an augmented electric field integral equation for layered medium green s function this paper proposes an augmented electric field integral equation a efie for layered medium green s function the newly developed matrix friendly formulation of layered medium green s function is applied in this method by separating charge as extra unknown list and enforcing the current continuity equation the traditional efie can be cast into a generalized saddle point system frequency scaling for the matrix friendly formulation is analyzed when frequency tends to zero rank deficiency and the charge neutrality enforcement of the a efie for layered medium green s function is discussed in detail the electrostatic limit of the a efie is also analyzed without any topological loop searching algorithm electrically small conducting structures embedded in a general layered medium can be simulated by using this new a efie formulation several numerical results are presented to validate this method at the end of this paper

feedback capacity of a class of symmetric finite state markov channels we consider the feedback capacity of a class of symmetric finite state markov channels here symmetry termed quasi symmetry is defined as a generalized version of the symmetry defined for discrete memoryless channels the symmetry yields the existence of a hidden markov noise process that depends on the channel s state process and facilitates the channel description as a function of input and noise where the function satisfies a desirable invertibility property we show that feedback does not increase capacity for such class of finite state channels and that both their nonfeedback and feedback capacities are achieved by an independent and uniformly distributed i u d input as a result the channel capacity is explicitly given as a difference of output and noise entropy rates where the output is driven by the i u d input

loop star decomposition of basis functions in the discretization of the efie a general and readily applicable scheme is presented for the determination of the basis functions that allow the decomposition of the surface current into a solenoidal part and a nonsolenoidal remainder the proposed approach brings into correspondence these two parts with two scalar functions and generates the known loop and star basis functions the completeness of the loop star basis is discussed employing the presented scheme the issue of the irrotational property of the nonsolenoidal functions is addressed

a hybrid 2 d 3 d multilevel green s function interpolation method for electrically large multilayered problems the multilevel green s function interpolation method has been implemented to solve the general electrically large multilayered problems a new hybrid 2 d and 3 d h2 d 3 d multilevel interpolation method and a cross level translation scheme are devised for the specific problems from which a quad tree is constructed the interpolation of the multilayered medium green s function using radial basis function is then studied to further accelerate the computation a subdomain fast fourier transform scheme and a sparse approximated inverse preconditioner with a new discarding strategy are also incorporated into the algorithm as numerical examples typical microstrip antenna arrays a metasurface antenna and electromagnetic bandgap integrated antenna arrays are analyzed with the proposed method and excellent performance is observed in both accuracy and efficiency

accurate approximation of green s functions in planar stratified media in terms of a finite sum of spherical and cylindrical waves a robust and computationally expedient methodology is presented for accurate closed form approximation of the green s functions used in the mixed potential integral equation statement of the electromagnetic boundary value problem in planar stratified media the proposed methodology is based on the fitting of the spectrum of the green s function after the extraction of the quasistatic part making use of rational functions the effectiveness and robustness of the proposed methodology rely upon the proper sampling of the spectrum in order to improve the accuracy of the rational function fit the resulting closed form approximation is in terms of both spherical and cylindrical waves thus high accuracy is obtained in the approximation of the green s function irrespective of the distance of the observation point from the source the methodology is validated through its application to the approximation of the green s function for a multi layered planar dielectric stack

jointly optimal lqg quantization and control policies for multi dimensional systems for controlled bbr n valued linear systems driven by gaussian noise under quadratic cost criteria we investigate the existence and the structure of optimal quantization and control policies for fully observed and partially observed systems we establish the global optimality of a class of predictive encoders and show that an optimal quantization policy exists provided that the quantizers allowed are ones which have convex codecells furthermore optimal control policies are linear in the conditional estimate of the state and a form of separation of estimation and control holds

source coding with limited look ahead side information at the decoder we characterize the rate distortion function for the source coding with decoder side information setting when the ith reconstruction symbol is allowed to depend only on the first i lscr side information symbols for some finite look ahead lscr in addition to the index from the encoder for the case of causal side information i e lscr 0 we find that the penalty of causality is the omission of the subtracted mutual information term in the wyner ziv rate distortion function for lscr 0 we derive a computable infinite letter expression for the rate distortion function when specialized to the near lossless case our results characterize the best achievable rate for the slepian wolf source coding problem with finite side information looka head and have some surprising implications we find that side information is useless for any fixed lscr when the joint probability mass function pmf of the source and side information satisfies the positivity condition p x y 0 for all x y more generally the optimal rate depends on the distribution of the pair x y only through the distribution of x and the bipartite graph whose edges represent the pairs x y for which p x y 0 on the other hand if side information look ahead is allowed to grow faster than logarithmic in the block length then h x y is achievable finally we apply our approach to derive a computable expression for channel capacity when state information is available at the encoder with limited look ahead

stochastic nestedness and the belief sharing information pattern solutions to decentralized stochastic optimization problems lead to recursions in which the state space enlarges with the time horizon thus leading to non tractability of classical dynamic programming a common joint information state supplied to each of the agents leads to a tractable recursion as is evident in the one step delayed information sharing structure case or when deterministic nestedness in information holds when there is a causality relationship as in the case of partially nested information structure however communication requirements for such conditions require exchange of very large data noiselessly hence these assumptions are generally impractical in this paper we present a weaker notion of nestedness which we term as stochastic nestedness which is characterized by a sequence of markov chain conditions it is shown that if the information structure is stochastically nested then an optimization problem is tractable and in particular for lqg problems the team optimal solution is linear despite the lack of deterministic nestedness or partial nestedness one other contribution of this paper is that by regarding the multiple decision makers as a single decision maker and using witsenhausen s equivalent model for discrete stochastic control it is shown that the common state required need not consist of observations and it suffices to share beliefs on the state and control actions a pattern we refer to as k stage belief sharing pattern we discuss the minimum amount of information exchange required to achieve such an information pattern for k 1 the information exchange needed is generally strictly less than what is needed for deterministic nestedness and is zero whenever stochastic nestedness applies in view of nestedness we present a discussion on the monotone values of information channels

the discrete fourier transform method of solving differential integral equations in scattering theory an accurate and efficient numerical method is presented for solving many differential integral equations arising from electromagnetic scattering theory it uses the discrete fourier transform technique to treat both the derivatives and the convolution integrals which often appear in these equations as a consequence this method is extremely simple to implement uses less computer memory than comparable methods and yields accurate predictions the differential integral equation is recast into a periodic form conducive to application of the discrete fourier convolution theorem the differential operators are approximated by appropriate finite difference and discrete convolution operators all these quantities are computed by using the fast fourier transform an approximate solution is obtained by using the conjugate gradient method results are compared to experimental data or analytical solutions for a 3 lambda 3 lambda metal plate where lambda is the wavelength a homogeneous and a layered infinite circular dielectric cylinder and a dielectric sphere the accuracy of the method is further illustrated by comparing predictions with independent measurements by r a ross 1966 on a 2 lambda 1 lambda metal plate at grazing incidence in all cases agreement is excellent

an efficient perfectly matched layer based multilevel fast multipole algorithm for large planar microwave structures an efficient multilevel fast multipole algorithm mlfma formalism to model radiation and scattering by from large planar microwave structures is presented the technique relies on an electric field integral equation efie formulation and a series expansion for the green dyadic based on the use of perfectly matched layers pml in this way a new pml mlfma is developed to efficiently evaluate matrix vector multiplications arising in the iterative solution of the scattering problem the computational complexity of the new algorithm scales down to o n for electrically large structures the theory is validated by means of several illustrative numerical examples

a spectral integral method sim for layered media a spectral integral method is presented for electromagnetic scattering from dielectric and perfectly electric conducting pec objects with a closed boundary embedded in a layered medium two dimensional layered medium green s functions are computed adaptively by using gaussian quadratures the singular terms in the green s functions and the non smooth terms in their derivatives are handled appropriately to achieve exponential convergence numerical results compared with the ones obtained by using other methods demonstrate the spectral accuracy and high efficiency of the proposed method they also confirm that the spectral integral method sim is applicable to concave objects

on the gaarder slepian tracking system conjecture source coding the authors examine under what conditions and with what notion of optimality the coder of an optimal system can be operated with the information which is also accessible to the decoder after a discussion of the difficulties involved a theorem is proved for markov sources which states that the extra memory of the coder can be substituted with independent randomization the result is not tied to any specific notion of optimality the main result is shown to hold for markov sources of order k under weak assumptions on the structure and with respect to any per letter fidelity criterion

a fast algorithm to compute the wave scattering solution of a large strip a truncated nonuniform finite array of strips does not have a closed form solution using translational symmetry a recursive algorithm that calculates the scattering solution with n log sup 2 n computational complexity is described first the algorithm is validated with the method of moments for both the tm to z and te to z polarizations then the scattering solution from a large strip is calculated for both te and tm polarizations the current distribution for the te polarization shows small length scale oscillations not present in the tm polarization 26 refs 10 figs

two level hierarchical fem method for modeling passive microwave devices in recent years multigrid methods have been proven to be very efficient for solving large systems of linear equations resulting from the discretization of positive definite differential equations by either the finite difference method or theh version of the finite element method in this paper an iterative method of the multiple level type is proposed for solving systems of algebraic equations which arise from thep version of the finite element analysis applied to indefinite problems a two levelv cycle algorithm has been implemented and studied with a gauss seidel iterative scheme used as a smoother the convergence of the method has been investigated and numerical results for a number of numerical examples are presented

preconditioned electric field integral equation using calderon identities and dual loop star basis functions an analytic preconditioner for the electric field integral equation based on the calderon identities is considered it is shown based on physical reasoning that rwg elements are not suitable for discretizing the electric field integral operator appearing in the preconditioner instead the geometrically dual basis functions proposed by buffa and christiansen are used however it is found that this preconditioner is vulnerable to roundoff errors at low frequencies a loop star decomposition of the buffa christiansen basis functions is presented along with numerical results demonstrating its effectiveness

a fast analysis of scattering and radiation of large microstrip antenna arrays an accurate and efficient method that combines the precorrected fast fourier transform fft method and the discrete complex image method dcim is presented to characterize the scattering and radiation properties of arbitrarily shaped microstrip patch antennas in this method the mixed potential integral equation mpie is discretized in the spatial domain by means of the discrete complex image method the resultant system is solved iteratively using the generalized conjugate residual method gcr and the precorrected fft technique is used to speed up the matrix vector multiplication the precorrected fft eliminates the need to generate and store the usual square impedance matrix and thus leads to a significant reduction in memory requirement and computational cost numerical results are presented for arbitrarily shaped microstrip antenna arrays to demonstrate the accuracy and efficiency of this technique

series representation of green dyadics for layered media using pmls the green dyadics for closed layered media i e layered media bounded by a perfectly conducting plate at the bottom and top of the structure can be expanded in a discrete surface wave series for open layered media with semi infinite layers at the top and or bottom of the structure the discrete series needs to be complemented by a branch cut integral of space waves in this paper we present a technique to circumvent this branch cut integral by truncating the semi infinite layers with a perfectly matched layer pml that is backed by a perfect electric conductor pec it is demonstrated that in this way it is possible to obtain an accurate series or closed form representation for the green dyadic of the open layered medium the series allows a very efficient calculation and storage of the green dyadic if it is needed for multiple observation and or excitation points very close to the source the series loses efficiency it is shown that the determination of the surface waves in the pml truncated layered medium has the same complexity as the determination of the surface waves in a pec truncated layered medium without a pml

a discontinuous galerkin augmented electric field integral equation for multiscale electromagnetic scattering problems a discontinuous galerkin dg augmented electric field integral equation method based on the domain decomposition is proposed in this paper for full wave solution of multiscale targets the conventional surface integral equation based dg method allowing both conformal and nonconformal discretizations for multiscale structures suffers from low frequency breakdown by augmenting the dg efie with current continuity equation the proposed scheme can alleviate the low frequency breakdown in the augmented system the electric field integral equation and the current continuity equation are discretized by using hybrid basis functions including rao wilton glisson rwg and half rwg basis functions since the half rwg basis is not divergence conforming line charge degrees of freedom on the adjoining edges are introduced in this paper it is observed that the resulting linear system is well conditioned at low frequencies which leads to a rapid convergence over wide frequency band numerical examples demonstrate the accuracy and efficiency of the augmented system

comments on application of fft and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies in the original paper ibid vol ap 34 no 5 p 635 40 1986 t k sarkar et al describe how the fast fourier transform fft and the conjugate gradient method cgm can be used to efficiently make use of the convolutional form of the electric field integral equation for straight wire antennas the commentators agree that the cgm converges more rapidly than the previously used method of steepest descent and the spectral iteration technique they also point out that experience with the dyadic green s function encountered in the two dimensional transverse electric te and three dimensional equations for dielectric bodies is not so encouraging it is found that for these cases the cgm convergence can be quite slow degrading the efficiency of the algorithm in addition the solution obtained using the pulse basis point matching method to discretize the integral equation are very inaccurate for the two dimensional te and three dimensional cases a reply to these comments from the authors of the original paper is included

on preconditioning and the eigensystems of electromagnetic radiation problems a formulation of the method of moments mom impedance matrix is presented that facilitates discussion of the behavior of its eigenvalues and eigenvectors this provides insight into the difficulties of producing iterative solutions to electromagnetic radiation problems which typically involve nonuniform meshes based on this analysis a localized self box inclusion sbi preconditioner is developed to overcome the aforementioned issues numerical results are shown using a parallel multilevel fast multipole algorithm mlfma library coupled with an implementation of the sbi preconditioner using these parallel libraries allows the solution of very large problems due to both excessive size and poor conditioning a model of an xm antenna mounted atop an automobile above a very large ground plane establishes the effectiveness of these methods for more than 3 5 million unknowns

a hybrid fem mom method for 3 d electromagnetic scattering in layered medium accurate and efficient prediction of electromagnetic scattering from inhomogeneous objects in layered medium is one of the most challenging issues in engineering applications this paper presents the first 3 d higher order hybrid finite element method fem and method of moments mom for the accurate modeling of inhomogeneous dielectric objects in multilayered medium the main challenges of this paper include 1 the integration of these algorithms for layered medium and 2 the higher order computational approach involved in layered medium for high efficiency in the proposed method the mom with the layered medium dyadic green s function is used as the exact radiation boundary condition in an inhomogeneous background and the fem is applied to model the inhomogeneous objects furthermore the higher order maximally orthogonal basis functions with curl conforming and divergence conforming properties are used in the fem and mom respectively to improve the modeling capability of this algorithm for 3 d inhomogeneous objects scattering in multilayered medium this new method requires a much more tightly truncated simulation domain than the traditional fem and provides much higher flexibility than the pure surface integral equation method finally some numerical results are provided to validate the accuracy efficiency and flexibility of this method

a fast full wave analysis of scattering and radiation from large finite arrays of microstrip antennas a fast full wave analysis technique that can be used to analyze the scattering and radiation from large finite arrays of microstrip antennas is presented the technique discretizes the mixed potential integral equation mpie in the spatial domain by means of a full wave discrete complex image method the del operators on the green s functions are transferred from the singular kernel to the expansion and testing functions the resultant system of equations is solved using the biconjugate gradient bcg method in which the matrix vector product is evaluated efficiently using the fast fourier transform fft this results in an efficient and accurate computation of the scattering and radiation from finite arrays of microstrip antennas several numerical results are presented demonstrating the accuracy efficiency and capability of this technique

a mixed form thin stratified medium fast multipole algorithm for both low and mid frequency problems a mixed form thin stratified medium fast multipole algorithm is proposed for fast simulation of general microstrip structures at both low and mid frequencies the newly developed matrix friendly formula of layered medium green s function is applied in this algorithm for well separated interactions the path deformation technique is implemented to achieve a smoother and exponentially convergent integral the two dimensional addition theorem is then incorporated into the integrand to expedite the matrix vector product in our approach multipole expansion low frequency fast multiple algorithm as well as the plane wave expansion mid frequency fast multipole algorithm of the translational addition theorem are combined into a single multilevel tree to capture quasi static physics and wave physics simultaneously the outgoing wave is represented first in terms of multipole expansion at leafy levels and then switched to plane wave expansion automatically at higher levels this seamless connection makes the algorithm applicable in simulations where subwavelength interaction and wave physics both exist

acceleration of perturbation based electric field integral equations using fast fourier transform in this communication the computation of the perturbation based electric field integral equation of the form r n 1 n 0 1 2 ldots is accelerated by using fast fourier transform fft technique as an effective solution of the low frequency problem the perturbation method employs the taylor expansion of the scalar green s function in free space however multiple impedance matrices have to be solved at different frequency orders and the computational cost becomes extremely high especially for large scale problems since the perturbed kernels still satisfy toeplitz property on the uniform cartesian grid the fft based on lagrange interpolation can be well incorporated to accelerate the multiple matrix vector products because of the nonsingularity property of high order kernels when n geq 1 we do not need to do any near field amendment finally the efficiency of the proposed method is validated in an iterative solver with numerical examples

on the structure of real time encoding and decoding functions in a multiterminal communication system a real time communication system with two encoders communicating with a single receiver over separate noisy channels is considered the two encoders make distinct partial observations of a markov source each encoder must encode its observations into a sequence of discrete symbols the symbols are transmitted over noisy channels to a finite memory receiver that attempts to reconstruct some function of the state of the markov source encoding and decoding must be done in real time that is the distortion measure does not tolerate delays under the assumption that the encoders observations are conditionally independent markov chains given an unobserved time invariant random variable results on the structure of optimal real time encoding and decoding functions are obtained it is shown that there exist finite dimensional sufficient statistics for the encoders the problem with noiseless channels and perfect memory at the receiver is then considered a new methodology to find the structure of optimal real time encoders is employed a sufficient statistic with a time invariant domain is found for this problem this methodology exploits the presence of common information between the encoders and the receiver when communication is over noiseless channels

hierarchical bases preconditioners for the electric field integral equation on multiply connected geometries this paper presents a formulation that allows to use hierarchical basis preconditioners applicable to the electric field integral equation efie on multiply connected geometries without searching for global loops currently available hierarchical basis preconditioners need an explicit representation of global loops finding these requires a computational complexity exceeding the linearithmic complexity of fast matrix vector multiplication methods instead of using an explicit representation of global loops we utilize helmholtz projectors to regularize the efie separately on the solenoidal non solenoidal and harmonic helmholtz subspaces thereby we avoid the explicit recovery of the global loops and maintain the leading complexity of fast multiplication methods numerical results prove the effectiveness of the proposed approach

universal zero delay joint source channel coding we consider zero delay joint source channel coding of individual source sequences for a general known channel given an arbitrary finite set of schemes with finite memory not necessarily time invariant decoders a scheme is devised that does essentially as well as the best in the set on all individual source sequences using this scheme we construct a universal zero delay joint source channel coding scheme that is guaranteed to achieve asymptotically the performance of the best zero delay encoding decoding scheme with a finite state encoder and a markov decoder on all individual sequences for the case where the channel is a discrete memoryless channel dmc we construct an implementable zero delay joint source channel coding scheme that is based on the follow the perturbed leader scheme of gyoumlrgy for lossy source coding of individual sequences our scheme is guaranteed to attain asymptotically the performance of the best in the set of all encoding decoding schemes with a symbol by symbol decoder and arbitrary encoder on all individual sequences

optimal causal coding decoding problems the symbols produced by a finite markov source are causally encoded so as to be transmitted through a noisy memoryless channel the encoder is assumed to have channel feedback information and the decoder to be causal the feedback information is shown to be useful in general separation results are derived and used to prove that encoding is useless for a class of symmetric channels

an impedance boundary condition efie that is low frequency and refinement stable a discretization of the impedance boundary condition electric field integral equation ibc efie is introduced that 1 yields the correct solution at arbitrarily small frequencies and 2 requires for its solution a number of matrix vector products bounded as the frequency tends to zero and as the mesh density increases the low frequency stabilization is based on a projector based discrete helmholtz splitting rescaling and recombination that depends on the low frequency behavior of both the efie operator and the surface impedance condition the dense mesh stabilization is a modification of the perfect electric conductor operator preconditioning approach taking into account the effect on the singular value spectrum of the ibc term

a quasi 3d thin stratified medium fast multipole algorithm for microstrip structures an accurate and efficient full wave simulation method is proposed for general microstrip structures it is called the quasi 3d thin stratified medium fast multipole algorithm tsm fma different from the 2d tsm fma method it is constructed on a vector wave function based dyadic green s function for layered medium dglm instead of the symmetric form dglm this new form of dglm is represented in terms of only two sommerfeld integrals and is suitable for developing fast algorithm in quasi 3d cases similar to the 2d tsm fma the path deformation technique and the multipole based acceleration is used to transform the sommerfeld integral and expedite the matrix vector multiplication the computational time per iteration and the memory requirement is o nlogn in the quasi 3d tsm fma it is suitable to perform a full wave analysis of a large microstrip array with less computational resource

hierarchical bases for nonhierarchic 3 d triangular meshes we describe a novel basis of hierarchical multiscale functions that are linear combinations of standard rao wilton glisson rwg functions when the basis is used for discretizing the electric field integral equation efie for pec objects it gives rise to a linear system immune from low frequency breakdown and well conditioned for dense meshes the proposed scheme can be applied to any mesh with triangular facets and therefore it can be used as if it were an algebraic preconditioner the properties of the new system are confirmed by numerical results that show fast convergence rates of iterative solvers significantly better than those for the loop tree basis as a byproduct of the basis generation a generalization of the rwg functions to nonsimplex cells is introduced

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

a newly developed formulation suitable for matrix manipulation of layered medium green s functions based on a recently developed formulation of the dyadic green s function for layered media dglm this work gives the matrix element representation of the dglm for general rwg basis functions including basis functions straddling across different layers and half rwg basis function attached to an infinite ground plane it has been rigorously proved that this representation is absent of any undesired line integrals the same as the popular michalski zheng s formulation of type c this work also gives the analytical solution for some typical cylindrically symmetric problems which can be used to validate any formulation for layered medium problems

on a low frequency and refinement stable pmchwt integral equation leveraging the quasi helmholtz projectors classical poggio miller chan harrington wu tsai pmchwt formulations for modeling radiation and scattering from penetrable objects suffer from ill conditioning when the frequency is low or when the mesh density is high the most effective techniques to solve these problems unfortunately either require the explicit detection of the so called global loops of the structure or suffer from numerical cancellation at extremely low frequency in this contribution a novel regularization method for the pmchwt equation is proposed which is based on the quasi helmholtz projectors this method not only solves both the low frequency and the dense mesh ill conditioning problems of the pmchwt but it is immune from low frequency numerical cancellations and it does not require the detection of global loops this is obtained by projecting the range space of the pmchwt operator onto a dual basis by rescaling the resulting quasi helmholtz components by replicating the strategy in the dual space and finally by combining the primal and the dual equations in a calderon like fashion implementation related treatments and details alternate the theoretical developments in order to maximize impact and practical applicability of the approach finally numerical results corroborate the theory and show the effectiveness of the new schemes in real case scenarios

higher order interpolatory vector bases for computational electromagnetics low order vector basis functions compatible with the nedelec 1980 representations are widely used for electromagnetic field problems higher order functions are receiving wider application but their development is hampered by the complex procedures used to generate them and lack of a consistent notation for both elements and bases in this paper fully interpolatory higher order vector basis functions of the nedelec type are defined in a unified and consistent manner for the most common element shapes it is shown that these functions can be obtained as the product of zeroth order nedelec representations and interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties of the vector functions are discussed and expressions for the vector functions of arbitrary polynomial order are presented sample numerical results confirm the faster convergence of the higher order functions

method of analytical regularization in the analysis of axially symmetric excitation of imperfect circular disk antennas abstract this work presents accurate numerical method and computational results in the modeling of the axisymmetric radiation of resistive and thin dielectric circular disk on substrate antennas to simulate resistive and thin dielectric disk features we use two side generalized boundary conditions gbc the analysis is based on the singular integral equations ies and the method of analytical regularization mar exploiting a galerkin method gm with judicious basis functions which convert ies into the fredholm second kind infinite matrix equations unlike previously known numerical techniques this guarantees convergence and enables us to compute the solution with controlled accuracy even in sharp resonances numerical results demonstrate the effect of disk losses and transparency on the fundamental radiation phenomena and help improve antenna characteristics such as radiation efficiency

fast frequency sweep using asymptotic waveform evaluation technique and thin dielectric sheet approximation the thin dielectric sheet tds surface integral equation sie combined with the asymptotic waveform evaluation awe technique is proposed to efficiently analyze wideband properties of thin dielectric layers such as radome and composite materials the tds sie is an efficient method for analyzing the thin dielectric layer because the number of unknowns of the tds sie is fewer than that of the volume integral equation vie and the condition number of the tds impedance matrix is small in addition the awe technique based on a taylor series and the pade approximation is a well known method for fast frequency sweep therefore the combination of these two methods makes analysis of the thin dielectric layer efficient in the wide frequency region because the advantages of each method are shown at the same time in order to determine the valid bandwidth of the approximated results for arbitrary problems using the tds combined with the awe the bandwidth estimation approach for the awe is applied the results of the proposed method for closed and open structures agree very well with the exact solutions and reveal the capability for fast frequency sweep

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

real time coding with limited lookahead a real time coding system with lookahead consists of a memoryless source a memoryless channel an encoder which encodes the source symbols sequentially with knowledge of future source symbols up to a fixed finite lookahead d with or without feedback of the past channel output symbols and a decoder which sequentially constructs the source symbols using the channel output the objective is to minimize the expected per symbol distortion for a fixed finite lookahead d 1 we invoke the theory of controlled markov chains to obtain an average cost optimality equation acoe the solution of which denoted by d d is the minimum expected per symbol distortion with increasing d d d bridges the gap between causal encoding d 0 where symbol by symbol encoding decoding is optimal and the infinite lookahead case d where shannon theoretic arguments show that separation is optimal we extend the analysis to a system with finite state decoders with or without noise free feedback for a bernoulli source and binary symmetric channel under hamming loss we compute the optimal distortion for various source and channel parameters and thus obtain computable bounds on d d we also identify regions of source and channel parameters where symbol by symbol encoding decoding is suboptimal finally we demonstrate the wide applicability of our approach by applying it in additional coding scenarios such as the case where the sequential decoder can take cost constrained actions affecting the quality or availability of side information about the source

the black box fast multipole method a new o n fast multipole formulation is proposed for non oscillatory kernels this algorithm is applicable to kernels k x y which are only known numerically that is their numerical value can be obtained for any x y this is quite different from many fast multipole methods which depend on analytical expansions of the far field behavior of k for x y large other black box or kernel independent fast multipole methods have been devised our approach has the advantage of requiring a small pre computation time even for very large systems and uses the minimal number of coefficients to represent the far field for a given l 2 tolerance error in the approximation this technique can be very useful for problems where the kernel is known analytically but is quite complicated or for kernels which are defined purely numerically

on optimal causal coding of partially observed markov sources in single and multiterminal settings the optimal causal zero delay coding of a partially observed markov process is studied where the cost to be minimized is a bounded nonnegative additive measurable single letter function of the source and the receiver output a structural result is obtained extending witsenhausen s and walrand varaiya s structural results on optimal causal coders to more general state spaces and to a partially observed setting the decentralized multiterminal setup is also considered for the case where the source is an i i d process it is shown that an optimal solution to the decentralized causal coding of correlated observations problem is memoryless for markov sources a counterexample to a natural separation conjecture is presented

two dimensional discrete complex image method dcim for closed form green s function of arbitrary 3d structures in general multilayered media the traditional discrete complex image method dcim is not efficient when the source and field points are in different layers because all the spatial coordinates can not be analytically included in the image terms in spatial domain a two dimensional method 2d dcim is introduced in this paper in the new methodology we reorganize the spectral kernel as a 2d function we use the 2d matrix pencil method 2d mpm to fit this 2d function and to generate a set of complex images independent of any spatial coordinates the closed form spatial domain green s function can be obtained for arbitrary locations of source and field points in general multilayered media compared with traditional 1d dcim we do not have to run mpm for each vertical combination of source and field points the efficiency of the matrix filling kernel of method of moments mom is significantly improved

structure theorems for real time variable rate coding with and without side information the output of a discrete markov source is to be encoded instantaneously by a variable rate encoder and decoded by a finite state decoder our performance measure is a linear combination of the distortion and the instantaneous rate structure theorems pertaining to the encoder and next state functions are derived for every given finite state decoder which can have access to side information

a multiresolution system of rao wilton glisson functions a multiresolution mr basis is described for the method of moments mom analysis of a generic 3 d conductor discretized with triangular cells the mr basis functions are constructed as linear combination of rao wilton glisson rwg basis functions thus allowing direct applicability on existing mom codes with respect to previous work by the authors the generation of the mr functions is significantly simplified yet keeping similar applicability and performance in terms of conditioning of the mom matrix convergence of the iterative solvers and possibility of sparsifying the mom matrix by clipping moreover with the proposed basis the basis change matrix from rwg to mr is highly sparse at all levels this allows a more efficient generation of the mr mom matrix

fast analysis of large antenna arrays using the characteristic basis function method and the adaptive cross approximation algorithm the characteristic basis function method cbfm has been hybridized with the adaptive cross approximation aca algorithm to construct a reduced matrix equation in a time efficient manner and to solve electrically large antenna array problems in core with a solve time orders of magnitude less than those in the conventional methods various numerical examples are presented that demonstrate that the proposed method has a very good accuracy computational efficiency and reduced memory storage requirement specifically we analyze large 1 d and 2 d arrays of electrically interconnected tapered slot antennas tsas the entire computational domain is subdivided into many smaller subdomains each of which supports a set of characteristic basis functions cbfs we also present a novel scheme for generating the cbfs that do not conform to the edge condition at the truncated edge of each subdomain and provide a minor overlap between the cbfs in adjacent subdomains as a result the cbfs preserve the continuity of the surface current across the subdomain interfaces thereby circumventing the need to use separate ldquoconnectionrdquo basis functions

thin dielectric sheet simulation by surface integral equation using modified rwg and pulse bases the conventional thin dielectric sheet surface integral equation proposed by harrington and mautz is reviewed due to its simplicity and inadequency for certain problems a new surface integral equation is proposed to fill the gap this new formulation takes both tangential and normal currents into account so that it can handle problems with high and low permittivity and grazing incident waves based on the d field formulation inhomogeneity and surface charge can be treated correctly modelling the geometry by triangles this surface integral equation is discretized and is suitable for the method of moments to solve rao wilson glisson and pulse functions are employed simultaneously for basis and testing functions and so the moment solution has full descriptions of polarization current in the thin dielectric layer several examples are examined by both analytical and other published numerical methods these results show excellent agreement and demonstrate the validity and effectiveness of this new integral equation

a single level low rank ie qr algorithm for pec scattering problems using efie formulation this paper presents a single level matrix compression algorithm termed ie qr based on a low rank approximation to speed up the electric field integral equation efie formulation it is shown with the number of groups chosen to be proportional to n sup 1 2 where n is the number of unknowns the memory and cpu time for the resulting algorithm are both o n sup 1 5 the unique features of the algorithm are a the ie qr algorithm is based on the near rank deficiency property for well separated groups this near rank deficiency assumption holds true for many integral equation methods such as laplacian radiation and scattering problems in electromagnetics em the same algorithm can be adapted to other applications outside em with few or no modifications and b the rank estimation is achieved by a dual rank process which ranks the transmitting and receiving groups respectively thus the ie qr algorithm can achieve matrix compression without assembling the entire system matrix also a geometric neighboring preconditioner is presented in this paper this geometric neighboring preconditioner when used in conjunction with gmres is proven to be both efficient and effective for solving the compressed matrix equations

a multiresolution curvilinear rao wilton glisson basis function for fast analysis of electromagnetic scattering a new set of multiresolution curvilinear rao wilton glisson mr crwg basis functions is proposed for the method of moments mom solution of integral equations for three dimensional 3 d electromagnetic em problems the mr crwg basis functions are constructed as linear combinations of curvilinear rao wilton glisson crwg basis functions which are defined over curvilinear triangular patches thus allowing direct application on the existing mom codes that using crwg basis the multiresolution property of the mr crwg basis can lead to the fast convergence of iterative solvers merely by a simple diagonal preconditioning to the corresponding mom matrices moreover the convergence of iterative solvers can be further improved by introducing a perturbation from the principle value term of the magnetic field integral equation mfie operator to construct diagonal preconditioners for efficient iterative solution of the electric field integral equation efie another important property of the mr crwg basis is that the mom matrices using the mr crwg basis can be highly sparsified without loss of accuracy the mr crwg basis has been applied to the 3 d electromagnetic scattering problems and the numerical results indicate that the mr crwg basis performs much better than the crwg basis

dual gpof dcim for fast computation of sommerfeld integrals and em scattering from an object partially embedded in dielectric half space a novel approach of dual gpof general pencil of functions combined with the dcim the discrete complex image method is developed to accelerate the sommerfeld integral evaluation when the mixed potential integral equation mpie is applied to numerically calculate scattering from a conductive object partially embedded in a dielectric half space where the field and source points are located in different media firstly the factors related with the field point are separated from the spectrum function and the gpof is used to find the complex image parameters at finite discrete source points secondly the gpof is used again to fit the functional relationship of each complex image parameter with the source positions to evaluate the complex image parameters for any source position in a closed functional summation comparing numerical results of dual gpof and direct numerical integration this dual gpof process is proved highly effective finally dual gpof dcim is applied to computation of electromagnetic scattering from a pec spherical object partially embedded in a dielectric half space medium and numerical scattering results upon different model parameters are presented and analyzed

fast full wave surface integral equation solver for multiscale structure modeling we describe a full wave solver to model large scale and complex multiscale structures it uses the augmented electric field integral equation a efie which includes both the charge and the current as unknowns to avoid the imbalance between the vector potential and the scalar potential in the conventional efie the formulation proves to be stable in the low frequency regime with the appropriate frequency scaling and the enforcement of charge neutrality to conquer large scale and complex problems we solve the equation using iterative methods design an efficient constraint preconditioning and employ the mixed form fast multipole algorithm fma to accelerate the matrix vector product numerical tests on various examples show high accuracy and fast convergence at last complex interconnect and packaging problems with over one million integral equation unknowns can be solved without the help of a parallel computer

a combined full wave cg fft method for rigorous analysis of large microstrip antenna arrays an accurate and efficient technique is presented for the analysis of large microstrip antenna arrays the technique consists of an amalgamation of a spatially discrete scheme consisting of the cg fft method and the complex discrete image cdi technique the unique feature of this approach is the use of the spatially discrete cg fft for analyzing microstrip structures the aliasing and truncation errors are thoroughly eliminated in this approach in addition the grad div operators are transformed from singular green s functions to differentiable expansion and testing functions by using galerkin s procedure thereby improving the accuracy and the rate of convergence to show the accuracy and efficiency of this technique a number of microstrip arrays including a large microstrip reflectarray have been studied it is found that the simulations carried out using this technique are in very good agreement with measurements

optimal zero delay coding of markov sources stationary and finite memory codes the optimal zero delay coding of a finite state markov source is considered the existence and structure of optimal codes are studied using a stochastic control formulation prior results in the literature established the optimality of deterministic markov walrand varaiya type coding policies for the finite time horizon problem and the optimality of both deterministic nonstationary and randomized stationary policies for the infinite time horizon problem our main result here shows that for any irreducible and aperiodic markov source with a finite alphabet deterministic and stationary markov coding policies are optimal for the infinite horizon problem in addition the finite block length time horizon performance of an optimal stationary and markov coding policy is shown to approach the infinite time horizon optimum at a rate o 1 t the results are extended to systems where zero delay communication takes place across a noisy channel with noiseless feedback

on causal source codes with side information we study the effect of the introduction of side information into the causal source coding setting of neuhoff and gilbert we find that the spirit of their result namely the sufficiency of time sharing scalar quantizers followed by appropriate lossless coding for attaining optimum performance within the family of causal source codes extends to many scenarios involving availability of side information at both encoder and decoder or only on one side for example in the case where side information is available at both encoder and decoder we find that time sharing side information dependent scalar quantizers at most two for each side information symbol attains optimum performance this remains true even when the reproduction sequence is allowed noncausal dependence on the side information and even for the case where the source and the side information rather than consisting of independent and identically distributed i i d pairs form respectively the output of a memoryless channel and its stationary ergodic input

loop star basis functions and a robust preconditioner for efie scattering problems an electric field integral equation efie formulation using the loop star basis functions has been developed for modeling plane wave scattering from perfect conducting objects a stability analysis at the dc limit shows that the use of the rao wilton glisson rwg basis functions results in a singular matrix operator however the use of the loop star basis functions results in a well conditioned matrix moreover a preconditioner constructed from a two step process based on near interactions and an incomplete factorization with a heuristic drop strategy has been proposed in conjunction with the conjugate gradient method to solve the resulting matrix equation the approach is shown to be effective for resolving both the low frequency instability and the bad conditioning of the efie method the computational complexity of the proposed approach is shown to be o n sup 2

loop star and loop tree decompositions analysis and efficient algorithms a new analysis of the spectral properties of loop star and loop tree decompositions is presented in this work the analysis will shed light on the behavior of these decompositions when used with regular operators such as the magnetic field and the calderon preconditioned electric field integral operators this work will explain the ill conditioning problems reported in literature and will provide a family of efficient algorithms to solve the ill conditioning and regularizing several loop star tree decomposed equations of interest for applications the theory will be corroborated by numerical results that will show the practical impact of the theoretical developments

a high performance upgrade of the perfectly matched layer multilevel fast multipole algorithm for large planar microwave structures an improvement of the perfectly matched layer multilevel fast multipole algorithm pml mlfma for simulating large planar microwave structures is presented by exploiting the low rank property of the pml mlfma multimodal aggregation and disaggregation matrices considerable reductions in memory usage and computation time are obtained the method has been extensively validated demonstrating complete error controllability when simulating large planar microwave structures reductions in memory requirements and cpu time of more than 60 and 40 have been achieved

optimal linear joint source channel coding with delay constraint the problem of joint source channel coding is considered for a stationary remote noisy gaussian source and a gaussian channel the encoder and decoder are assumed to be causal and their combined operations are subject to a delay constraint it is shown that under the mean square error distortion metric an optimal encoder decoder pair from the linear and time invariant lti class can be found by minimization of a convex functional and a spectral factorization the functional to be minimized is the sum of the well known cost in a corresponding wiener filter problem and a new term which is induced by the channel noise and whose coefficient is the inverse of the channel s signal to noise ratio this result is shown to also hold in the case of vector valued signals assuming parallel additive white gaussian noise channels it is also shown that optimal lti encoders and decoders generally require infinite memory which implies that approximations are necessary a numerical example is provided which compares the performance to the lower bound provided by rate distortion theory less

on optimal zero delay coding of vector markov sources optimal zero delay coding quantization of a vector valued markov source driven by a noise process is consid ered using a stochastic control problem formulation the exis tence and structure of optimal quantization policies are studied for a finite horizon problem with bounded per stage distortion measure the existence of an optimal zero delay quantization policy is shown provided that the quantizers allowed are ones with convex codecells the bounded distortion assumption is relaxed to cover cases that include the linear quadratic gaussian problem for the infinite horizon problem and a stationary markov source the optimality of deterministic markov coding policies is shown the existence of optimal stationary markov quantization policies is also shown provided randomization that is shared by the encoder and the decoder is allowed

a new encoder for continuous time gaussian signals with fixed rate and reconstruction delay in this paper we propose a method for encoding continuous time gaussian signals subject to a usual data rate constraint and more importantly a reconstruction delay constraint we first apply a karhunen loeve decomposition to reparameterize the continuous time signal as a discrete sequence of vectors we then study the optimal recursive quantization of this sequence of vectors since the optimal scheme turns out to have a very cumbersome design we consider a simplified method for which a numerical example suggests that the incurred performance loss is negligible in this simplified method we first build a state space model for the vector sequence and then use bayesian tracking to sequentially encode each vector the tracking task is performed using particle filtering numerical experiments show that the proposed approach offers visible advantages over other available approaches especially when the reconstruction delay is small

on a well conditioned electric field integral operator for multiply connected geometries all known integral equation techniques for simulating scattering and radiation from arbitrarily shaped perfect electrically conducting objects suffer from one or more of the following shortcomings i they give rise to ill conditioned systems when the frequency is low ii and or when the discretization density is high iii their applicability is limited to the quasi static regime iv they require a search for global topological loops v they suffer from numerical cancellations in the solution when the frequency is very low this work presents an equation that does not suffer from any of the above drawbacks when applied to smooth and closed objects the new formulation is obtained starting from a helmholtz decomposition of two discretizations of the electric field integral operator obtained by using rwgs and dual bases respectively the new decomposition does not leverage loop and star tree basis functions but projectors that derive from them following the decomposition the two discretizations are combined in a calderon like fashion resulting in a new overall equation that is shown to exhibit self regularizing properties without suffering from the limitations of existing formulations numerical results show the usefulness of the proposed method both for closed and open structures

fast solution methods in electromagnetics various methods for efficiently solving electromagnetic problems are presented electromagnetic scattering problems can be roughly classified into surface and volume problems while fast methods are either differential or integral equation based the resultant systems of linear equations are either solved directly or iteratively a review of various differential equation solvers their complexities and memory requirements is given the issues of grid dispersion and hybridization with integral equation solvers are discussed several fast integral equation solvers for surface and volume scatterers are presented these solvers have reduced computational complexities and memory requirements

a single level dual rank ie qr algorithm to model large microstrip antenna arrays a single level dual rank ie qr algorithm is introduced so that the resulting dense method of moments mom matrix is efficiently compressed for a system of n equations an amount of work of the order o n sup 2 has traditionally been required for both matrix assembly and matrix vector multiplication in an iterative matrix solver the algorithm of the present paper reduces the memory requirement and cpu time for both matrix assembly and matrix vector multiplication to o n sup 3 2 making it practical to solve for large antenna arrays with full wave approach in conjunction with a geometric neighboring preconditioner for matrix solution using gmres the current approach solves problems involving large antenna arrays using only a fraction of what are needed by conventional mom both in term of memory and total cpu time

numerical analysis of large scale finite periodic arrays using a macro block characteristic basis function method numerical analysis of a large scale finite periodic array is accurate but quite costly when the array is analyzed as a finite array the computational cost for the numerical analysis can be reduced greatly when the array is approximated as an infinite periodic structure however the edge effect that strongly affects the active impedance or current distribution of the array elements near the edge is neglected in this paper a macro block characteristic basis function method mb cbfm for numerical analysis of a large scale finite periodic array with a uniform amplitude and linear phased excitation is proposed the mb cbfm utilizes blocks and macro blocks to group the elements in order to reduce its computational cost without degrading accuracy numerical simulations demonstrate that the cpu time and computer memory of the mb cbfm are o n when the size of array is sufficiently large

a kernel independent adaptive fast multipole algorithm in two and three dimensions we present a new fast multipole method for particle simulations the main feature of our algorithm is that it does not require the implementation of multipole expansions of the underlying kernel and it is based only on kernel evaluations instead of using analytic expansions to represent the potential generated by sources inside a box of the hierarchical fmm tree we use a continuous distribution of an equivalent density on a surface enclosing the box to find this equivalent density we match its potential to the potential of the original sources at a surface in the far field by solving local dirichlet type boundary value problems the far field evaluations are sparsified with singular value decomposition in 2d or fast fourier transforms in 3d we have tested the new method on the single and double layer operators for the laplacian the modified laplacian the stokes the modified stokes the navier and the modified navier operators in two and three dimensions our numerical results indicate that our method compares very well with the best known implementations of the analytic fmm method for both the laplacian and modified laplacian kernels its advantage is the relative simplicity of the implementation and its immediate extension to more general kernels

a dc stable and large time step well balanced td efie based on quasi helmholtz projectors the marching on in time mot solution of the time domain electric field integral equation td efie has traditionally suffered from a number of issues including the emergence of spurious static currents dc instability and ill conditioning at large time steps low frequencies in this contribution a space time galerkin discretization of the td efie is proposed which separates the loop and star components of both the equation and the unknown judiciously integrating or differentiating these components with respect to time leads to an equation which is free from dc instability by choosing the correct temporal basis and testing functions for each of the components a stable mot system is obtained furthermore the scaling of these basis and testing functions ensure that the system remains well conditioned for large time steps the loop star decomposition is performed using quasi helmholtz projectors to avoid the explicit transformation to the unstable bases of loops and stars or trees and to avoid the search for global loops which is a computationally expensive operation

on the structure of optimal real time encoders and decoders in noisy communication the output of a discrete time markov source must be encoded into a sequence of discrete variables the encoded sequence is transmitted through a noisy channel to a receiver that must attempt to reproduce reliably the source sequence encoding and decoding must be done in real time and the distortion measure does not tolerate delays the structure of real time encoding and decoding strategies that jointly minimize an average distortion measure over a finite horizon is determined the results are extended to the real time broadcast problem and a real time variation of the wyner ziv problem

a mixed form fast multipole algorithm the fast multipole algorithm manifests in two very different forms at low frequencies and at mid frequencies each can operate in their respective regimes but are not tenable in the other regimes the paper reports on a way to factorize the green s function for fast algorithm using a mixed form the low frequency fast multipole algorithm lf fma will be used at low frequencies or the long wavelength regime and the multilevel fast multipole algorithm mlfma will be used for the mid frequencies or the shorter wavelength regime for object modeling where both long wavelength and wave physics are important we propose a mixed form fast multipole algorithm mf fma this algorithm has no low frequency break down and it can work seamlessly from static where circuit physics is important to dynamic where wave physics is important

zeroth order complete discretizations of integral equation formulations involving conducting or dielectric objects at very low frequencies we present the self loop basis functions a divergence conforming set with zero charge density these basis functions allow a rearrangement of the linear linear basis functions set to overcome the low frequency breakdown we show the accuracy and stability at very low frequencies of the linear linear discretizations of i electric field integral equation for perfectly conducting objects and ii the poggio miller chang harrington wu tsai formulation for dielectric bodies

a surface integral formulation of maxwell equations for topologically complex conducting domains a general and effective method is presented to numerically solve the electric field integral equation efie for topologically complex conducting domains by the finite element method a new technique is proposed to decompose the surface current density into a solenoidal part and a nonsolenoidal remainder to avoid the low frequency breakdown the surface current density field is approximated through div conforming facet elements the solenoidal part is represented through the null space of the discrete approximation d of the surface divergence operator in the subspace spanned by the facet elements whereas the nonsolenoidal remainder is represented through its complement the basis functions of the null space and its complement are evaluated respectively by the null and pseudo inverse of the matrix d the completeness of the null pinv basis functions is studied unlike the loop star and loop tree basis functions the null pinv basis functions allow to deal with topologically complex conducting domains in a general and readily applicable way a topological interpretation of the null pinv decomposition is given and a general and simple method to evaluate the null and pseudo inverse of d is proposed the computational complexity of the proposed method is discussed

optimal design of sequential real time communication systems optimal design of sequential real time communication of a markov source over a noisy channel is investigated in such a system the delay between the source output and its reconstruction at the receiver should equal a fixed prespecified amount an optimal communication strategy must minimize the total expected symbol by symbol distortion between the source output and its reconstruction design techniques or performance bounds for such real time communication systems are unknown in this paper a systematic methodology based on the concepts of information structures and information states to search for an optimal real time communication strategy is presented this methodology trades off complexity in communication length linear in contrast to doubly exponential with complexity in alphabet sizes doubly exponential in contrast to exponential as the communication length is usually order of magnitudes bigger than the alphabet sizes the proposed methodology simplifies the search for an optimal communication strategy in spite of this simplification the resultant optimality equations cannot be solved efficiently using existing algorithmic techniques the main idea is to formulate a zero delay communication problem as a dynamic team with nonclassical information structure then an appropriate choice of information states converts the dynamic team problem into a centralized stochastic control problem in function space thereafter markov decision theory is used to derive nested optimality equations for choosing an optimal design for infinite horizon problems these optimality equations give rise to a fixed point functional equation communication systems with fixed finite delay constraint a higher order markov source and channels with memory are treated in the same manner after an appropriate expansion of the state space thus this paper presents a comprehensive methodology to study different variations of real time communication

connected patch array analysis using the characteristic basis function method the characteristic basis function method cbfm is extended to apply to efficient analysis of dual polarized connected patch arrays where neighboring patches are connected via two wire transmission lines and a groundplane comparison with a reference solution shows that the use of tertiary basis functions can significantly improve the cbfm approximation to the array currents and radiation patterns a simple procedure for estimating the error in the cbfm current is shown to produce good approximations to the true error and therefore may be useful more generally in determining suitable parameters of the cbfm basis the technique is applied to a prototype phased array feed for a next generation radio telescope a thin dielectric supporting the array patches is shown to produce a loading effect that modifies the radiation patterns good agreement with the results of other techniques and measured data has been obtained

on the existence of branch points in the eigenvalues of the electric field integral equation operator in the complex frequency plane it is demonstrated by specific examples that eigenvalues of the electric field integral equation efie operator for finite extent objects in lossless media can have branch points in the complex frequency s plane specifically it is shown from the analysis of the spheroidal wave equation in the s plane that branch points are present in the eigenvalues of the integral operator associated with the scalar scattering problem from a perfectly conducting spheroid similarly it is concluded from the analysis of the mathieu s differential equation that branch points besides that associated with the infinite extent of the object exist in the s plane behavior of the eigenvalues of the efie operator for a perfectly conducting infinite elliptic cylinder a proof is given that branch point singularities cannot occur in the eigenvalues of efie operators for structures in which geometrical symmetry completely determines the eigenfunctions and hence they are frequency independent it is conjectured that branch points may always be present when sufficient object symmetry is lacking this conjecture is supported by the fact that branch points appear when a sphere is deformed into a spheroid or when a circular cylinder is deformed into an elliptic one an analogous phenomenon has been observed in circuit and transmission line problems for example it is shown that when the taper parameter of an exponential transmission line goes to zero the line becomes uniform and thus a symmetrical structure the branch points in the eigenvalues of the impedance matrix move away to infinity

a new green s function formulation for modeling homogeneous objects in layered medium a new green s function formulation is developed systematically for modeling general homogeneous dielectric or magnetic objects in a layered medium the dyadic form of the green s function is first derived based on the pilot vector potential approach the matrix representation in the moment method implementation is then derived by applying integration by parts and vector identities the line integral issue in the matrix representation is investigated based on the continuity property of the propagation factor and the consistency of the primary term and the secondary term the extinction theorem is then revisited in the inhomogeneous background and a surface integral equation for general homogeneous objects is set up different from the popular mixed potential integral equation formulation this method avoids the artificial definition of scalar potential the singularity of the matrix representation of the green s function can be made as weak as possible several numerical results are demonstrated to validate the formulation developed in this paper finally the duality principle of the layered medium green s function is discussed in the appendix to make the formulation succinct