closed form uniform asymptotic expansions of green s functions in layered media far field closed form expressions are derived for spatial domain multilayered green s functions gf for the derivation of these far field expressions the spectral domain multilayered gf are approximated by means of the total least square algorithm tlsa in terms of the spectral variable u0 k 2 k02 1 2 and uniform asymptotic expansions are determined for the sommerfeld integrals of the resulting tlsa approximations numerical results show that the far field asymptotic expressions are accurate within 0 1 for distances between source and field points larger than one free space wavelength also it is shown that the hybrid use of the discrete complex image method and the tlsa in terms of the spectral variable k leads to near field closed form expressions of multilayered gf that are typically accurate within 0 1 for distances between source and field points smaller than one free space wavelength therefore the combination of the novel far field asymptotic expressions and the well known near field expressions makes it possible to compute multilayered gf with a great accuracy in the whole range of distances between source and field points and in a wide range of frequencies

numerical integration of related hankel transforms by quadrature and continued fraction expansion an algorithm is presented for the accurate evaluation of hankel or bessel transforms of algebraically related kernel functions defined here as the non bessel function portion of the integrand that is more widely applicable than the standard digital filter methods without enormous increases in computational burden the algorithm performs the automatic integration of the product of the kernel and bessel functions between the asymptotic zero crossings of the latter and sums the series of partial integrations using a continued fraction expansion equivalent to an analytic continuation of the series the integrands may be saved to allow the rapid computation of related transforms without recalculating the kernel or bessel functions and the integration steps use interlacing quadrature formulas so that no function evaluations are wasted when it is necessary to increase the order of the quadrature rule the continued fraction algorithm allows very slowly divergent or even formally divergent integrals to be computed quite easily the local error is controlled at each step in the algorithm and accuracy is limited largely by machine resolution the algorithm is written in fortran and is listed in an appendix along with a driver program that illustrates its features the driver program and subroutine are available from the seg business offtce

an asymptotic closed form microstrip surface green s function for the efficient moment method analysis of mutual coupling in microstrip antennas a relatively simple closed form asymptotic representation for the single layer microstrip dyadic surface green s function is developed the large parameter in this asymptotic development is proportional to the lateral separation between the source and field points along the air dielectric interface this asymptotic solution remains surprisingly accurate even for very small a few tenths of a free space wavelength lateral separation of the source and field points thus using the present asymptotic approximation of the green s function can lead to a very efficient moment method mm solution for the currents on an array of microstrip antenna patches and feed lines numerical results based on the efficient mm analysis using the present closed form asymptotic approximation to the microstrip surface green s function are given for the mutual coupling between a pair of printed dipoles on a single layer grounded dielectric slab the accuracy of the latter calculation is confirmed by comparison with numerical results based on a mm analysis which employs an exact integral representation for the microstrip green s function

fast computation of sommerfeld integral tails via direct integration based on double exponential type quadrature formulas a direct integration algorithm based on double exponential type quadrature rules is presented for the efficient computation of the sommerfeld integral tails arising in the evaluation of multilayered green s functions the proposed scheme maintains the error controllable nature of the so called partition extrapolation methods often used to tackle this problem whereas it requires substantially reduced computational time moreover the proposed method is very easy to implement since the associated weights and abscissas can be precomputed the overall behavior of the proposed method both in terms of accuracy and efficiency is demonstrated through a series of representative numerical experiments where compared with one of the most proven methods available in the literature

complex reflection groups braid groups hecke algebras presentations a la coxeter are given for all irreducible nite com plex re ection groups they provide presentations for the corresponding generalized braid groups for all but six cases which allow us to generalize some of the known properties of nite coxeter groups and their associated braid groups such as the computation of the center of the braid group and the construction of deformations of the nite group algebra hecke algebras we introduce monodromy representations of the braid groups which factorize through the hecke algebras extending results of cherednik opdam kohno and others summary introduction complex re ection groups and their presentations a background from complex re ection groups b presentations braid groups and their diagrams a generalities about hyperplane complements b generalities about the braid groups c the braid diagrams proofs of the main theorems for the braid groups b de e r a notation and prerequisites b computation of b de e r and of its center for d c computation of b e e r and of its center hecke algebras a background from di erential equations and monodromy b a family of monodromy representations of the braid group c hecke algebras diagrams and tables appendix generators of the monodromy around a divisor appendix tables to mathematics subject classi cation primary g we thank jean michel peter orlik pierre vogel for useful conversations and the isaac newton institute for its hospitality while the last version of this manuscript was written up the second named author gratefully acknowledges nancial support by the fondation alexander von humboldt for his stays in paris michel brou e gunter malle raphael rouquier

symmetries of linear systems of second order ordinary differential equations in this paper several problems concerning the lie algebra structure of symmetries and variational symmetries of a general linear system of second order ordinary differential equations are studied in particular a necessary and sufficient condition is obtained in terms of the coefficients of the system for the system s symmetry algebra to be of maximal dimension i e n2 4n 3 and isomorphic to sl n 2 r the well known symmetry algebra of the free particle equation x 0 when this condition is satisfied it is proved that the system is lagrangian and that its variational symmetry algebra is isomorphic to a fixed n2 3n 6 2 dimensional lie algebra whose structure levi mal cev decomposition and realization by means of a matrix algebra is determined for the particular case of isotropic systems which includes as far as is known all the examples treated in the literature explicit formulas for the generators of both the symmetry algebra and the variational symmetry algebra are obtained

the numerical evaluation of very oscillatory infinite integrals by extrapolation recently the author has given two modifications of a nonlinear extrapolation method due to levin and sidi which enable one to accurately and economically compute certain infinite integrals whose integrands have a simple oscillatory behavior at infinity in this work these modifications are extended to cover the case of very oscillatory infinite integrals whose integrands have a complicated and increasingly rapid oscillatory behavior at infinity the new method is applied to a number of complicated integrals among them the solution to a problem in viscoelasticity some convergence results for this method are presented

a complex image reduction technique using genetic algorithm for the mom solution of half space mpie the discrete complex image method dcim has been widely used to analytically approximate the sommerfeld integrals sis of green s functions in layered media this method has been greatly improved in accuracy and generality in the past years but has resulted in a large amount of complex images it is found that using so many complex images for si approximation in method of moment mom applications is redundant and inefficient to reduce the number of complex images a technique by means of genetic algorithm is proposed and applied to the mom solution of the half space mixed potential integral equation mpie

the weighted averages algorithm revisited the classic weighted averages wa algorithm for the evaluation of sommerfeld like integrals is reviewed and reappraised as a result a new version of the wa algorithm called generalized wa is introduced the new version can be considered as a generalization of the well established holder and cesaro means used to sum divergent series generalized wa exhibits a more compact formulation devoid of iterative and recursive steps and a wider range of applications it is more robust as it provides a unique formulation valid for monotonic and oscillating functions the implementation of the new version is easier and more economical in terms of basic operations preliminary numerical examples show that generalized wa also outperforms in terms of accuracy the classic wa algorithm which is currently recognized as the most competitive algorithm to evaluate sommerfeld integral tails

a numerical method for electromagnetic scattering by 3 d dielectric objects buried under 2 d locally rough surfaces in this work a numerical method is developed to solve a forward scattering problem of three dimensional 3 d objects buried into two half space media with two dimensional 2 d locally rough interface the proposed method exploits the electric field integral equation efie formulation of the scattered field which involves the dyadic green s function of the background medium since the required green s function has no analytical expression in general buried object approach boa is applied to calculate it numerically method of moments mom is then used to solve the efie the presented method is numerically validated by comparing it with finite difference time domain fdtd method furthermore an elaborative numerical analysis of the proposed method is presented to show its feasibility for various roughness profiles and buried objects

convergence speeding convergence and summability abstract four general principles are proposed for use in constructing convergence speeding methods five old methods and about 15 more recent non linear methods are discussed with reference to their range of applicability and rate of convergence speeding when applied to alternating monotonic slightly erratic fourier and alternating divergent series several of these methods are proved to give analytic continuations while even asymptotic series with zero radius of convergence can be summed accurately divergent series of positive terms may also in some cases be interpreted with moderate accuracy using four different methods convergence tests are reviewed in the light of these convergence speeding methods and analytic continuation

analysis of a plane wave excited subwavelength circular aperture in a planar conducting screen illuminating a multilayer uniaxial sample a spectral domain analysis is presented of a plane wave excited subwavelength circular aperture in a planar perfectly conducting screen in close proximity to a multilayer stack which may comprise uniaxially anisotropic slices the formulation employs the bethe bouwkamp aperture model for the general case of oblique incidence and it combines the hankel transform method with a transmission line network analogue of the medium which facilitates the inclusion of any number of material layers the electromagnetic fields are expressed in terms of one dimensional 1 d hankel transform integrals which are efficiently evaluated by a numerical quadrature along a suitably selected path with convergence acceleration by extrapolation sample numerical results are presented to demonstrate the validity of the method and its utility in the modeling of multilayer near field lenses and aperture type probes of near field optical microscopy

an asymptotic closed form representation for the grounded double layer surface green s function an efficient closed form asymptotic representation for the grounded double layer substrate superstrate green s function is presented the formulation is valid for both source a horizontal electric dipole and observation points anywhere inside the superstate or at the interfaces the asymptotic expressions are developed via a steepest descent evaluation of the original sommerfeld type integral representation of the green s function and the large parameter in this asymptotic development is proportional to the lateral separation between source and observation points the asymptotic solution is shown to agree with the exact green s function for lateral distances even as small as a few tenths of the free space wavelengths thus constituting a very efficient tool for analyzing printed circuits antennas since the asymptotic approximation gives separate contributions pertaining to the different wave phenomena it provides physical insight into the field behavior as shown by examples

paraxial space domain formulation for surface fields on a large dielectric coated circular cylinder a new method to evaluate the surface fields excited within the paraxial nearly axial region of an electrically large dielectric coated circular cylinder is presented this representation is obtained by performing the watson s transformation in the standard eigenfunction solution and using the fact that the circumferentially propagating series representation of the appropriate green s function is periodic in one of its two variables therefore it can be approximated by a fourier series where the two leading terms of the expansion yield engineering accuracy in most cases this work can be used in conjunction with a method of moments solution for the design analysis of conformal microstrip antennas and arrays numerical results are presented and compared with a standard eigenfunction expansion

asymptotic green s function of a surface magnetic current element on a perfect electric conductor plane covered by a lossy dielectric substrate published analyses of radiation modeling for slot structures on dielectric substrate are empirical or numerical this paper proposes exact analytical asymptotic expressions of the far field green s functions of a surface magnetic current element on a perfect electric conductor plane covered by a lossy dielectric substrate of finite thickness from these expressions the radiation pattern of both the space wave and surface wave far away from an arbitrary shaped slot antenna structure can be calculated provided the source distribution across the slot is known the potentials used in the analysis are defined and their boundary conditions are expressed the helmholtz equation is solved in the laplace domain and the solutions are transformed into the space domain using the inverse hankel transform and steepest descent method the influences of the substrate thickness and dielectric constant are analyzed using the calculated expressions the model is validated by comparison with surface wave and space wave measurements and with numerical results obtained from a commercial electromagnetic simulator

analytical technique to evaluate the asymptotic part of the impedance matrix of sommerfeld type integrals the propagation of electromagnetic waves in a grounded dielectric slab has numerous applications in printed antenna technology and in the analysis of microwave and millimeter wave integrated circuits for the accurate analysis of microstrip dipoles and circuits based on the moment of method mom a crucial step is the precise evaluation of the impedance matrix elements which contain the integration of sommerfeld type integrals the integral transform method with the asymptotic extraction technique is formulated for calculating a sommerfeld type integral problem this formulation allows the infinite double integral of the asymptotic part of the impedance matrix to be transformed into a finite one dimensional 1 d integral this finite 1 d integral contains a spherical legendre function and can be easily evaluated numerically after the singular part of the integral is performed analytically it is shown that the proposed method dramatically reduces the computation time and improves the accuracy over the conventional method to evaluate the asymptotic part of impedance matrix

application of dcim to mpie mom analysis of 3d pec objects in multilayered media the formulation c green s functions for multilayered media are reformulated in this paper to extract z dependent part when the source and observation points are in different layers the discrete complex image method dcim is applied to obtain complex images independent on z but dependent on z spl acute for simulation of three dimensional 3 d perfectly electrical conduction pec objects penetrating two or more layers tables of complex images are built in a z spl acute grid during the matrix filling stage of the mixed potential integral equation together with method of moments mpie mom the spatial domain green s functions are interpolated from values in the z spl acute grid while these values are calculated from complex images in the z spl acute grid this interpolation scheme is more efficient than those directly storing the spatial domain green s functions numerical examples are given for analyzing a dipole in a two layered media

some convergence considerations in space domain moment method analysis of a class of wide band microstrip antennas the method of moments mom analysis of probe fed rectangular microstrip patches requires the inclusion of a probe to patch attachment mode expansion function when the substrate thickness d spl ges 0 02 spl lambda where spl lambda is the free space wavelength the results for the input impedance showed increased divergence with measurements when the attachment mode was omitted from the full wave analysis the attachment mode can be expressed as an infinite eigenfunction series that increases the fill time of the impedance matrix in an mom analysis in an earlier investigation the infinite eigenfunction series was reduced to a residue series that required one or two terms compared to about 55 terms for the eigenfunction series in this paper the convergence properties of the eigenfunction and residue series are investigated in view of rigorous mom analysis the relative errors resulting from replacing the eigenfunction by the residue series for the attachment mode are compared by numerically evaluating a class of two dimensional 2 d spatial integrals shown to be closely related to the elements of an mom impedance matrix additionally the computation times for the evaluation of these integrals for the two forms of the attachment mode expansion function are also included based on the superior convergence properties of the residue series for the attachment mode expansion function it is mathematically justified that this form can readily be used for analytic reduction of the spatial reaction integrals from four to 2 d forms this feature allows further reduction of the fill time of the mom impedance matrix suggesting the possibility of developing an efficient space domain mom technique for modeling of wide band microstrip antennas

computation of the sommerfeld integral tails using the matrix pencil method the oscillating infinite domain sommerfeld integrals si are difficult to integrate using a numerical procedure when dealing with structures in a layered media even though several researchers have attempted to do that generally integration along the real axis is used to compute the si however significant computational effort is required to integrate the oscillating and slowly decaying function along the tail extrapolation methods are generally applied to accelerate the rate of convergence of these integrals however there are difficulties with the extrapolation methods such as locations for the breakpoints in this paper we illustrate a simplified approach for accurate and efficient calculation of the integrals dealing with the tails of the si in this paper we fit the tail by a sum of finite usually 10 to 20 complex exponentials using the matrix pencil method mpm the integral of the tail of the si is then simply calculated by summing some complex numbers no numerical integration is needed in this process as the integrals can be done analytically good accuracy is achieved with a small number of evaluations for the integral kernel 60 points for the mpm as compared with hundreds or thousands of functional evaluations using the traditional extrapolation methods along the tails of the si simulation results show that to obtain the similar accuracy in the evaluation of the si the mpm is approximately 10 times faster than the traditional extrapolation methods moreover since the mpm is robust to the effects of noise this method is more stable especially for large values of the horizontal distances the method proposed in this paper is thus a new and better technique to obtain accurate results for the computation of the green s function for a layered media in the spatial domain

analysis of printed antennas mounted on a coated circular cylinder of arbitrary size an efficient numerical algorithm for the analysis of printed antennas on a dielectric coated circular cylinder is presented the formulation employs the spectral domain approach green s function is evaluated via olver s uniform asymptotic expansions the fourier summation is transformed into integration and the asymptotic part of the integral is evaluated in closed form the whole procedure results in a numerical algorithm that is at least as accurate and efficient as the respective one for the planar structure the present approach can be applied for any source receiver position and any cylinder radius

some new convergence acceleration methods abstract the algorithm is a general extrapolation method which includes most of thesequence transformations actually known some new convergence acceleration methods arederived from the f algorithm by applying the so called procedure the algorithms thusobtained are studied some theoretical results are proved and numerical examples are given 1 introduction the general idea for accelerating the convergence of a slowlyconvergent sequence is to transform it into another sequence which will undercertain assumptions converge faster to the same limit among the most famoussequence transformations are linear summation processes richardson polynomialextrapolation aitken s a2 process 1 and shanks transformation 15 wynn s algorithm 17 an extensive study of these methods can be found in 3 whilenumerical examples applications and fortran subroutines are given in 4 each of these methods usually works in some particular cases since a universalmethod accelerating the convergence of wide classes of sequences cannot exist 10 however numerical examples 11 16 and also some theoretical results 6 8 revealthat the best sequence transformations that is those working in most of theexamples seem to be levin s u and v transforms 14 and the algorithm 2 the algorithm is a method derived from the rule of the e algorithm by a procedurewhich will be recalled in the next section recently a general sequence transformation as well as the corresponding recursivealgorithm was obtained by havie 13 and brezinski 5 this transformation calledthe transformation includes most of the convergence acceleration methods actu ally known thus it seemed interesting to apply to the algorithm the sameprocedure which was used to derive the algorithm from the e algorithm and tostudy the new convergence acceleration methods obtained in that way it is the aimof this paper 2 the procedure 8 let us first begin by some reminiscences about shanks transformation and the e algorithm let sn be a sequence of real or complex numbers shanks transformationconsists in transforming sn into a set of sequences ek sn given by

a new technique for the derivation of closed form electromagnetic green s functions for unbounded planar layered media a closed form electromagnetic green s function for unbounded planar layered media is derived in terms of a finite sum of hankel functions the derivation is based on the direct inverse hankel transform of a pole residue representation of the spectral domain form of the green s function such a pole residue form is obtained through the solution of the spectral domain form of the governing green s function equation numerically through a finite difference approximation rather than analytically the proposed methodology can handle any number of layers including the general case where the planar media exhibit arbitrary variation in their electrical properties in the vertical direction the numerical implementation of the proposed methodology is straightforward and robust and does not require any preprocessing of the spectrum of the green s function for the extraction of surface wave poles or its quasi static part the number of terms in the derived closed form expression is chosen adaptively with the distance between source and observation point as parameter the development of the closed form green s function is presented for both vertical and horizontal dipoles its accuracy is verified through a series of numerical examples and comparisons with results from other established methods

analytical and numerical studies of the convergence behavior of the j transformation abstract a new nonlinear sequence transformation the iterative j transformation was proposed recently by the author 1993 for this transformation a derivation based on the method of hierarchical consistency alternative recursive representations general properties an explicit expression for the kernel model sequences and its relation to other sequence transformations have been given the author 1994 the j transformation is of similar generality as the well known e algorithm brezinski 1980 havie 1979 in the present contribution some results on convergence acceleration properties of the j transformation are proved numerical test results are presented which show that the j transformation is a very powerful computational tool for convergence acceleration extrapolation and summation of divergent series

efficient analysis of phased arrays of microstrip patches using a hybrid generalized forward backward method green s function technique with a dft based acceleration algorithm a hybrid method based on the combination of generalized forward backward method gfbm and green s function for the grounded dielectric slab together with the acceleration of the combination via a discrete fourier transform dft based algorithm is developed for the efficient and accurate analysis of electromagnetic radiation scattering from electrically large irregularly contoured two dimensional arrays consisting of finite number of probe fed microstrip patches in this method unknown current coefficients corresponding to a single patch are first solved by a conventional galerkin type hybrid method of moments mom green s function technique that uses the grounded dielectric slab s green s function because the current distribution on the microstrip patch can be expanded using an arbitrary number of subsectional basis functions the patch can have any shape the solution for the array currents is then found through gfbm where it sweeps the current computation element by element the computational complexity of this method which is originally being the total number of unknowns for each iteration is reduced to using a dft based acceleration algorithm making use of the fact that array elements are identical and the array is periodic numerical results in the form of array current distribution are given for various sized arrays of probe fed microstrip patches with elliptical and or circular boundaries and are compared with the conventional mom results to illustrate the efficiency and accuracy of the method

a domain integral equation approach for simulating two dimensional transverse electric scattering in a layered medium with a gabor frame discretization abstract we solve the 2d transverse electrically polarized domain integral equation in a layered background medium by applying a gabor frame as a projection method this algorithm employs both a spatial and a spectral discretization of the electric field and the contrast current in the direction of the layer extent in the spectral domain we use a representation on the complex plane that avoids the poles and branchcuts found in the green function because of the special choice of the complex plane path in the spectral domain and because of the choice to use a gabor frame to represent functions on this path fast algorithms based on ffts are available to transform to and from the spectral domain yielding an o n log n scaling in computation time

the expansion wave concept i efficient calculation of spatial green s functions in a stratified dielectric medium a procedure is given to perform the inverse fourier transformation relating a spatial green s function to its spectral equivalent the procedure is applied to the spectral green s functions of the double scalar mixed potential integral expression formulation of the electromagnetic field in a stratified dielectric medium the extraction technique is used to annihilate every type of problematic behavior of the spectral green s functions every annihilating function is inverse fourier transformed analytically it is shown that the annihilation of both the surface wave poles and the singularities at the branch point results in a set of analytical spatial functions which are a very good approximation of the exact spatial green s function down to relatively small lateral distances

an algorithm for a special case of a generalization of the richardson extrapolation process a special case of a generalization of the richardson extrapolation process is considered and its complete solution is given in closed form using this an algorithm for implementing the extrapolation is devised it is shown that this algorithm needs a very small amount of arithmetic operations and very little storage convergence and stability properties for some cases are also considered

efficient evaluation of the finite part of pole free sommerfeld integrals in half space problems with predefined accuracy this communication presents a novel simple and robust approach for the computation of the finite part of pole free sommerfeld integrals sis in half space problems with high and controllable accuracy over a large range of source observer distances the approach includes the following techniques 1 cancellation of the branch point singularities based on the square root change of variables for numerical integration 2 approximation of real axis integration path in order to enhance the singularity cancellation for arbitrary low loss dielectrics 3 thresholds for truncation of the interval of integration for given accuracy which improve the efficiency of computation and 4 prediction formulas that estimate the required number of integration points for a given accuracy up to 1000 wavelengths of source observer distance the proposed approach is verified through numerical examples and comparison to reference methods

sl 3 r as the group of symmetry transformations for all one dimensional linear systems the converse problem of similarity analysis is solved in general for the finite symmetry transformations of any inhomogeneous ordinary linear differential equation of the second order x f2 t x f1 t x f0 t the eight parameter realizations of the symmetry group are obtained in the form f 1p2 f where f stands for transformations of t x that depend exclusively on the fundamental solutions of the equation and where p2 is an arbitrary projective transformation in the plane thus it is shown that the full point symmetry group corresponds to sl 3 r indeed without recourse to the lie algebra also a technique is obtained for calculating the finite point symmetry realization of sl 3 r for any given one dimensional linear system some miscellaneous examples are given

numerical analysis 2000 vol ii interpolation and extrapolation multivariate polynomial interpolation is a basic and fundamental subject in approximation theory and numerical analysis which has received and continues receiving not deep but constant attention in this short survey we review its development in the rst 75 years of this century including a pioneering paper by kronecker in the 19th century c 2000 elsevier science b v all rights reserved

multilayered media green s functions in integral equation formulations a compact representation is given of the electric and magnetic type dyadic green s functions for plane stratified multilayered uniaxial media based on the transmission line network analog along the aids normal to the stratification furthermore mixed potential integral equations are derived within the framework of this transmission line formalism for arbitrarily shaped conducting or penetrable objects embedded in the multilayered medium the development emphasizes laterally unbounded environments but an extension to the case of a medium enclosed by a rectangular shield is also included

accurate and efficient computation of layered medium doubly periodic green s function in matrix friendly formulation this communication proposes a novel approach to evaluate the doubly periodic green s function for layered medium in matrix friendly formulation several techniques including factorization of the green s function generalized pencil of function method and high order taylor expansion are employed in a delicate manner to derive the high order asymptotic expressions which are then evaluated by new fast convergent series derived from ewald transformation this approach delivers fast and highly accurate results as well as high order convergence and also allows fast frequency sweep for calculating brillouin diagram in eigenvalue problem and for normal incidence in scattering problem

finite complex reflection arrangements are k pi 1 let v be a finite dimensional complex vector space and w gl v be a finite complex reflection group let v reg be the complement in v of the reflecting hyperplanes we prove that v reg is a k 1 space this was predicted by a classical conjecture originally stated by brieskorn for complexified real reflection groups the complexified real case follows from a theorem of deligne and after contributions by nakamura and orliksolomon only six exceptional cases remained open in addition to solving these six cases our approach is applicable to most previously known cases including complexified real groups for which we obtain a new proof based on new geometric objects we also address a number of questions about 1 w v the braid group of w this includes a description of periodic elements in terms of a braid analog of springer s theory of regular elements

a hybrid evaluation method for the full wave analysis of microstrip structures a hybrid evaluation method using both the spectral and the spatial domain techniques is proposed for the evaluation of the sommerfeld type integrals resulting from the full wave analysis of microstrip structures this method combines the advantages of the spectral domain for the evaluation of near fields and the spatial domain method for the evaluation of far fields this method is simple and needs no additional formulations it also provides an easy alternative method to handle the inefficiency of calculation with the singularity of the green s function numerical results are used to demonstrate the simplicity and the accuracy of this method

indefinite integration of oscillatory functions by the chebyshev series expansion abstract an automatic quadrature scheme is presented for evaluating the indefinite integral of oscillatory function x 0 t e i t dt 0 x 1 of a given function t which is usually assumed to be smooth the function t is expanded in the chebyshev series to make an efficient evaluation of the indefinite integral combining the automatic quadrature method obtained and sidi s extrapolation method makes an effective quadrature scheme for oscillatory infinite integral a x cos x d x for which numerical examples are also presented

numerical comparisons of nonlinear convergence accelerators as part of a continuing program of numerical tests of convergence accelerators we have compared the iterated aitken s a2 method wynn s algorithm brezinski s 0 algorithm and levin s u transform on a broad range of test problems linearly convergence alternating monotone and irregular sign series logarithmically convergent series power method and bernoulli method sequences alternating and monotone asymptotic series and some perturba tion series arising in applications in each category either the algorithm or the u transform gives the best results of the four methods tested in some cases differences among methods are slight and in others they are quite striking 1 introduction we reported in 19 on a numerical test program that compared eleven different scalar convergence accelerators on a broad range of infinite series problems in an attempt to find an across the board accelerator that would handle both linear and logarithmic convergence and both alternating and monotone series or sequences the best candidates to emerge from that study were levin s u transform 14 and brezinski s 0 algorithm 6 we also provided some theoretical support for that conclusion in terms of the wide range of series summed exactly by these methods and by proving that 02 and the levin transforms all accelerate linear convergence the other levin transforms t and v produced essentially equivalent numerical results to u except that t fails on logarithmic convergence we have continued the test program started with 19 to include monotone linearly convergent series series with irregular sign patterns specifically fourier series and sequences whose terms do not depend explicitly on the previous term and or the index e g bernoulli s method since convergence accelerators are often known to transform divergent series to convergent ones we have also included in our test program divergent power series asymptotic series and a few perturbation series the methods considered in this paper are the u and 0 algorithms noted above and

complex plane generalization of scalar levin transforms a robust rapidly convergent method to compute potentials and fields in multi layered media abstract we propose the complex plane generalization of a powerful algebraic sequence acceleration algorithm the method of weighted averages mwa to guarantee exponential cum algebraic convergence of fourier and fourier hankel f h integral transforms this complex plane mwa effected via a linear path detour in the complex plane results in rapid absolute convergence of field and potential solutions in multi layered environments regardless of the source observer geometry and anisotropy loss of the media present in this work we first introduce a new integration path used to evaluate the field contribution arising from the radiation spectra subsequently we 1 exhibit the foundational relations behind the complex plane extension to a general levin type sequence convergence accelerator 2 specialize this analysis to one member of the levin transform family the mwa 3 address and circumvent restrictions arising for two dimensional integrals associated with wave dynamics problems through minimal complex plane detour restrictions and a novel partition of the integration domain 4 develop and compare two formulations based on standard real axis mwa variants and 5 present validation results and convergence characteristics for one of these two formulations

new method for the efficient summation of double infinite series arising from the spectral domain analysis of frequency selective surfaces when the method of moments mom in the spectral domain is applied to the analysis of frequency selective surfaces the entries of the mom matrix are slowly convergent double infinite series in this paper a two step acceleration technique is developed which makes it possible the fast and accurate computation of these double series in the particular case where subsectional rooftops are used as basis functions the technique is based on a combination of the use of kummer s transformation the use of poisson s transformation and the determination of judicious chebyshev polynomial interpolations of some of the spectral discrete functions involved in the infinite series the results obtained show that when all the double series of the mom matrix are to be computed with an accuracy of three significant figures the new acceleration technique turns out to be about one thousand times faster than brute force computation and a few times faster than the acceleration technique based on fast fourier transform

an algorithm for a generalization of the richardson extrapolation process in this paper we present a recursive method designated the w m algorithm for implementing a generalization of the richardson extrapolation process that has been ntroduced in 8 compared to the direct solution of the linear systems of equations defining the extrapolation procedure this method requires a small number of arithmetic operations and very little storage the technique is also applied to solve recursively the coefficient problem associated with the rational approximations obtained by applying the d transformation of 6 13 to power series in the course of development a new recursive algorithm for implementing a very general extrapolation procedure is introduced which is similar to that given in 2 4 for solving the same problem a fortran program for the w m algorithm is also appended

the gauss bonnet theorem for cone manifolds and volumes of moduli spaces this paper generalizes the gauss bonnet formula to a class of stratied spaces called riemannian cone manifolds as an application we compute the volumes of the moduli spacesm0 n with respect to the complex hyperbolic metrics introduced by picard deligne mostow and thurston

real axis integration of sommerfeld integrals with applications to printed circuit antennas printed circuit antennas are becoming an integral part of imaging arrays in microwave millimeter and submillimeter wave frequencies the electrical characteristics of such antennas can be analyzed by solving integral equations of the fredholm first kind the kernel involves sommerfeld integrals which are particularly difficult to solve when source and field points lie on an electrical discontinuity as it occurs in the determination of the characteristics of printed circuit antennas an analytic numeric real axis integration technique has been developed for such integrals and it is combined with piece wise sinusoidal expansions to solve the fredholm integral equation for the unknown current density

techniques for evaluating the uniform current vector potential at the isolated singularity of the cylindrical wire kernel the cylindrical wire kernel possesses a singularity which must be properly treated in order to evaluate the uniform current vector potential traditionally the singular part of the kernel is extracted resulting in a slowly varying function which is convenient for numerical integration this paper provides some new accurate and computationally efficient methods for evaluating the remaining singular integral it is shown that this double integral may be converted to a single integral which no longer possesses a singular integrand and consequently may be efficiently evaluated numerically this form of the integral is independent of the restrictions involving wire length and radius which are inherent in various approximations also presented is a highly convergent exact series representation of the integral which is valid except in the immediate vicinity of the singularity finally a new approximation is derived which is found to be an improvement over the classical thin wire approximation it is demonstrated that each of these methods provides extremely accurate as well as efficient results for a wide range of wire radii and field point locations

exact closed form expression of a sommerfeld integral for the impedance plane problem a sommerfeld integral for an impedance half plane is one of the classical problems in electromagnetic theory in this paper the integral is evaluated into two series representations which are expressed in terms of the exponential integral and the lommel function respectively it is shown that the series expansions absolutely converge for any parameters such as distance or surface impedance then based on the lommel function expansion an exact closed form expression of the integral is formulated this expression is written in terms of incomplete weber integrals which are directly related to incomplete cylindrical functions such as incomplete lipschitz hankel integrals additionally a complete asymptotic series of the integral is obtained based on the exponential integral expansion with conventional methods such as steepest descent method it is cumbersome to derive the divergent series the validity of all the formulations derived in this paper is demonstrated through a comparison with a numerical integration of the integral for various situations

a novel analysis of microstrip structures using the gaussian green s function method a novel closed form expression is derived for spatial green s functions of microstrip structures by expanding the spectral green s function into a gaussian series this innovative method is called the gaussian green s function ggf method due to the gaussian form in the closed form green s function representation the main advantage of the ggf method lies in its precision as well as rapid convergence to demonstrate the versatility of this method the current distribution of a microstrip antenna is achieved via the combination of the method of moments mom and ggf method it is shown that this method can be computationally very efficient with less than 1 error compared to the numerical integration of the spectral integral also the results of the ggf method have been compared to the results of the commercial full wave software of agilent ads

complex time representation of the sommerfeld type integrals and its application to 1 d periodic structures the concept of complex time is employed to derive the time domain representation of the green s function of a periodic structure for the first time the spatial domain green s function of the periodic structure in the frequency domain is separated into singular and nonsingular terms the nonsingular terms are approximated by using exponential functions resulting in the well known complex time representation of the time domain green s function in order to find a closed form expression for the singular terms a novel time domain representation of the sommerfeld type integrals is derived the proposed procedure is applied to the computation of the time domain green s function of a one dimensional periodic structure numerical experiments demonstrate the high accuracy of this method

extrapolation methods for divergent oscillatory infinite integrals that are defined in the sense of summability in a recent work by the author an extrapolation method the w transformation was developed by which a large class of oscillatory infinite integrals can be computed very efficiently the results of this work are extended to a class of divergent oscillatory infinite integrals in the present paper it is shown in particular that these divergent integrals exist in the sense of abel summability and that the w transformation can be applied to them without any modifications convergence results are stated and numerical examples given

evaluation of efficient closed form green s function in a cylindrically stratified medium an efficient technique is proposed for the removal of the spatial singularity for a z directed current source in a cylindrically layered structure by decomposing the spectral domain green s function into the particular and homogeneous parts the particular part with the singularity is converted into the spatial domain using sommerfeld s identity while the dcim with general pencil of function technique is applied on the spectral domain homogeneous part the use of the ratio form of the reflection transmission matrices the debye approximation and the subsequent envelope extraction for the treatment of the spatial domain singularity is thus avoided in addition a very significant reduction in the number of modes required for convergence is also achieved the technique is applied for evaluating the input impedance of several antennas in the cylindrical multilayer structure together with a coupling configuration for the excitation of the multilayer structure

efficient analysis of input impedance and mutual coupling of microstrip antennas mounted on large coated cylinders an efficient and accurate hybrid method based on the combination of the method of moments mom with a special green s function in the space domain is presented to analyze antennas and array elements conformal to electrically large material coated circular cylinders the efficiency and accuracy of the method depend strongly on the computation of the green s function which is the kernel of the integral equation that is solved via mom for the unknown equivalent currents representing only the antenna elements three types of space domain green s function representations are used each accurate and computationally efficient in a given region of space consequently a computationally optimized analysis tool for conformal microstrip antennas is obtained input impedance of various microstrip antennas and mutual coupling between two identical antennas are calculated and compared with published results to assess the accuracy of this hybrid method

improved formulation for investigation of proximity coupled microstrip antenna in homogeneous dielectric half space analytical evaluation of asymptotic part of the green s function in product with piece wise sinusoidal entire domain and travelling wave mode basis functions is presented the sommerfeld type double integral in spectral domain is solved and reduced into a single integral in spatial domain with very short integration range the derived results lead to develop a computational efficiency improved code which has been found 27 times faster than the earlier validated common method of moments code

exact invariants for a class of time dependent nonlinear hamiltonian systems a method of generalizing a class of invariants for a time dependent linear oscillator is developed for the motion of a mass point in one dimension with a general time dependent nonlinear potential formulas are derived for the allowable time dependent potentials and for the corresponding invariants the method by which these conclusions are reached is interesting theoretically and is explained in detail

new non arithmetic complex hyperbolic lattices we produce a family of new non arithmetic lattices in mathrm pu 2 1 all previously known examples were commensurable with lattices constructed by picard mostow and deligne mostow and fell into nine commensurability classes our groups produce five new distinct commensurability classes most of the techniques are completely general and provide efficient geometric and computational tools for constructing fundamental domains for discrete groups acting on the complex hyperbolic plane

extrapolation methods for sommerfeld integral tails a review is presented of the extrapolation methods for accelerating the convergence of sommerfeld type integrals i e semi infinite range integrals with bessel function kernels which arise in problems involving antennas or scatterers embedded in planar multilayered media attention is limited to partition extrapolation procedures in which the sommerfeld integral is evaluated as a sum of a series of partial integrals over finite subintervals and is accelerated by an extrapolation method applied over the real axis tail segment spl alpha spl infin of the integration path where spl alpha 0 is selected to ensure that the integrand is well behaved an analytical form of the asymptotic truncation error or the remainder which characterizes the convergence properties of the sequence of partial sums and serves as a basis for some of the most efficient extrapolation methods is derived several extrapolation algorithms deemed to be the most suitable for the sommerfeld integrals are described and their performance is compared it is demonstrated that the performance of these methods is strongly affected by the horizontal displacement of the source and field points spl rho and by the choice of the subinterval break points furthermore it is found that some well known extrapolation techniques may fail for a number of values of spl rho and ways to remedy this are suggested finally the most effective extrapolation methods for accelerating sommerfeld integral tails are recommended

generalizations of noether s theorem in classical mechanics in this paper a review is presented of various approaches to the generalization of the version of noether s theorem which is presented in most textbooks on classical mechanics its motivation is the controversy still persisting around the possible scope of a noether type theorem allowing for velocity dependent transformations our analysis is centered around the one factor common to all known treatments namely the structure of the related first integral we first discuss the most general framework in which a function of the above mentioned structure constitutes a first integral of a given lagrangian system and show that one cannot really talk about an interrelationship between symmetries and first integrals there we then compare different proposed generalizations of noether s theorem by describing the nature of the restrictions which characterize them when they are situated within the broadest framework we prove a seemingly new equivalence result between the two main approaches that of invaria

characteristic functional structure of infinitesimal symmetry mappings of classical dynamical systems iv classical velocity independent mappings of second order differential equations in a recent paper j math phys 26 3080 1985 the first of this series it was shown that velocity dependent symmetry mappings of second order dynamical systems have a characteristic functional structure which is the same for all dynamical systems the present paper continues the investigation of this characteristic functional structure a shortened improved conceptionally simpler proof of the existence of the characteristic structure is given it is shown how this characteristic functional structure may be formally incorporated into a new procedure for the determination of classical velocity independent symmetries of dynamical systems in addition to providing insight into symmetry analysis this new procedure is also a practical alternative to existing symmetry methods for those dynamical systems for which there exist sufficient knowledge of the form of the dynamical solution so that it is feasible to determine constants of motion by inversion or the converse application of the procedure to

on the location of proper and improper surface wave poles for the grounded dielectric slab microstrip antennas a recently obtained closed form asymptotic representation due to s barkeshli 1988 of the microstrip surface green s function is known to provide an efficient moment method analysis of microstrip problems however in order to make this closed form expression accurate even for very small separation of source and field points to within a few tenths of a wavelength both the proper and improper surface wave transition effects must be included in the solution this requires finding the location of the corresponding proper and improper poles a good initial estimate that allows the poles to be located rapidly by using an iterative procedure is presented the number of proper and improper surface wave poles that have to be considered and their values are tabulated

complete closed form expression of dyadic green s function and its far and near field approximations for an impedance half plane a closed form expression of the dyadic green s function is formulated for an impedance half plane which is written in terms of the incomplete cylindrical function of poisson form due to the branch cut of the logarithm function that is required to calculate the input argument of the incomplete cylindrical function the closed form representation consists of two formulations since the closed form expression contains a singularity at 0 the small argument expansion of the expression is also derived to rigorously characterize the behavior of the function at 0 the previously reported complete asymptotic expansion for the sommerfeld integral for an impedance half plane is not accurate for practically important cases such as near earth propagation and or when the surface is highly conductive hence in this paper a new complete asymptotic series of the sommerfeld integral are derived for the case that the existing asymptotic series is not accurate the two asymptotic series not only allow efficient numerical computation but also provide more accurate results for virtually all propagation scenarios based on the two asymptotic series the complete asymptotic series of the dyadic green s function is derived all derived formulations are numerically verified and their accuracies are investigated

an asymptotic extraction technique for evaluating sommerfeld type integrals an asymptotic extraction process is developed which leads to an efficient method for the evaluation of the electric field from a hertzian dipole in a layered geometry this technique allows for a rapidly converging expression for the electric field which remains well behaved as the source and observation heights z z coincide a useful application of this method is in the calculation of mutual impedance between printed dipoles

a user friendly extrapolation method for oscillatory infinite integrals developpement d une methode d extrapolation flexible pour les integrales infinies oscillatoires

on the plane wave excited subwavelength circular aperture in a thin perfectly conducting flat screen the electromagnetic field transmitted by a subwavelength circular aperture in a perfectly conducting screen of infinitesimal thickness and illuminated by an obliquely incident plane wave is analyzed based on the bethe bouwkamp quasi static model of the field in the aperture plane the problem is formulated in the spectral domain and the solution is expressed in terms of a minimum number of one dimensional hankel transform integrals involving products of bessel functions and spherical bessel functions an efficient computational scheme for these integrals is implemented based on numerical quadrature with convergence acceleration by extrapolation from the rigorous spectral domain formulation closed form expressions are also derived for the transmitted near zone and far zone fields sample numerical results are presented to demonstrate the validity of the method and its utility in the modeling of aperture type near field optical probes

analytical evaluation of the asymptotic impedance matrix of a grounded dielectric slab with roof top functions an analytical technique is derived to solve the asymptotic part of impedance matrix elements for printed circuit structures using roof top subdomain expansions the key to this problem is the analytical transformation from an infinite double integral to a suitable finite one dimensional 1 d integral the newly developed formula is applied to the monostatic radar cross section rcs of a microstrip patch comparisons are made with measurements and conventional method of moments predictions

evaluating infinite integrals involving bessel functions of arbitrary order abstract the evaluation of intergrals of the form i n 0 x j n x d x is considered in the past the method of dividing an oscillatory integral at its zeros forming a sequence of partial sums and using extrapolation to accelerate convergence has been found to be the most efficient technique available where the oscillation is due to a trigonometric function or a bessel function of order n 0 1 here we compare various extrapolation techniques as well as choices of endpoints in dividing the integral and establish the most efficient method for evaluating infinite integrals involving bessel functions of any order n not just zero or one we also outline a simple but very effective technique for calculating bessel function zeros