fdtd analysis of electromagnetic wave radiation from systems containing horn antennas the application of the finite difference time domain fdtd method to various radiating structures is considered these structures include two and three dimensional waveguides flared horns a two dimensional parabolic reflector and a two dimensional hyperthermia application numerical results for the horns waveguides and parabolic reflectors are compared with results from using the method of moments mm the results for the hyperthermia application are shown as extensions of the previously validated models this new application of the fdtd method is shown to be useful when other numerical or analytic methods cannot be applied

an efficient laguerre based bor fdtd method using gauss seidel procedure in this paper an efficient laguerre based body of revolution finite difference time domain bor fdtd method is proposed a perturbation term and the gauss seidel method are introduced to get the new algorithm the splitting error caused by the perturbation term can be reduced to a low level by using the iterative method to be different from its counterpart in the cartesian coordinate system the perturbation term used for the off axis field is not applicable to the field on the axis in the proposed method on the axis it is not necessary to add the perturbation term and no nonphysical intermediate variable is involved no splitting error compensatory term is used for the field on the axis during the iteration another difference is that the perturbation term in the proposed method causes a pronounced splitting error on the field point which is close to the axis several local iterations near the axis are needed since the splitting error near the axis is especially large to validate the proposed method two numerical examples are given numerical results show that it obtains a good convergence meanwhile the comparison of the computational expenditure between the proposed method and several other methods indicates its performance

on the linear complexity of nonuniformity decimated pn sequences a lower bound is derived on the probability that when a pn sequence of period n 2 sup n 1 is nonuniformly decimated by means of a sequence whose period divides m the decimated sequence will have maximum linear complexity nm it is shown that by choosing m and n appropriately this probability can be made arbitrarily close to one with nm arbitrarily large

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

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

forward error analysis of gaussian elimination part i error and residual estimates part i of this work deals with the forward error analysis of gaussian elimination for general linear algebraic systems the error analysis is based on a linearization method which determines first

on the linear complexity of nonlinearly filtered pn sequences binary sequences of period 2 sup n 1 generated by a linear feedback shift register lfsr whose stages are filtered by a nonlinear function f are studied new iterative formulas are derived for the calculation of the linear complexity of the output sequences it is shown that these tools provide an efficient mechanism for controlling the linear complexity of the nonlinearly filtered maximal length sequences

minimal linear equivalent analysis of a variable memory binary sequence generator starting from a memory based nonlinear generator due to p r geffe 1973 a binary sequence generator mem bsg consisting of three linear feedback shift registers and a variable memory is defined and analyzed the mem bsg is shown to be convenient for generating fast binary sequences of large period and linear complexity which may be useful in spread spectrum and cryptographic applications

high order fdtd methods via derivative matching for maxwell s equations with material interfaces this paper introduces a series of novel hierarchical implicit derivative matching methods to restore the accuracy of high order finite difference time domain fdtd schemes of computational electromagnetics cem with material interfaces in one 1d and two spatial dimensions 2d by making use of fictitious points systematic approaches are proposed to locally enforce the physical jump conditions at material interfaces in a preprocessing stage to arbitrarily high orders of accuracy in principle while often limited by numerical instability orders up to 16 and 12 are achieved respectively in 1d and 2d detailed stability analyses are presented for the present approach to examine the upper limit in constructing embedded fdtd methods as natural generalizations of the high order fdtd schemes the proposed derivative matching methods automatically reduce to the standard fdtd schemes when the material interfaces are absent an interesting feature of the present approach is that it encompasses a variety of schemes of different orders in a single code another feature of the present approach is that it can be robustly implemented with other high accuracy time domain approaches such as the multiresolution time domain method and the local spectral time domain method to cope with material interfaces numerical experiments on both 1d and 2d problems are carried out to test the convergence examine the stability access the efficiency and explore the limitation of the proposed methods it is found that operating at their best capacity the proposed high order schemes could be over 2000 times more efficient than their fourth order versions in 2d in conclusion the present work indicates that the proposed hierarchical derivative matching methods might lead to practical high order schemes for numerical solution of time domain maxwell s equations with material interfaces

finite difference on grids with nearly uniform cell area and line spacing for the wave equation on complex domains a finite difference time dependent numerical method for the wave equation supported by recently derived novel elliptic grids is analyzed the method is successfully applied to single and multiple two dimensional acoustic scattering problems including soft and hard obstacles with complexly shaped boundaries the new grids have nearly uniform cell area j grids and nearly uniform grid line spacing email protected numerical experiments reveal the positive impact of these two grid properties on the scattered field convergence to its harmonic steady state the restriction imposed by stability conditions on the time step size is relaxed due to the near uniformity cell areas and grid line spacing as a consequence moderately large time steps can be used for relatively fine spatial grids resulting in greater accuracy at a lower computational cost also numerical solutions for wave problems inside annular regions of complex shapes are obtained the use of the new grids results in late time stability in contrast with other classical finite difference time dependent methods

absorbing boundary conditions on arbitrary boundaries for the scalar and vector wave equations the solution of open region scattering problems involving inhomogeneous arbitrarily shaped objects may be performed through the use of partial differential equation techniques which require enclosing the scatterer by an outer boundary on which an absorbing boundary condition abc is applied in order to minimize the size of the domain to be meshed and consequently the number of unknowns if may be advisable to implement abc s devised for outer boundaries of arbitrary shapes such abc s are obtained for the 3d scalar and vector wave equations they incorporate most of existing boundary conditions when used in conjunction with a finite element technique the numerical results derived by using a simplified form of these abc s compare favourably to those obtained by using a rigorous hybrid finite element integral equation formulation these boundary conditions have been obtained in the frequency domain framework they may however be used in time domain calculations

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

time dependent numerical method with boundary conforming curvilinear coordinates applied to wave interactions with prototypical antennas a new unstaggered finite difference time dependent technique to accurately model scattring from prototypical 2d antenna structures is devised the unbounded boundary value problems defining these phenomena are redefined over bounded domains using appropriate radiation operators over finite artificial boundaries generalized curvilinear coordinates are generated such that physical boundaries correspond to coordinate lines a numerical procedure to generate almost orthogonal boundary conforming fine grids over these bounded regions is developed once the governing equations are written in terms of the new curvilinear coordinates a time dependent numerical method is applied to obtain time harmonic steady state solutions to these problems the electric field wave amplitude as well as the wave pattern inside the waveguide and the scattered field from the prototypical antennas are obtained accuracy and computational cost are compared when almost orthogonal and nonorthogonal grids are in use an optical theorem for a flanged waveguide antenna with perfect electrical conductor walls is derived it is verified that the approximate solutions obtained by application of the time dependent numerical method with boundary conforming curvilinear coordinates satisfy the optical theorem

products of linear recurring sequences with maximum complexity conditions are derived which guarantee that products of linear recurring sequences attain maximum linear complexity it is shown that the product of any number of maximum length gf q sequences has maximum linear complexity provided only the degrees of the corresponding minimal polynomials are distinct and greater than two it is also shown that if the roots of any number of not necessarily irreducible minimal polynomials are simple and lie in extension fields of pairwise relatively prime degrees then the product of the corresponding gf q sequences attains maximum linear complexity provided only that no two roots of any minimal polynomial are linearly dependent over the groundfield gf q which is automatically satisfied when q 2 the results obtained for products are extended to arbitrary linear combinations of product sequences

an explicit fourth order orthogonal curvilinear staggered grid fdtd method for maxwell s equations the explicit fourth order staggered finite difference time domain scheme previously proposed for a cartesian grid is extended to maxwell s equations in an orthogonal curvilinear coordinate system and applied to electromagnetic wave problems a simple technique is also presented for generating orthogonal curvilinear grids that conform to the material boundaries and interfaces of the problem numerical experiments are presented to illustrate the efficiency and accuracy of the method

three dimensional contour fdtd modeling of scattering from single and multiple bodies this paper introduces a generalization of the three dimensional finite difference time domain fdtd method the three dimensional contour fdtd cfdtd method is introduced the fdtd method represents curved media boundaries as stepped edges through the use of subcell modeling the cfdtd method conformably models bodies with curved surfaces yet retains the ability to model corners and edges electromagnetic scattering from single and multiple bodies is presented

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

time filtered leapfrog integration of maxwell equations using unstaggered temporal grids a finite difference time domain method for integration of maxwell equations is presented the computational algorithm is based on the leapfrog time stepping scheme with unstaggered temporal grids it uses a fourth order implicit time filter that reduces computational modes and fourth order finite difference approximations for spatial derivatives the method can be applied within both staggered and collocated spatial grids it has the advantage of allowing explicit treatment of terms involving electric current density and application of selective numerical smoothing which can be used to smooth out errors generated by finite differencing in addition the method does not require iteration of the electric constitutive relation in nonlinear electromagnetic propagation problems the numerical method is shown to be effective and stable when employed within perfectly matched layers pml stability analysis demonstrates that the proposed method is effective in stabilizing and controlling numerical instabilities of computational modes arising in wave propagation problems with physical damping and artificial smoothing terms while maintaining higher accuracy for the physical modes comparison of simulation results obtained from the proposed method and those computed by the classical time filtered leapfrog where maxwell equations are integrated for a lossy medium within pml regions and for kerr nonlinear media show that the proposed method is robust and accurate the performance of the computational algorithm is also verified by analyzing parametric four wave mixing in an optical nonlinear kerr medium the algorithm is found to accurately predict frequencies and amplitudes of nonlinearly converted waves under realistic conditions proposed in the literature

a general three dimensional tensor fdtd formulation for electrically inhomogeneous lossy media using the z transform a general three dimensional tensor finite difference time domain tfdtd formulation is derived to model electrically inhomogeneous lossy media of arbitrary shapes the time domain representation of electric losses is achieved using z transforms the regular cubical grid structure is maintained everywhere in the calculation domain by defining a 3 d face fraction based 3 x 3 permittivity tensor on the interfaces that describes the relationship between the known average flux density vector and the unknown local electric field vector for electrically lossy media this tensor is complex in the frequency domain however it can be modified for use with the z transform only this modified real form is inverted then transformed from the frequency into the z domain and finally into the time domain furthermore a local interface matrix is used to describe the relationship between the local electric field in the grid node and its counterpart on the other side of the interface this matrix is complex in the frequency domain for lossy media by applying the z transform this matrix can also be transformed into the time domain using only real modified matrix elements the accuracy of the method is confirmed by comparisons with analytical solutions

locally conformal fdtd for anisotropic conductive interfaces locally conformal discretizations have been developed for the finite difference time domain fdtd method to mitigate staircasing errors that arise in the modeling of arbitrary e g curved slanted interfaces by regular orthogonal grids in particular locally conformal algorithms based on the computation of effective material parameters in partially filled fdtd cells are attractive because they are simple to implement and maintain the basic conditional stability of fdtd with only minor changes on the courant limit in this paper we propose a new locally conformal implementation for fdtd tailored for anisotropic conductive interfaces instead of employing arithmetic or geometrical averages we invoke the quasi static relationship between the current density and the electric field to derive the effective conductivities of partially filled fdtd cells

flux limiting embedded boundary technique for electromagnetic fdtd a general approach for incorporating embedded boundaries into an electromagnetic finite difference time domain fdtd code is presented this algorithm is shown to satisfy gauss s law and enforces no magnetic monopoles while maintaining a globally second order result first order at physical boundaries with no added time step restriction theoretically predicted superior results are shown with an 11 time step reduction from the courant stability limit this is achieved through a physics based flux limiting scheme near physical boundaries stability local truncation error and energy conservation analysis are also provided

a new 3 d conformal pec fdtd scheme with user defined geometric precision and derived stability criterion a new conformal finite difference time domain cfdtd updating scheme for metallic surfaces nonaligned in the grid is presented in this paper in contrast to existing conformal models the new model can be formulated with the original yee fdtd update equation therefore the proposed scheme can be easily added in standard fdtd codes even if the codes are already parallelized or hardware accelerated in addition based on the commonly used conventional stability criterion a derivation of the stability is presented and based on the conformal geometric information a time step reduction formula is presented the time step reduction is used as a user defined parameter to tradeoff speed versus accuracy the achievable geometric precision is optimized to a given time step therefore even with the conventional time step no reduction the presented scheme profits from the conformal discretization to show the performance and the robustness of the proposed scheme canonical validations and two real world applications were investigated a broadband low profile circular antenna was successfully simulated showing the benefit of the conformal fdtd method compared to the conventional scheme furthermore a cad based mobile phone was conformally discretized and successfully simulated showing that the proposed scheme is highly suited for the simulation of advanced engineering problems

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

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

a higher order fdtd method in integral formulation we present a fourth order 4 4 finite difference time domain fdtd like algorithm based on the integral form of maxwell s equations the algorithm which is called the integro difference time domain idtd method achieves its fourth order accuracy in space and time by taking into account the spatial and temporal variations of electromagnetic fields within each computational cell in the algorithm the electromagnetic fields within each cell are represented by space and time integrals or integral averages of the fields i e the electric and magnetic fluxes d b are represented by the surface integral average and the electric and magnetic fields e h by the line and time integral average in order to relate the integral average fields in the staggered update equations we have obtained constitutive relations for these fields it is shown that the idtd update equations combined with the constitutive relations are fourth order accurate both in space and time the fourth order correction terms are represented by the modified coefficients in the update equations the numerical structure remains the same as the conventional second order update equations and more importantly does not require the storage of field variables at the previous time steps to obtain the fourth order accuracy in time furthermore the courant friedrichs lewy cfl stability criteria of this fourth order algorithm turns out to be identical to the stability limits of conventional second order fdtd scheme based on differential formulation

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

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

domain decomposition fdtd algorithm for the analysis of a new type of e plane sectorial horn with aperture field distribution optimization in this paper a universal and efficient approach of domain decomposition finite difference time domain fdtd dd fdtd is presented for the analysis of a new type of horn antenna e plane sectorial horn with field amplitude taper and phase correction in the aperture the power fed into the horn is redistributed to achieve the optimal field amplitude distribution in the aperture and meanwhile the field phase is corrected by metal lens compared with conventional e plane sectorial horns the new horn antenna takes the advantages of low sidelobe level short physical length and wide flare angle etc moreover the most important property of this horn is the weak coupling with each other when it is used as the element of a phased array antenna the field analysis of such a horn antenna is an extremely complicated three dimensional em boundary value problem the domain decomposition fdtd method is presented in this paper to break through the drawback the whole horn is decomposed into several subdomains and the meshes are created in local coordinates in the iteration procedure of fdtd the data are exchanged between adjacent subdomains with overlapped meshes the aperture field distribution voltage standing wave ratio and pattern calculated by the dd fdtd method are in good agreement with the experimental data

on the linear complexity of functions of periodic gf q sequences it is proved that the product of arbitrary periodic gf q sequences attains maximum linear complexity if their periods are pairwise coprime the necessary and sufficient conditions are derived for maximum linear complexity of the product of two periodic gf q sequences with irreducible minimal characteristic polynomials for a linear combination of products of arbitrary periodic gf q sequences it is shown that maximum linear complexity is achieved if their periods are pairwise coprime and the polynomial x 1 does not divide any of their minimal characteristic polynomials assuming only that their periods are pairwise coprime the author establishes a lower bound on the linear complexity which is of the same order of magnitude as maximum linear complexity boolean functions are derived that are optimal with respect to the maximum linear complexity possible applications of the results in the design of sequence generators are discussed

a stochastic roundoff error analysis for the convolution we study the accuracy of an algorithm which computes the convolution via radix 2 fast fourier transforms upper bounds are derived for the expected value and the variance of the accompanying linear forms in terms of the expected value and variance of the relative roundoff errors for the elementary operations of addition and multiplication these results are compared with the corresponding ones for two algorithms computing the convolution directly via homer s sums and using cascade summation respectively

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

a novel fdtd time stepping scheme to calculate rcs of curved conducting objects using adaptively adjusted time steps the chief shortcoming of the conventional conformal finite difference time domain cfdtd method is a global time step reduction to ensure stability due to the small irregular cells truncated by the curved conducting geometry introducing the local time stepping into the cfdtd method is an efficient way and has been numerically proven in our previous work in this paper we further employ the concept of the equivalent material constants into the integral form of faraday s law to analyze the curved configuration with or without the coating hence we can theoretically derive the stability criterion of each irregular cell based on the same procedure for the courant friedrichs lewy cfl stability criterion therefore the local time step size of each small irregular cell can be chosen adaptively an adaptively adjusted time stepping procedure is presented and is theoretically proven to ensure numerical stability the radar cross section rcs results of various curved conducting objects with the coating are computed comparisons of accuracy and efficiency of our method with other established methods are performed

a second order 3d electromagnetics algorithm for curved interfaces between anisotropic dielectrics on a yee mesh a new frequency domain electromagnetics algorithm is developed for simulating curved interfaces between anisotropic dielectrics embedded in a yee mesh with second order error in resonant frequencies the algorithm is systematically derived using the finite integration formulation of maxwell s equations on the yee mesh second order convergence of the error in resonant frequencies is achieved by guaranteeing first order error on dielectric boundaries and second order error in bulk possibly anisotropic regions convergence studies conducted for an analytically solvable problem and for a photonic crystal of ellipsoids with anisotropic dielectric constant both show second order convergence of frequency error the convergence is sufficiently smooth that richardson extrapolation yields roughly third order convergence the convergence of electric fields near the dielectric interface for the analytic problem is also presented

numerical stability of nonorthogonal fdtd methods in this paper a sufficient test for the numerical stability of generalized grid finite difference time domain fdtd schemes is presented it is shown that the projection operators of such schemes must be symmetric positive definite without this property such schemes can exhibit late time instabilities the origin and the characteristics of these late time instabilities are also uncovered based on this study nonorthogonal grid fdtd schemes nfdtd and the generalized yee gy methods are proposed that are numerically stable in the late time for quadrilateral prism elements allowing these methods to be extended to problems requiring very long time simulations the study of numerical stability that is presented is very general and can be applied to most solutions of maxwell s equations based on explicit time domain schemes

accurate computation of the radiation from simple antennas using the finite difference time domain method two antennas are considered a cylindrical monopole and a conical monopole both are driven through an image plane from a coaxial transmission line each of these antennas corresponds to a well posed theoretical electromagnetic boundary value problem and a realizable experimental model these antennas are analyzed by a straightforward application of the finite difference time domain fd td method the computed results for these antennas are shown to be in excellent agreement with accurate experimental measurements for both the time domain and the frequency domain the graphical displays presented for the transient near zone and far zone radiation from these antennas provide physical insight into the radiation process

accurate interfacing of heterogeneous structured fdtd grid components we study strategies to interface finite difference time domain fdtd update equations in heterogeneous structured grid components for overset composite fdtd grids an overset composite grid or chimera grid is a heterogeneous grid formed by the combination of structured fdtd subgrid components chosen to better conform to local geometrical features we study the performance of various analytical filters and phase matching techniques to reduce problems associated with such heterogeneous grid interfacing including spatial frequency aliasing and numerical phase velocity mismatch we demonstrate the performance of interfacing algorithms in some canonical examples

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

conical horn gain and amplitude patterns the conical horn radiation characteristics gain aperture phase distributions loss factors and amplitude patterns are revisited based on the spherical and quadratic aperture phase distributions calculations of the conical horn gain using over the aperture either the dominant mode of a circular waveguide or the modal variations of a conical waveguide are calculated using the aperture phase distribution represented by spherical and quadratic wavefronts the gains are compared with the classical data by gray and schelkunoff in an attempt to confirm their validity and accuracy and to determine whether they were derived based on spherical or quadratic phase distribution in addition more accurate loss factors to account for amplitude and phase tapering over the conical horn aperture are derived which improve the conical horn gain new formulas for the design of optimum gain conical horns based on the more accurate spherical aperture phase distribution are derived and reported and guidelines are provided for their utility this paper also introduces a method to calculate accurately the far zone amplitude patterns in the e and h planes including those in the far side and back lobe regions of a conical horn by utilizing geometrical optics and diffraction theory

contour path fdtd method for analysis of pyramidal horns with composite inner e plane walls the contour path finite difference time domain fdtd method is used for modeling pyramidal horn antennas with or without composite e plane inner walls to model the pyramidal horn surface a locally distorted grid is used modified equations are obtained based on the locally distorted grid and the assumptions of the contour path method the developed algorithm is validated by comparing computed antenna gain patterns with and without the presence of composite material with available measurements

frequency domain and time domain finite element solution of maxwell s equations using spectral lanczos decomposition method an efficient solver is described for the solution of the electromagnetic fields in both time and frequency domains the proposed method employs the node based and the edge based finite element method fem to discretize maxwell s equations the resultant matrix equation is solved by the spectral lanczos decomposition method sldm which is based on the krylov subspace lanczos approximation of the solution first a new explicit axisymmetric solver for the diffusion of electromagnetic fields in an inhomogeneous medium is introduced the procedure is then extended to treat the three dimensional problems in the low frequency regime finally maxwell s equations in their general form are solved in frequency and time domains depending on the application our method requires the implementation of the lanczos process only at the largest or smallest time or frequency of interest consequently a multiple time and frequency domain analysis of the electromagnetic fields is achieved in a negligible amount of extra computing time the efficiency and effectiveness of this new technique are illustrated by using various practical numerical examples

uat analysis of e plane near and far field patterns of electromagnetic horn antennas the uniform asymptotic theory uat of diffraction has been applied to arrive at expressions valid for both the near as well as far field patterns of antenna with edges namely an electromagnetic horn it is found that the theoretically computed results agree very well with experiment the agreement is found to be better than that reported by earlier authors in the far sidelobe and backlobe regions the same theory is valid for near field as well with the pertinent values of radial distance where the uniform theory of diffraction utd requires a slope diffraction correction

a domain decomposition finite difference method for parallel numerical implementation of time dependent maxwell s equations a domain decomposition technique together with an implicit finite difference scheme is used to design a parallel algorithm to solve for electromagnetic scattering in the time domain by an infinite square metallic cylinder the implicit difference scheme yields second order accuracy unconditional stability and at each time step a large system of linear equations the domain decomposition technique reduces the solution of this large system to that of many independent smaller subsystems the present algorithm can be easily implemented on coarse grain parallel vector supercomputers to obtain a speedup close to the number of available central processing units cpus

a finite edge gtd analysis of the h plane horn radiation pattern the earlier geometrical theory of diffraction gtd approach to the h plane horn radiation problem is reconsidered with spherical source excitation corner diffraction terms are included to provide a gtd model for the finiteness of the horn edges a new heuristic corner slope diffraction csd coefficient for a finite edge in a conducting plane is presented the h plane horn pattern obtained with the addition of the corner diffraction and the new csd terms to the earlier infinite edge gtd approach is found to be in better agreement with measured results compared to earlier gtd formulations

a recursive doubling algorithm for solution of tridiagonal systems on hypercube multiprocessors abstract the recursive doubling algorithm as developed by stone can be used to solve a tridiagonal linear system of size n on a parallel computer with n processors using o log n parallel arithmetic steps in this paper we give a limited processor version of the recursive doubling algorithm for the solution of tridiagonal linear systems using o n p log p parallel arithmetic steps on a parallel computer with p n processors the main technique relies on fast parallel prefix algorithms which can be efficiently mapped on the hypercube architecture using the binary reflected gray code for p n this algorithm achieves linear speedup and constant efficiency over its sequential implementation as well as over the sequential lu decomposition algorithm these results are confirmed by numerical experiments obtained on an intel ipsc d5 hypercube multiprocessor

fdtd simulations of tem horns and the implications for staircased representations two dimensional 2 d tem horns are modeled using the finite difference time domain fdtd method the boundary walls are perfect electric conductors and one wall which does not align with the cartesian grid is approximated using a staircased representation by carefully comparing the fdtd results to those of the analytic solution one can make conclusions about the coarseness with which a boundary can be represented it is found that staircasing errors are small when the staircase diagonal the hypotenuse of the right triangle created by the stairstep is smaller than half a wavelength at the highest significant frequency in the excitation this rule of thumb is put forward as a necessary condition for the discretization of general problems results are also provided for some simple fdtd schemes that are designed to reduce staircasing errors by using large aspect ratio cells a grid can be constructed that satisfies the rule of thumb given above while this approach eliminates general staircasing errors some errors persist owing to the presence of step discontinuities immediately adjacent to the horn feed these errors can be further reduced by using a cell splitting approach it is shown that the contour path fdtd technique can be used to eliminate nearly all staircasing errors while some additional improvement is shown to be provided by using a stabilized contour path fdtd approach finally a recently proposed conformal technique that permits simple implementation is shown to provide results comparable with those of the stabilized contour path approach

a gtd study of pyramidal horns for offset reflector antenna applications an efficient computational method is demonstrated for determining the far field patterns of reflectors illuminated by pyramidal horns a uniform geometrical theory of diffraction gtd formulation is used to determine the near and far fields of the horn the far field patterns of the offset reflector are constructed using the physical optics po formulation in conjunction with the jacobi bessel expansion method many representative results are shown for the far field patterns of the reflector in particular the concept of the optimum phase center for the best location of a horn illuminating a reflector is carefully studied and some useful observations are made

a transformation from the fibonacci to the galois nlfsrs conventional nonlinear feedback shift registers nlfsrs use the fibonacci configuration in which the feedback is applied to the last bit only in this paper we show how to transform a fibonacci nlfsr into an equivalent nlfsr in the galois configuration in which the feedback can be applied to every bit such a transformation can potentially reduce the depth of the circuits implementing feedback functions thus decreasing the propagation time and increasing the throughput

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

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 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

low frequency finite difference time domain modeling of a pec sphere based on a quasi analytical coupled dipole approximation a computational formulation is presented for the low frequency single cell finite difference time domain fdtd modeling of a perfectly electric conducting pec sphere the approach is based on the fact that the scattered field from electrically small objects can be expressed in terms of an electric and magnetic dipole these dipoles can be decomposed with respect to the dipole moments that can be defined along the discrete field components that comprise the cell wherein the pec sphere is inscribed the dipole moment components couple to each other and this mechanism is quantified by a quasi analytical coupled dipole approximation cda the quasi analyticity requires to substitute the involved dyadic green s function dgf terms in the cda formula by their numerically computed fdtd compatible equivalents the material properties of the equivalent electric and magnetic spheres are derived using the quasi analytical cda that leads to expressions that resemble the claussius mossotti mixing formula the theoretically derived results are supported by numerical simulations

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

analysis of microstrip antennas on a curved surface using the conformal grids fd td method the need for small portable antennas for mobile communications has spurred the study of microstrip antennas msa msa are quite flexible and have been used as conformal antennas on arbitrary curved surfaces the characteristics of conformal msa can be expected to differ from those of planar models dependable numerical analyses will obviate many of the costs and other inconveniences associated with experiments but as antennas may be mounted on surfaces of arbitrary topological complexity analysis methods must have a general applicability the curvilinear finite difference time domain fd td method has shown excellent versatility this method is applied to analyze microstrip antennas mounted on curved surfaces the numerical predictions are compared with the experimental values the results confirm the predictions within acceptable limits and appear to confirm the validity of the method as a result it was confirmed that the input impedance and directivity of msa on curved surfaces are different from the flat msa

forward error analysis of gaussian elimination part ii establishes a priori error and residual estimates for the solutions of linear algebraic systems whose matrices are totally nonnegative or signregular 2 orm matrices 3 in addition stability estimates and a priori error estimates for the computation of pivot elements and of the determinant are given particular attention is paid to stability constants and growth factors of band matrices

a finite difference time domain solution to scattering from a rough pressure release surface the finite difference time domain fdtd method is a numerical technique that makes no explicit physical approximations to the underlying problem the quality of a fdtd based solution typically is determined by the discretization of the computational domain the smaller the spacing the more accurate the solution unfortunately for large computational domains i e ones spanning many wavelengths the small spatial step size needed to obtain a high fidelity solution may lead to a prohibitively large number of unknowns here it is shown how the fdtd method can be used to model accurately scattering from pressure release surfaces above a homogeneous water column to keep the computational cost manageable a number of enhancements to the standard fdtd algorithm are employed these enhancements include correcting for numerical dispersion along the specular direction of the incident insonification using locally conformal cells at the pressure release boundary and propagating the field through the homogeneous water column via an analytic method the accuracy of the fdtd approach is demonstrated by comparison with an integral equation based reference solution to the same rough surface scattering problem thorsos proceedings of the reverberation and scattering workshop pp 3 2 3 20 1994 naval research laboratory book contribution nrl be 7181 96 001

perturbation theory for evaluation algorithms of arithmetic expressions the paper presents the theoretical foundation of a forward error analysis of numerical algorithms under data perturbations rounding error in arithmetic floating point operations and approximations in built in functions the error analysis is based on the linearization method that has been proposed by many authors in various forms fundamental tools of the forward error analysis are systems of linear absolute and relative a priori and a posteriori error equations and associated condition numbers constituting optimal bounds of possible accumulated or total errors derivations representations and properties of these condition numbers are studied in detail the condition numbers enable simple general quantitative definitions of numerical stability backward analysis welland ill conditioning of a problem and an algorithm the well known illustration of algorithms and their linear error equations by graphs is extended to a method of deriving condition numbers and associated bounds for many algorithms the associated condition numbers can be determined analytically a priori and be computed numerically a posteriori the theoretical results of the paper have been applied to a series of concrete algorithms including gaussian elimination and have proved to be very effective means of both a priori and a posteriori error analysis introduction evaluation algorithms are defined by finite sequences f fo f of input operations evaluations of built in functions and arithmetic operations for determining sequences u uo u of input data intermediate and final results in the form 1 ut f u t 0 n it is presupposed in the following that fo is a constant function and the function values ft x depend on xo xt1 but not on xt x for t 1 i n under perturbations an evaluation algorithm yields approximations vt of ut that can be written in the form 2 vt 1 e ft v t o n the so called local errors et are the relative errors of the data input function evaluation or rounding in the arithmetic floating point operation in step t of the algorithm we shall assume that the local errors are bounded by je1j yt7 for t o n where yt are suitable nonnegative weights and q is an accuracy constant received june 12 1979 revised november 26 1979 and august 27 1980 1980 mathematics subject classification primary 65g05

a 3 d tensor fdtd formulation for treatment of sloped interfaces in electrically inhomogeneous media a general integral finite difference time domain fdtd formulation on cubical grids for the modeling of electrically inhomogeneous media of arbitrary shape is derived the simple cubical structure is maintained and no modifications of the integral paths are necessary instead a three dimensional tensor relationship between the average electric flux density and electric field is determined beforehand and used during the simulation to account for discontinuities in the neighborhood of sloped interfaces the accuracy of the method is confirmed by comparisons with analytical solutions

a modified fdtd 2 4 scheme for modeling electrically large structures with high phase accuracy a new fourth order finite difference time domain fdtd scheme has been developed that exhibits extremely low phase errors at low grid resolutions compared to the conventional fdtd scheme moreover this new scheme is capable of combining with the standard yee 1966 scheme to produce a stable hybrid algorithm the problem of wave propagation through a building is simulated using this new hybrid algorithm to demonstrate the large savings in computing resources it could afford with this new development the fdtd method can now be used to successfully model structures that are thousands of wavelengths large using the present day computer technology

simple conformal methods for finite difference time domain modeling of pressure release surfaces the finite difference time domain fdtd method provides a simple and accurate means of simulating a wide range of acoustic wave propagation problems unfortunately the method has a voracious appetite for computational resources for example to accurately model scattering from a continuously varying pressure release boundary an fdtd grid is typically required that has a much finer discretization than is necessary to model propagation in a homogeneous space such a fine discretization can become prohibitive when considering large scale problems two simple conformal techniques are presented for acoustic fdtd simulations of problems involving pressure release boundaries these techniques which rely upon splitting velocity cells adjacent to the pressure release boundary significantly improve the accuracy of the results over those of the standard staircase representation of the boundary these methods permit the use of a coarser fdtd grid than would otherwise be practical and yet add negligible computa

analysis of rectangular horn antennas via uniform asymptotic theory approximate analytic expressions for the far field radiation pattern and modal reflection coefficient of the three dimensional horn antenna have been developed based upon a multiple image model of the two dimensional horn waveguide structure this approach offers greater generality than previously proposed ray analyses with comparable complexity and accuracy the uniform asymptotic theory uat which is employed throughout provides information when this approach is valid for a desired degree of accuracy in the solution it is demonstrated that in most cases the far field pattern of the horn is reducible to the pattern of a simple slit in an absorbing screen illuminated by an array of patterned line sources the measured patterns of several horns are convincingly recovered by the prediction of the analytical model the same model is used to calculate the modal reflection coefficient of the horn waveguide structure and again comparison with measured results is excellent

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

hybrid finite difference time domain modeling of curved surfaces using tetrahedral edge elements a hybrid finite difference time domain fdtd method is proposed for solving transient electromagnetic problems associated with structures of curved surfaces the method employs the conventional fdtd method for most of the regular region but introduces the tetrahedral edge based finite element scheme to model the region near the curved surfaces without any interpolation for the fields on the curved surface nor any additional stability constraint due to the finer division near the curved surfaces the novel finite element scheme is found to have second order accuracy unconditional stability programming ease and computational efficiency the hybrid method is applied to solve the electromagnetic scattering of three dimensional 3 d arbitrarily shaped dielectric objects to demonstrate its superior performance