than the grid step such as wires and thin slots we provide a technique that automatically generates new fdtd update equations for small objects our presentation focusses on 2d fdtd we start from the fdtd equations in a fine grid where the time derivative is not discretised this yields a large state space model that is drastically reduced with a reduced order modeling technique the reduced state space model is then translated into new fdtd update equations that can be used in an fdtd simulation in the same way as the existing update equations for wires and thin slots this technique is applied to a number of numerical problems showing the accuracy and versatility of the proposed method

high order compact schemes for incompressible flows a simple and efficient method with quasi spectral accuracy in this paper a finite difference code for direct and large eddy simulation dns les of incompressible flows is presented this code is an intermediate tool between fully spectral navier stokes solvers limited to academic geometry through fourier or chebyshev representation and more versatile codes based on standard numerical schemes typically only second order accurate the interest of high order schemes is discussed in terms of implementation easiness computational efficiency and accuracy improvement considered through simplified benchmark problems and practical calculations the equivalence rules between operations in physical and spectral spaces are efficiently used to solve the poisson equation introduced by the projection method it is shown that for the pressure treatment an accurate fourier representation can be used for more flexible boundary conditions than periodicity or free slip using the concept of the modified wave number the incompressibility can be enforced up to the machine accuracy the benefit offered by this alternative method is found to be very satisfactory even when a formal second order error is introduced locally by boundary conditions that are neither periodic nor symmetric the usefulness of high order schemes combined with an immersed boundary method ibm is also demonstrated despite the second order accuracy introduced by this wall modelling strategy in particular the interest of a partially staggered mesh is exhibited in this specific context three dimensional calculations of transitional and turbulent channel flows emphasize the ability of present high order schemes to reduce the computational cost for a given accuracy the main conclusion of this paper is that finite difference schemes with quasi spectral accuracy can be very efficient for dns les of incompressible flows while allowing flexibility for the boundary conditions and easiness in the code development therefore this compromise fits particularly well for very high resolution simulations of turbulent flows with relatively complex geometries without requiring heavy numerical developments

a hybrid moment method finite difference time domain approach to electromagnetic coupling and aperture penetration into complex geometries an approach is presented for the direct modeling of electromagnetic penetration problems which involves a hybrid technique combining the frequency domain method of moments mm and the finite difference time domain fd td method the hybriding is based upon a novel use of a field equivalence theorem due to schelkunoff which permits a field penetration problem to be analyzed in steps by treating the relatively simple external region and the relatively complex internal region separately the method involves first determination of an equivalent short circuit current excitation in the aperture regions of the structure using mm for a given external illumination this equivalent current excitation over the aperture is next used to excite the complex loaded interior region and the penetrating fields and induced currents are computed by the fd td method a significant advantage of this frequency domain time domain hybriding is that no green s function need be calculated for the interior region this hybrid approach takes advantage of the ability of mm to solve exterior problems using patch models and also takes advantage of the ability of fd td to model in great detail localized space regions containing metal structures dielectrics permeable media anisotropic or nonlinear media as well as wires

an efficient surface impedance boundary condition for thin wires of finite conductivity to include dispersive loss into a sub cell thin wire model a new implementation of a surface impedance boundary condition sibc is proposed the surface impedance function is approximated in the frequency domain by a series of first order rational functions allowing straightforward transform into time domain the contribution of the wire radius is included in the surface impedance function extending the model to very thin or poorly conducting metal wires further the sibc includes the direct current dc resistance the approximation for the sibc is chosen such that the dependence on the wire radius and conductivity can be removed prior to the computation of the approximation coefficients consequently the wire radius and conductivity can be varied without re computing the coefficients the proposed model is compared with an existing sibc wire model based on the high frequency approximation and prony s method nec 2 generated reference data and analytical results the results indicate enhanced accuracy at a reduced computational cost as compared with an existing model

orthogonal rational functions on a semi infinite interval abstract by applying a mapping to the chebyshev polynomials we define a new spectral basis the rational chebyshev functions on the semi infinite interval denoted by tl n y continuing earlier work by the author and by grosch and orszag we show that these rational functions inherit most of the good numerical characteristics of the chebyshev polynomials orthogonality completeness exponential or infinite order convergence matrix sparsity for equations with polynomial coefficients and simplicity seven numerical examples illustrate their versatility the charney stability problem of meteorology for example is solved to show the feasibility of applying spectral methods to a semi infinite atmosphere for functions that are singular at both endpoints such as k 1 y one may combine rational chebyshev functions with a preliminary mapping to obtain a single exponentially convergent expansion on y 0 finally we successfully generalize the wkb method to obtain for the j 0 bessel function an amplitude phase approximation which is convergent rather than asymptotic and is accurate not merely for large y but for all y even the origin

new oblique thin wire formalism in the fdtd method with multiwire junctions a new oblique thin wire formalism based on holland s approach is proposed in the fdtd method the principal achievement of this new formalism is to enable us to model a junction correctly between several oblique wires to this end an important criterion is proposed the continuity of the current traces in the grid must be maintained at each node of the yee cell that contains a part of one or several wires this condition prevents undamped parasite oscillations on the wire current responses in addition our approach offers versatility in its usage first the extremities of the wire can be placed freely in a yee cell second it operates in lossy medium and finally the sensitivity of the wire is minimized when inclined or shifted with regards to this last point the in cell inductance of a wire segment is formulated to take account of the segment position and its obliquity in the yee cell

spectral methods using rational basis functions on an infinite interval by using the map y l cot t where l is a constant differential equations on the interval y can be transformed into t 0 and solved by an ordinary fourier series in this article earlier work by grosch and orszag j comput phys 25 273 1977 cain ferziger and reynolds j comput phys 56 272 1984 and boyd j comput phys 25 43 1982 57 454 1985 siam j numer anal 1987 is extended in several ways first the series of orthogonal rational functions converge on the exterior of bipolar coordinate surfaces in the complex y plane second galerkin s method will convert differential equations with polynomial or rational coefficients into banded matrix problems third with orthogonal rational functions it is possible to obtain exponential convergence even for u y that asymptote to a constant although this behavior would wreck alternatives such as hermite or sinc expansions fourth boundary conditions are usually natural rather than essential in the sense that the singularities of the differential equation will force the numerical solution to have the correct behavior at infinity even if no constraints are imposed on the basis functions fifth mapping a finite interval to an infinite one and then applying the rational chebyshev functions gives an exponentially convergent method for functions with bounded endpoint singularities these concepts are illustrated by five numerical examples

a fictitious domain method for conformal modeling of the perfect electric conductors in the fdtd method we present a fictitious domain method to avoid the staircase approximation in the study of perfect electric conductors pec in the finite difference time domain fdtd method the idea is to extend the electromagnetic field inside the pec and to introduce a new unknown the surface electric current density to ensure the vanishing of the tangential components of the electric field on the boundary of the pec this requires the use of two independent meshes a regular three dimensional 3 d cubic lattice for the electromagnetic field and a triangular surface patching for the surface electric current density the intersection of these two meshes gives a simple coupling law between the electric field and the surface electric current density an interesting property of this method is that it provides the surface electric current density at each time step furthermore this method looks like fdtd with a special model for the pec numerical results for several objects are presented

an rwg basis function based near to far field transformation for 2 d triangular grid finite difference time domain method a near to far field transformation ntft based on the rao wilton glisson rwg basis function is proposed for a 2 d triangular grid fdtd method the surface equivalence theorem is applied and the equivalent current density j sub z in the tm sub z case or m sub z in the te sub z case on the radiation contour is interpolated by using rwg basis functions the interpolation is valid for the ntft in either the time or frequency domain formulations for the interpolation scheme and the ntft are presented for the tm sub z case the scattering by an infinite dielectric circular cylinder due to an electric line source is simulated by using the triangular grid fdtd as well as the proposed ntft numerical results in both the time domain and frequency domain are demonstrated and verified by comparison with analytical solutions

a two dimensional time domain near zone to far zone transformation a 2d version of a time domain transformation useful for extrapolating 3d near zone finite difference time domain fdtd results to the far zone is outlined while the 3d transformation produced a physically observable far zone time domain field this is not convenient for the 2d case however a representative 2d far zone time domain result can be obtained directly this result can then be transformed to the frequency domain using a fast fourier transform corrected with a simple multiplicative factor and used for example to calculate the complex wideband scattering width of a target if an actual time domain far zone result is required it can be obtained by inverse fourier transform of the final frequency domain result

revisiting wall heating the results of computing a shock reflection are found to strongly depend on the chosen coordinate system lagrangian or eulerian this is seen by comparing the amount of wall heating associated with the solutions to noh s shock reflection problem computed in each reference frame here an explanation is offered that places a greater burden on the role of phase error or effective wave speed in producing this effect the reason for the greater difficulties in the lagrangian frame are the non uniformity of the mass coordinates in a converging geometry this produces a non steady state discrete shock profile

far field time domain calculation from aperture radiators using the fdtd method it is often desirable to determine the far field radiation pattern from an aperture in a metal plate the use of time domain methods like the finite difference time domain fdtd method is problematic because of the necessity of modeling the entire space of interest this is often circumvented by using the equivalence principle to determine the far field by equivalent currents generated in the near field however these transformations are often mathematically complex this paper presents an extremely simple formulation for calculating the time domain fields from some types of aperture radiators by using wavelet analysis the pertinent parameters can be compressed and stored to be used later to resynthesize the radiated fields

hybrid chebyshev function bases for sparse spectral methods in parity mixed pdes on an infinite domain abstract we present a numerical spectral method to solve systems of differential equations on an infinite interval y in presence of linear differential operators of the form q y y b where q y is a rational fraction and b a positive integer even when these operators are not parity preserving we demonstrate how a mixed expansion in interleaved chebyshev rational functions t b n y and s b n y preserves the sparsity of their discretization this paves the way for fast o n ln n and spectrally accurate mixed implicit explicit time marching of sets of linear and nonlinear equations in unbounded geometries

cartesian shift thin wire formalism in the fdtd method with multiwire junctions the holland and simpson thin wire formalism is a versatile technique to deal with wires in the fdtd method this paper develops an approach to correctly perform a junction between several wires at any yee s cell location the application context is the wires parallel to cartesian axes with any translation in the yee s cell the sensitivity of the thin wire current to cartesian shift is also minimized in our enhanced formalism the method is presented in a general framework with non uniform fdtd spatial steps beside the wire segment length can be different of the fdtd spatial steps and also the wire position does not need to coincide with any edge or node of the yee s cell

a random sampling method for a family of temple class systems of conservation laws the aw rascle zhang traffic model a model of sedimentation and other applications lead to nonlinear 2 times 2 systems of conservation laws that are governed by a single scalar system velocity such systems are of the temple class since rarefaction wave curves and hugoniot curves coincide moreover one characteristic field is genuinely nonlinear almost everywhere and the other is linearly degenerate two well known problems associated with these systems are handled via a random sampling approach firstly godunov s and related methods produce spurious oscillations near contact discontinuities since the numerical solution invariably leaves the invariant region of the exact solution it is shown that alternating between averaging av and remap steps similar to the approach by chalons and goatin commun math sci 5 533 551 2007 generates numerical solutions that do satisfy an invariant region property if the remap step is made by random sampling rs then combined techniques due to glimm commun pure appl math 18 697 715 1965 leveque and temple trans am math soc 288 115 123 1985 prove that the resulting av rs scheme converges to a weak solution numerical examples illustrate that the new scheme is superior to godunov s method in accuracy and resolution secondly the vacuum state which may form even from positive initial data causes potential problems of non uniqueness and instability this is resolved by introducing an alternative riemann solution concept

a spectral method for unbounded domains a spectral method for an unbounded domain is presented rational basis functions which are algebraically mapped legendre functions are used for expansion in the radial direction of polar coordinates r or r z they satisfy the pole condition exactly at the coordinate singularity and their behavior asr is suitable for expanding smooth functions which decay algebraically or exponentially asr the method is not stiff when it is applied to initial value problems despite the presence of the coordinate singularity solenoidal vector fields are treated efficiently by the toroidal and poloidal decomposition which reduces the number of dependent variables from 3 to 2 examples include the computation of vortex dynamics in two and three dimensions

fdtd calculation of wide band antenna gain and efficiency absolute gain and radiation efficiency are calculated using the finite difference time domain fdtd method the method described utilizes pulsed excitation so that wideband results are available from a single fdtd computation the approach is demonstrated for a simple wire antenna geometry and is validated by comparison with results obtained using the method of moments

calculation and experimental validation of induced currents on coupled wires in an arbitrary shaped cavity an efficient numerical technique is presented for the calculation of induced electric currents on coupled wires and multiconductor bundles placed in an arbitrary shaped cavity and excited by an external incident plane wave the method is based upon the finite difference time domain fd td formulation the concept of equivalent radius is used to replace wire bundles with single wires in the fd td model then the radius of the equivalent wire is accounted by a modified fd td time stepping expression based on a faraday s law contour path formulation for the looping magnetic fields adjacent to the wire fd td computed fields at a virtual surface fully enclosing the equivalent wire are then obtained permitting calculation of the currents on the wires of the original bundle using a standard electric field integral equation efie substantial analytical and experimental validations are reported for both time harmonic and broad band excitations of wires in free space and in a high q metal cavity