a method to extend the spectral iteration technique a method has been developed to extend the spectral iteration technique to encompass a more general class of subdomain type basis functions while retaining the advantages of the spectral iteration technique this method enables the usage of basis functions other than piecewise constant basis functions in expressing the unknown current distribution advantages of this technique with the choice of piecewise sinusoidal basis functions as compared to piecewise constant basis functions have been demonstrated for both antenna and scattering problems this choice of basis functions is found to result in a further reduction in the number of unknowns required to represent the current distribution numerical results of the input impedance for a cylindrical antenna and the scattering cross section of a thin fiat plate are presented and discussed

two dimensional scattering from an inhomogeneous dielectric cylinder embedded in a stratified medium case of tm polarization two dimensional scattering of a tm polarized electromagnetic wave from a transversely inhomogeneous isotropic body buried in a homogeneous layer of an arbitrarily stratified isotropic medium has been considered using the integral equation formulation over the cross section of the body and the moment method the arising system of linear algebraic equations is solved with the aid of the conjugate gradient method and the one dimensional fast fourier transform illustrative numerical results are presented for both an inclusion in a half space and in a layer on a homogeneous substrate

diffraction by an arbitrary angled dielectric wedge ii correction to physical optics solution for pt i see ibid vol 39 no 9 p 1272 81 1991 the error of the physical optics solution for the e polarized plane wave incidence in connection with diffraction by an arbitrary angled dielectric wedge is corrected by calculating the nonuniform current distributed along the dielectric interfaces two kinds of series expansions to the nonuniform current are employed one is an asymptotic expansion as the multipole line source located at the edge of the dielectric wedge since the correction field seems to be a cylindrical wave emanating from the edge in the far field region the other is arbitrary electric and magnetic surface currents expanded by infinite series of the bessel functions i e the neumann expansion of which fractional order is chosen to satisfy the edge condition near the edge of the dielectric wedge in the static limit both of the two different expansion coefficients for a wedge angle of 45 degrees relative dielectric constants 2 10 and 100 and the e polarized incident angle of 150 degrees are evaluated by solving the dual series equation numerically after finite truncation

reduction of the number of unknowns in large stacked planar structures by a fringe aperture formulation for scattering problems comprising a combination of planar structures the total number of unknowns may be significantly reduced if an aperture formulation is employed rather than a patch formulation the rationale behind using the aperture formulation is based on the recognition that the decay rate of the scattered aperture field is independent of the size of the scatterer therefore any scatterer may be surrounded by an aperture of fixed width over which an integral equation is formulated the area of this aperture is proportional to the perimeter of the scatterer rather than its area and it becomes much smaller compared with the entire scatterer area as the size of the scatterer increases hence the reduction in the number of independent unknowns a truncation criterion for the finite aperture is determined via a numerical study of the aperture field behavior for various angles of incidence in addition the a priori knowledge of the physical optics component is also taken into account reducing the unknown function to an aperture field component that is the outcome of the remaining fringe current only the total current distribution can be subsequently derived from this field by adding the known physical optics field and invoking the inverse of the green s function in the spectral domain this analysis of isolated planar scatterers results in a spectral scattering matrix representation that is subsequently used for cascading of stacked structures

green s function for the harmonic potential of the three dimensional wedge transmission problem the point source static potential in a wedge geometry consisting of two homogeneous media is solved via the kontorovich lebedev and fourier transforms inverse transforms enable the solution of laplace s equation to be expressed in terms of image contributions plus residue sums fourier series of toroidal functions as in previous wave equation solutions for isovelocity wedges explicit expressions for the poles that are the site of the residues are exploited when the wedge angle is a rational multiple of spl pi

on the singularity of the full spectral green s dyad the full 3 times 3 spectral dyadic green s function exhibits certain properties that its popular 2 times 2 transversal portion does not in particular it is shown that the dyad is identically singular the singularity being a manifestation of the plane wave properties of each spectral component this singularity has an impact on the use of certain computational algorithms which in general would require an inversion of the dyad other plane wave properties being dual to maxwell s equations are also discussed

summed squared distance error reduction by simultaneous multiprojections and applications a parallel projection scheme in which projections are performed simultaneously on all constraints at each iteration is presented it is a multiprojections scheme because different distance functions can be minimized for each projection as long as they are based on weighted l 2 norms the use of multiple distance functions enables simplifications of the various projection operations leading to an efficient implementation of this algorithm this is true especially for constrained deconvolution type problems due to the inherent parallelism of the algorithm projections onto more than two sets can be performed even if one or more of the sets are nonconvex maintaining a monotone decrease of a cost functional with no further restrictions this is in contrast to the serial projections onto convex sets pocs algorithm where no more than two sets can be treated if one of the sets is nonconvex our method is a special case of a multiprojections method proposed by censor and elfving where generalized distance functions of the bregman type are used the restriction to weighted l 2 norms leads to a simple and explicit form of this algorithm and allows relaxation and the use of nonconvex sets

numerical analysis of quasioptical multireflector antennas in 2 d with the method of discrete singularities e wave case numerical method for modeling the e polarized wave scattering by electrically large quasioptical two dimensional 2 d reflectors is presented reflectors are assumed zero thickness and perfectly electrically conducting efficient numerical solution is obtained from the coupled singular integral equations discretized using new quadrature formulas of interpolation type it has controlled accuracy and deals with small size matrices to simulate a small horn feeding the incident field is taken as a beam generated by a complex source point csp current presented numerical results validate empirical rule of 10 db edge illumination needed to provide the best electromagnetic performance of reflector

the diaphanous wedge complete solutions for the scattering by a diaphanous wedge meaning a wedge with identical wavenumbers inside and outside the wedge are presented the results are obtained from an integral equation for the fields on the wedge which is solved by the mellin and kantorovich lebedev transforms in the static and dynamic cases respectively pertinent formulations of gegenbauer s addition theorems play an important part in the derivation of the results which are presented in closed form

image solution for poisson s equation in wedge geometry the poisson s equation for a dielectric wedge is solved by deriving a static image that corresponds to the potential contribution of the wedge the problem is studied mainly in three dimensions but the solution for the analog two dimensional problem is also provided it appears that the use of image sources provides numerically a simple and efficient method to compute the potential inside and outside the wedge image sources for the exterior and interior regions consist of a line charge that decays exponentially as a function of complex angle and a set of point charges that can be interpreted as reflection or transmission images of a dielectric plane all known closed form solutions in terms of elementary functions are derived for an electrically and magnetically conducting half plane

guaranteed convergence method of analysis of the scattering by an arbitrarily oriented zero thickness pec disk buried in a lossy half space in this paper a guaranteed convergence method for the accurate and efficient analysis of the electromagnetic scattering by an arbitrarily oriented zero thickness perfectly electrically conducting pec disk buried in a lossy half space is presented an electric field integral equation efie in the vector hankel transform domain is obtained by expanding the unknown surface current density in cylindrical harmonics a convergence of exponential type is achieved by means of galerkin s method with expansion functions reconstructing the expected physical behavior of the bm n th harmonic at the center and the edge of the disk the obtained coefficient matrix can be quickly computed since its elements can be reviewed as the sum of single integrals efficiently evaluable by means of an analytical acceleration technique and double integrals of exponentially decaying functions

a spectral iteration technique for analyzing a corrugated surface twist polarizer for scanning reflector antennas an analysis of the corrugated surface twist polarizer which finds application in the design of scanning reflector antennas is presented the spectrai interation technique a novel procedure which combines the use of the fourier transform method with an iterative procedure is employed the first step in the spectral iteration method is the conversion of the original integral equation for the interface field into a form which is suitable for iteration using a method developed previously an important feature of the technique is that it takes advantage of the discrete fourier transform dft type of kernel of the integral equation and evaluates the integral operators efficiently using the fast fourier transform fft algorithm thus in contrast to the conventional techniques e g the moment method the spectral iteration approach requires no matrix inversion and is capable of handling a large number of unknowns furthermore the method has a built in check on the satisfaction of the boundary conditions at each iteration

on the solutions of a class of dual integral equations occurring in diffraction problems it is shown that there exists a category of two dimensional diffraction problems which can be put into a standard form of dual integral equations these diffraction problems include diffraction of electromagnetic waves by a finite strip a finite slit the diffraction of scalar or vector elastic waves by a rigid strip or crack etc a general method for solving such dual integral equations is given by the artifice of constructing a set of functions of compact support biorthogonal to another given set of functions the sufficient conditions for a given dual integral equations to be solvable in this manner are also determined hence the method forms a complement to the weiner hopf method to illustrate the method solutions are obtained for a bench mark problem the diffraction of light by a finite perfectly conducting strip or equivalently the diffraction of sh waves by a crack comparison with results obtained by others for low intermediate and high frequencies show the utility and accuracy of the method for the entire range of frequencies both the near field and the far field are obtained the latter is shown to correspond to the fraunhoffer diffraction pattern for high frequency it is also shown that for the equivalent crack problem the stress intensity factor sif fluctuates rapidly with changes in the angle of incidence for high frequencies thus making the sif especially sensitive to angle of incidence at high frequencies

on deriving a locally corrected nystrom scheme from a quadrature sampled moment method a novel high order method of moment procedure with quadrature point based discretization is presented the scheme is equivalent to a moment method employing smooth basis and testing functions applying a fixed point numerical quadrature approximation for the outer integral mapping the current to the quadrature points then leads to a formulation that is equivalent to that derived via the locally corrected nystrom method the convergence properties of the current density and rcs for smooth and singular geometries in two and three dimensions are also studied

general solutions of the narrow strip and slot integral equations analytic solutions of the integral equations for the current induced on a narrow conducting strip are obtained by two methods one method follows from an expansion of the strip current in a series of chebyshev polynomials while the other is based on a special power series expansion in the former fourier type coefficients depending on integrals of the excitation are derived while in the latter the coefficients depend upon derivatives of the excitation from knowledge of the strip current simple expressions for the far zone scattered field are derived explicit results are given for plane wave excitation the solution methods apply to the equations for the narrow slot in a planar conducting screen

the method of polarized traces for the 2d helmholtz equation we present a solver for the 2d high frequency helmholtz equation in heterogeneous acoustic media with online parallel complexity that scales optimally as o n l where n is the number of volume unknowns and l is the number of processors as long as l grows at most like a small fractional power of n the solver decomposes the domain into layers and uses transmission conditions in boundary integral form to explicitly define polarized traces i e up and down going waves sampled at interfaces local direct solvers are used in each layer to precompute traces of local green s functions in an embarrassingly parallel way the offline part and incomplete green s formulas are used to propagate interface data in a sweeping fashion as a preconditioner inside a gmres loop the online part adaptive low rank partitioning of the integral kernels is used to speed up their application to interface data the method uses second order finite differences the complexity scalings are empirical but motivated by an analysis of ranks of off diagonal blocks of oscillatory integrals they continue to hold in the context of standard geophysical community models such as bp and marmousi 2 where convergence occurs in 5 to 10 gmres iterations while the parallelism in this paper stems from decomposing the domain we do not explore the alternative of parallelizing the systems solves with distributed linear algebra routines

a simple evaluation of some principal value integrals for dyadic green s function using symmetry property for some special principal volume area the principal value integrals given by van bladel and yaghjian are evaluated using a reasoning of symmetry this approach is quite simple and the result of the two dimensional case is believed to be new

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

iterative computational techniques in scattering based upon the integrated square error criterion an iterative technique is developed to rigorously compute the electromagnetic time and frequency domain scattering problems the method is based upon a wave function expansion technique this also includes the integral representation techniques in which the electromagnetic field equations and causality conditions are satisfied analytically while the boundary conditions or the constitutive relations have to be satisfied in a computational manner the latter is accomplished by an iterative minimization of the integrated square error for the solution of an integral equation it is shown how to obtain optimum convergence some numerical results pertaining to a number of representative problems illustrate the numerical advantages and disadvantages of the iterative method

tm scattering by perfectly conducting polygonal cross section cylinders a new surface current density expansion retaining up to the second order edge behavior in the analysis of scattering by perfectly conducting cylinders with polygonal cross section by means of surface integral operator formulations fast convergence can be achieved by expanding the surface current density on each side with basis functions factorizing the correct behavior of the fields on the wedges usually the factorized edge behavior is chosen to be coincident with the first order behavior prescribed by meixner s theory however it could not be the correct one and consequently the convergence of the method becomes increasingly slow as the theoretical behavior differs from the real one this phenomenon is particularly notable when one or more of the predicted singularities unexpectedly disappear to overcome this problem in this work the analysis of tm scattering is made by introducing a new expansion devised so that only the first two terms are responsible for the reconstruction of the singularities while the remaining part of the expansion factorizes the second order edge behavior actually the proposed expansion outperforms the one introduced by the authors in a previous work factorizing the first order edge behavior even when this is the correct one

convergence criteria for the extended matrix version of the spectral iteration technique em scattering an extended matrix version of the spectral iteration technique sit has been reported recently where it was shown to offer the possibility of significantly improving the convergence rate for homogeneous dielectric or conducting scatterers by introducing a taper it is shown that there are good grounds for introducing such a taper and that it can sometimes significantly improve the convergence of the method for example if a 64 64 grid size allows with a taper convergence in five iterations whereas a 42 42 grid size requires 23 iterations a noticeable improvement in total computer time is effected also there are cases where a taper must be introduced if the sit method is to converge at all without the application of a full orthogonalization procedure the technique requires a correct choice of arbitrary values in the extended matrix and guidelines are presented for such a choice

electromagnetic scattering from electrically large coated flat and curved strips entire domain galerkin formulation efficient numerical solutions are presented for electromagnetic scattering for classes of electrically large coated perfectly conducting strips which are flat or curved the formulation is based on the solution of a coupled system of electric and magnetic field integral equations using the method of moments mm entire domain galerkin representations for the currents are used on the surface of the coating and at the coating conductor interface the resulting symmetric matrix equation is well conditioned and admits rapid accurate solutions numerical results are presented for various coating thicknesses strip widths and curvatures for the transverse electric te and transverse magnetic tm cases the convergence of the galerkin solution is examined as a function of these parameters the effect of the edge approximation on the choice of expansion functions is discussed the numerical results are compared with experimental measurements

te scattering by arbitrarily connected conducting strips the scattering by an arbitrary collection of perfectly conducting connected strips is analyzed for te incidence the studied configurations include both closed and open polygonal cross section cylinders as well as more complicated structures in which more than two strips are connected at a point the proposed method is very efficient as few expansion functions are needed in a galerkin scheme this is achieved by means of expansion functions factorizing the correct edge singularity of the electromagnetic field and ensuring the continuity of the current at connecting points

a generalization of van den berg s integral square error iterative computational technique for scattering van den berg shows a way of using spectral iteration si within a scheme that shows good convergence his method can be reinterpreted as a global expansion of the field quantities in terms of a set of basis functions it is shown here that the orthogonalization of these basis functions can considerably improve convergence rates this involves extra storage requirements but only a negligible decrease in speed of computation

scattering by polygonal cross section dielectric cylinders at oblique incidence we analyze the scattering by polygonal cross section lossless dielectric cylinders illuminated by an obliquely incident plane wave the problem is formulated in terms of a system of surface integral equations opportunely devised so as to be valid for objects with edges and incident angles including the total reflection limit angle by means of galerkin s method in the spectral domain with analytically fourier transformable expansion functions factorizing the correct edge behaviors and continuity conditions of the unknowns convergence of exponential type is achieved and the coefficients of the scattering matrix are reduced to single integrals that can be efficiently evaluated numerical results for both near field and far field parameters are presented showing the quick convergence of the method even when applied to composite cylindrical objects

efficient scalable parallel higher order direct mom sie method with hierarchically semiseparable structures for 3 d scattering a novel fast scalable parallel algorithm is proposed for the solution of large 3 d scattering problems based on 1 the double geometrical and current approximation higher order dho method of moments mom in the surface integral equation sie formulation and 2 a direct solver for dense linear systems utilizing hierarchically semiseparable hss structures namely an hss matrix representation is used for compression factorization and solution of the system matrix in addition a rank revealing qr decomposition for memory compression is used with a stopping criterion in terms of the relative rank tolerance value a method for geometrical preprocessing of the scatterers based on the cobblestone distance sorting technique is employed in order to enhance the hss algorithm accuracy and parallelization numerical examples show how the accuracy of the dho hss mom sie method is easily controllable by using the relative tolerance for the matrix compression moreover the examples demonstrate low memory consumption as well as much faster simulation time when compared to the direct lu decomposition the method enables dramatically faster monostatic scattering computations than iterative solvers and reduced number of unknowns when compared to low order discretizations finally great scalability of the algorithm is demonstrated on more than one thousand processes

mellin transform solution for the static line source excitation of a dielectric wedge an integral transform analysis of the static scattering of the two dimensional potential radiated by a line source in the vicinity of a penetrable wedge is presented the mellin transform is used to derive the exact static solution to laplace s equation for the dielectric wedge in the form of a modal series the important dielectric edge condition behavior is explicitly contained in this analytic solution

method of lines numerical analysis of conformal antennas this paper presents a generalization of the method of lines mol numerical algorithm for the analysis of integrated structures with a finite local curvature starting from the derivation of the generalized transmission line equations in a generic orthogonal reference system and in a bianisotropic material it is shown the possibility of solving the electromagnetic problem associated to an integrated structure with arbitrary curvature and or loaded by complex dielectric materials via a mol approach the introduction of new algorithms that extend and complete the original method is required in the most general case a detailed description of this new extended version of the mol is presented through the paper and its full coincidence with the original algorithm in the case of structures with simple loading materials is also shown finally some numerical results obtained analyzing microwave conformal antennas and resonators are presented and compared with analyzes performed employing other numerical methods and available in the literature

exponentially converging nystrom methods in oblique diffraction of arbitrarily polarized waves by bianisotropic chiral cylinders with arbitrary smooth cross section we study oblique diffraction of arbitrarily polarized plane waves by a uniform homogeneous bianisotropic cylinder with arbitrarily shaped smooth boundary following a boundary integral equations formulation we develop a 4 4 system of combined field integral equations and another 4 4 system of muller type fredholm integral equations both these systems having the tangential to the surface of the cylinder components of the electric and magnetic fields as the unknowns are of the second kind and uniquely solvable efficient discretization via simple and rapidly converging nystrom algorithms enables one to obtain highly accurate results even for electrically large objects the proposed solution technique a fully accounts for the singular nature of the kernels b yields simple closed form expressions for all matrix elements and c appears to converge exponentially versus matrix size the analogous diffraction problem for an arbitrarily shaped smooth chiral cylinder may be treated as a simple special case of the present analysis

solution of helmholtz equation in the exterior domain by elementary boundary integral methods in this paper elementary boundary integral equations for the helmholtz equation in the exterior domain based on green s formula or through representation of the solution by layer potentials are considered even when the partial differential equation has a unique solution for any given closed boundary i these elementary boundary integral equations can be shown to be singular at a countable set of characteristic wavenumbers spectral properties and conditioning of the boundary integral operators and their discrete boundary element counterparts are studied near characteristic wavenumbers with a view to assessing the suitability of these formulations for the solution of the exterior helmholtz equation collocation methods are used for the discretisation of the boundary integral equations which are either of the fredholm first kind second kind or hyper singular type the effect of quadrature errors on the accuracy of the discrete collocation methods is systematically investigated

a spectral iteration technique for analyzing scattering from arbitrary bodies part ii conducting cylinders with h wave incidence the stacked two dimensional spectral iteration technique sit introduced in an accompanying paper is further developed and extended to the case of an h polarized field incident on an arbitrary conducting cylinder as before the method takes advantage of the simplicity with which the relationships between planar sources and fields are expressed in the spectral domain

the direct electromagnetic scattering problem from an imperfectly conducting cylinder at oblique incidence abstract we consider the scattering of a time harmonic electromagnetic wave by an imperfectly conducting infinite cylinder at oblique incidence we assume that the cylinder is embedded in an inhomogeneous medium but both the cylinder and the medium are uniform along the axis of the cylinder since the x components and y components of electric field and magnetic field can be expressed in terms of their z components if the cylinder is parallel to the z axis we can derive from maxwell s equations and the leontovich impedance boundary condition that our scattering problem is modeled as a boundary value problem for their z components with oblique boundary condition using rellich s lemma the uniqueness of solutions to the boundary value problem is justified to show the existence of its solution the lax phillips method is used the key point for that is to prove the solvability of the associated oblique derivative problem in a bounded domain consisting of two boundaries which are the boundary of the cross section of the cylinder with coupled oblique boundary condition and that of a domain containing this cross section with dirichlet boundary condition

a new method of solution of hallen s problem a wide class of electromagnetic scattering problems can be expressed as a system of dual integral equations this kind of integral equation occurring in boundary value problems wherein there is one equation for a certain region and another for the dual domain is usual in diffraction problems considerable attention has been drawn by many researchers in the field of optics acoustics scattering of elastic waves accelerator physics and antenna theory wiener hopf techniques enable us to solve such kinds of integral equations when the two regions are contiguous and semi infinite unfortunately wiener hopf techniques do not apply if one of the regions is finite this is the case for realistic scatterers such as irises antennas and drift tubes in accelerators in this article a general method for solving such dual integral equations is discussed and applied to a particular case hallen s equation of cylindrical antennas this method consists of a transformation of the dual integral equations into a fre

rouquier blocks in chevalley groups of type e abstract in finite chevalley groups of type e we shall find a rouquier like block algebra in non defining characteristic we construct a morita equivalence between this block and a principal block of a local subgroup as an application of the equivalence we shall determine some decomposition numbers in type e

analysis of cylindrical antennas a spectral iteration technique the cylindrical antenna problem has been tackled using the spectral iteration technique an iterative scheme is employed for improving on an initially assumed form of the current distribution use is made of the fast fourier transform fft algorithm and the cumbersome process of matrix inversion is circumvented consequently this method is capable of handling a larger number of unknown coefficients in the expansion of the current distribution furthermore it provides a convenient means of testing for the satisfaction of the boundary conditions on the surface of the antenna convergence criteria for the iteration process have been established and the use of an acceleration procedure is illustrated different types of source models have been investigated and the convergence of both local and nonlocal parameters is also discussed

exponentially converging nystrom methods applied to the integral integrodifferential equations of oblique scattering hybrid wave propagation in presence of composite dielectric cylinders of arbitrary cross section systems of singular integral integrodifferential equations are studied that pertain to 2 d oblique scattering and to hybrid wave propagation in presence of a dielectric cylinder with arbitrarily shaped smooth boundary these systems having the tangential to the surface of the cylinder components of the electric and magnetic fields as the unknowns are solved via fast highly accurate algorithms that rely on the nystrom method nm because of our specialized treatment the present solution technique has the following characteristics 1 it fully accounts for the singular nature of the kernels 2 it appears to converge exponentially and 3 it yields simple closed form expressions for all matrix elements in addition an extension of the analysis is presented to account for composite dielectric cylinders that contain arbitrarily shaped dielectric or conducting cylindrical inclusions numerical examples and case studies illustrate the simplicity flexibility and efficiency of the algorithms exhaustive comparisons with available results for several special cases serve to test the correctness of the implementation and bring to light the extremely high accuracy of our algorithms

diffraction by three semi infinite planes an explicit solution to the scattering of a plane wave by three parallel equidistant semi infinite planes is derived the solution involves a wiener hopf factorization of a 2 2 matrix various properties of the scattered field are obtained

study of mixed order basis functions for the locally corrected nystro spl uml m method a high order locally corrected nystro spl uml m lcn method employing the mixed order basis functions proposed by c 80al spl iota s 80kan and peterson is presented for the electromagnetic scattering by targets composed of both dielectric and conducting bodies an integral operator based on a combined field formulation for conducting surfaces and a mu spl uml ller formulation for dielectric surfaces is used it is found that for general scattering objects mixed order basis functions accelerate the convergence of the lcn solution can eliminate spurious charges and can significantly reduce the condition number of the impedance matrix

matrix interpretation of the spectral iteration technique electromagnetic scattering a matrix interpretation of the spectral iteration technique is presented to illustrate improvements in accuracy and convergence for both transverse magnetic and transverse electric waves incident on two dimensional homogeneous scatterers producing solutions identical to a method of moments scheme in this scheme it is possible to improve the convergence rate of the technique by the use of nonphysical green s function terms in the extended matrix these terms result in the generation of a nonphysical field outside the scatterer while still maintaining the correct solution of the current although the problem of nonconvergence has not been entirely overcome a particular taper method used in the examples provided shows an improvement over their nontapered counterparts

image solution for the 3 d static green s function of a vertically stratified two layer half space the general form of 3 d static green s function for a general structure consisting of n arbitrary adjacent dielectric wedges is derived using the kontorovich lebedev and fourier transforms it consists of several point sources in physical space and a line image source in complex space for each region of the problem geometry while the point sources can be treated conventionally the line image distributions are obtained by extracting a proper asymptotic behavior of the solution which can be numerically computed as an example the case of a vertically stratified two layer half space is investigated and the respective point and line image sources are obtained the efficiency of the proposed solution method is demonstrated by comparing the computational time for a given structure with that required by a commercially available numerical code using the finite integration technique

iterative analysis of finite sized planar frequency selective surfaces with rectangular patches or perforations frequency selective surfaces fss and other periodic gratings are often analyzed under the assumption that they are infinite in extent most existing methods for analyzing periodic structures are based on the use of a floquet type representation of the fields in a unit cell whose dimensions are typically comparable to the wavelength in this work a finite truncated version of an infinite periodic structure is dealt with directly without the benefit of the assumption that the structure is periodic this in turn requires the handling of a large number of unknowns and makes it difficult to solve the problem using conventional matrix methods two different iteration approaches to solving the finite fss problem are discussed in the paper both of which employ the spectral domain formulation the first of these employs the spectral iteration technique and the second one uses the conjugate gradient cg iteration algorithm convergence characteristics of both of these methods are investigated and the results are reported

high order numerical solutions of the mfie for the linear dipole the magnetic field integral equation mfie was applied to a dipole using three different discretization methods and high order basis functions for moderate order and higher basis functions it was found that the different discretization methods produced essentially the same results continuity of current and its first derivative was observed at cell boundaries even though continuity of current was not explicitly enforced there the mfie provided lower condition numbers than the hallen equation over the range of dipole radii examined in close proximity to surface discontinuities including hidden ones residual errors could not be significantly reduced by increasing the order of the basis functions implying the need for better modeling at discontinuities and calling into question the use of faceting to represent curved surfaces

a uniform asymptotic solution for the diffraction by a right angled dielectric wedge we propose a uniform asymptotic solution for the field diffracted by a lossless right angled dielectric wedge illuminated by a plane wave at normal incidence the diffraction problem is solved by splitting the observation domain in the inner region of the wedge and the surrounding free space the scattered electric field in each region is assumed to be originated by a set of equivalent electric and magnetic surface currents involved in the well known radiation integral such currents are localized on the interior and exterior faces of the wedge and expressed in terms of the corresponding geometrical optics field useful analytical manipulations and asymptotic evaluations of the resulting integrals allow one to obtain the diffraction coefficients in terms of the fresnel s reflection and transmission coefficients of the structure and the transition function of the uniform geometrical theory of diffraction the related diffracted field compensates the discontinuities of the geometrical optics field and gives total field levels in good agreement with finite difference time domain results

convergence of the conjugate gradient method when applied to matrix equations representing electromagnetic scattering problems an iterative procedure based on the conjugate gradient method is used to solve a variety of matrix equations representing electromagnetic scattering problems in an attempt to characterize the typical rate of convergence of that method it is found that this rate depends on the cell density per wavelength used in the discretization the presence of symmetries in the solution and the degree to which mixed cell sizes are used in the models assuming cell densities used in the discretization are in the range of ten per linear wavelength the iterative algorithm typically requires n 4 to n 2 steps to converge to necessary accuracy where n is the order of the matrix under consideration

a spectral iteration technique for analyzing scattering from arbitrary bodies part i cylindrical scatterers with e wave incidence in the past methods for solving electromagnetic scattering problems in the frequency domain have been developed largely for the low frequency moment method and high frequency asymptotic techniques regimes the intermediate frequency range has been analyzed by combinations of these two approaches or by separation of variables when possible this paper is devoted to the development of an independent approach viz the stacked spectral iteration technique which is capable of handling arbitrary scatterers with dimensions ranging from small to moderately large the method takes advantage of the simplicity with which the planar source planar field relationships are expressed in the spectral domain the boundary conditions or constitutive relationships on the other hand are expressed most simply in the spatial domain alternating between the two domains is carried out with the aid of the fast fourier transform fft algorithm the spectral iteration technique sit was applied in the past to thin planar structures which allow the analysis to be carried out on a plane the generalization of the two dimensional formulation to arbitrary three dimensional bodies can be accomplished by sampling the current distribution on the scatterer over a number of parallel planes and using the simple spectral domain interaction relationships between the planes this new approach involves no matrix inversion and is capable of analyzing scatterers whose sizes far exceed those treatable by the moment method in addition to being arbitrarily shaped the scatterer may be conducting dielectric or lossy dielectric thus the sit provides an efficient approach to filling the much needed gap between low and high frequency conventional techniques e g the moment method mom and the geometrical theory of diffraction gtd and to extending the range of applicability to dielectric scatterers with or without loss though the concepts presented herein are applicable to arbitrary three dimensional scatterers the problem of arbitrary cylinders with e polarized excitation is addressed in this paper while the h case is treated in an accompanying work the three dimensional case is to be reported in a future communication which treats the problem of scattering by a lossy inhomogeneons dielectric cylinder of finite length

numerical solution of the helmholtz equation in 2d and 3d using a high order nystrom discretization we show how to solve time harmonic scattering problems by means of a high order nystrom discretization of the boundary integral equations of wave scattering in 2d and 3d the novel aspect of our new method is its use of local corrections to the discretized kernel in the vicinity of the kernel singularity enhanced by local corrections the new algorithm has the simplicity and speed advantages of the traditional nystrom method but also enjoys the advantages of high order convergence for controlling solution error we explain the practical details of implementing a scattering code based on a high order nystrom discretization and demonstrate by numerical example that a scattering code based on this algorithm can achieve high order convergence to the correct answer we also demonstrate its performance advantages over a high order galerkin code

acoustic inverse scattering via helmholtz operator factorization and optimization we present a joint acoustic seismic inverse scattering and finite frequency reflection tomography program formulated as a coupled set of optimization problems in terms of inhomogeneous helmholtz equations we use a higher order finite difference scheme for these helmholtz equations to guarantee sufficient accuracy we adapt a structured approximate direct solver for the relevant systems of algebraic equations which addresses storage requirements through compression to yield a complexity for computing the gradients or images in the optimization problems that consists of two parts viz the cost for all the matrix factorizations which is roughly o rn for example o rnlogn when d 2 times the number of frequencies and the cost for all solutions by substitution which is roughly o n for example o nlog rlogn when d 2 times the number of frequencies times the number of sources events where n n d if n is the number of grid samples in any direction and r is a parameter depending on the preset accuracy and the problem at hand with this complexity the multi frequency approach to inverse scattering and finite frequency tomography becomes computationally feasible with large data sets in dimensions d 2 and 3

an improved pulse basis conjugate gradient fft method for the thin conducting plate problem a conjugate gradient fast fourier transform cg fft formulation for the scattering by a thin perfectly conducting plate is presented pulse basis functions and a dirac delta function are used for expansion and testing purposes respectively particular attention is paid to the generation of the terms in the impedance matrix of the resulting matrix equation except for the self coupling terms all the other terms are computed by explicit integrations comparison with two previously reported pulse basis cg fft formulations shows that the present method is more stable when the error tolerance of the solution is reduced when sufficient cell discretizations are used smooth distributions can be obtained which resemble those obtained via rooftop cg fft formulation the numerical results are further validated by comparing the far field radar cross section with an analytical technique for a circular plate

the diffraction of stress waves by a plane finite crack in two dimensions uniqueness and existence in this paper we consider the two dimensional problem of the diffraction of stress waves by a finite plane crack in a homogeneous isotropic elastic solid we prove that provided the elastic displacement is bounded this problem has at most one solution also by introducing a new class of green functions we are able to give a constructive proof of existence the solution is given in terms of the solution of any one of a class of fredholm integral equations of the second kind

the decomposition numbers of the hecke algebra of type letw be the finite coxeter group of typef4 andhr q be the associated hecke algebra with parameter a prime powerq defined over a valuation ringr in a large enough extension field ofq with residue class field of characteristicr in this paper ther modular decomposition numbers ofhr q are determined for allq andr such thatr does not divideq the methods of the proofs involve the study of the generic hecke algebra of typef4 over the ringa u1 2 u 1 2 of laurent polynomials in an indeterminateu1 2 and its specializations onto the ring of integers in various cyclotomic number fields substancial use of computers and computer program systems gap maple meat axe has been made

on a class of finite step iterative methods conjugate directions for the solution of an operator equation arising in electromagnetics a class of finite step iterative methods for the solution of linear operator equations is presented specifically the basic principles of the method of conjugate directions are developed gaussian elimination and the method of conjugate gradients are then presented as two special cases with an arbitrary initial guess the method of conjugate gradient always converges to the solution in at most n iterations where n is the number of independent eigenvalues for the operator in the finite dimensional space in which the problem is being solved the conjugate gradient method requires much less storage sim 5n than the conventional matrix methods sim n 2 in the solution of problems of higher complexity also after each iteration the quality of the solution is known in the conjugate gradient method the conjugate gradient method is also superior to the spectral iterative method as the latter does not always converge and it doubles the complexity of a given problem unnecessarily four versions of the conjugate gradient method are presented in detail and numerical results for a thin wire scatterer are given to illustrate various properties of each version

exponentially converging nystro spl uml m s methods for systems of singular integral equations with applications to open closed strip or slot loaded 2 d structures this paper concerns the fast highly accurate and exponentially convergent solution of three sets of integral equations pertaining to two dimensional generalized microstrip or microslot structures the analysis relies on nystroumlm s method with due regard to all singular integrals and slowly converging series that appear in the kernels the sophisticated treatment and efficient computation of such series and integrals is of paramount importance entailing the use of advanced techniques as a result of our specialized treatment the discretization procedures developed herein a fully account for both the singular nature of the kernels and the singularities of the solution at the edges b obviate the need for taking inner products with testing functions c appear to converge exponentially versus matrix size and d enable expressing all matrix elements via single finite sums detailed numerical examples and case studies illustrate the simplicity flexibility and remarkable efficiency of the algorithms

diffraction of elastic waves by a penny shaped crack analytical and numerical results the diffraction of time harmonic stress waves by a penny shaped crack in an infinite elastic solid is an important problem in fracture mechanics and in the theory of the ultrasonic inspection of materials martin proc r soc lond a 378 263 1981 has proved that the corresponding linear boundary value problem has precisely one solution and that this solution can be constructed by solving a two dimensional fredholm integral equation of the second kind however this integral equation has a complicated matrix kernel and the components of its vector solution are coupled the main purpose of the present paper is to show how martin s integral equation can be explicitly solved in terms of a sequence of functions each of which satisfies a very simple scalar integral equation of the second kind this simplification may be made for any incident wave for an incident plane wave further simplifications are possible we show that the solution at an arbitrary angle of incidence can be derived from the solution at a particular angle of incidence namely grazing incidence the resulting computational procedure is especially attractive if only the stressintensity factors or the far field displacements are required finally we present some numerical results for the scattering of a p wave at normal incidence and an sv wave at oblique incidence and compare these with those of other authors

isometries and extra special sylow groups of order p3 abstract a new type of isometry between the sets of irreducible characters of blocks is introduced and a conjecture is stated using the classifications of finite simple groups and saturated fusion systems over an extra special group p of order p 3 and exponent p we check that the conjecture is affirmatively answered for the principal blocks of finite groups with sylow p subgroup p

a spectral iteration approach for analyzing scattering from frequency selective surfaces a novel technique called the spectral iteration approach for analyzing the problem of scattering from periodically perforated screens which find useful applications as radomes optical filters artificial dielectrics and so on is applied the formulation is carried out in the spectral domain where a set of algebraic equations is obtained directly for the spectral coefficients of the aperture field distribution or the induced current density rather than via an integral equation formulation these equations are then solved simultaneously using an iterative procedure developed in this paper that circumvents the need for matrix inversion because the matrix solution is avoided in the spectral approach it is capable of handling large aperture sizes in a computationally efficient manner the efficiency of computation results from the use of the fast fourier transform fft algorithm which is employed in the derivation of the algebraic equations and in the iteration procedure a unique feature of the spectral iteration approach is that it has a built in boundary condition check which provides a reliable indication of the accuracy of the solution it is also shown that the spectral domain technique can be applied to even a wider class of geometries e g the step discontinuity in a waveguide

a study of combined field formulations for material scattering for a locally corrected nystro spl uml m discretization a study of the error convergence and condition number of three integral equation formulations derived for penetrable material scattering objects the poggio miller chang harrington wu and tsai pmchwt the mu spl uml ller and the pmchwt formulations is presented for a variety of problems when discretized via a locally corrected nystro spl uml m method the pmchwt formulation is a first kind integral equation with a hypersingular operator the mu spl uml ller formulation leads to a second kind equation consisting of a diagonal term plus a compact operator this form is both frequency and mesh stable however unlike the pmchwt formulation the error grows with the refractive index the pmchwt formulation is in the form of a second kind equation but has a hypersingular term

an isotropic elastic medium containing a cylindrical borehole with a rigid plug abstract an analytical and numerical analysis is made of an isotropic elastic medium containing a cylindrical borehole of infinite length in which is located a tightly fitting rigid plug of finite length both the pulling of the plug and the occurrence of a radial misfit are considered the boundary conditions are mixed with zero radial and shear stresses at the bore surface outside the plug region and displacements given across the plug surface using integral representations for a love auxiliary function the crucial step is the analytical incorporation of the square root singularity at boundary condition junctions this is done by using neumann bessel function series representations of the integrand kernels of boundary condition stresses such that discontinuous weber schafheitlin integrals can be used to satisfy these conditions exactly displacement conditions are solved in terms of integrals of products of bessel functions the solutions provide expressions for the far field behaviour of a kelvin point load solution for the plug pull case and a combined centre of expansion plus double force for radial misfit numerical results show good convergence of the method and the correct singular behaviours of borehole surface stresses

efficient scalable algorithms for solving dense linear systems with hierarchically semiseparable structures hierarchically semiseparable hss matrix techniques are emerging in constructing superfast direct solvers for both dense and sparse linear systems here we develop a set of novel parallel algorithms for key hss operations that are used for solving large linear systems these are parallel rank revealing qr factorization hss constructions with hierarchical compression ulv hss factorization and hss solutions the hss tree based parallelism is fully exploited at the coarse level the textttblacs and textttscalapack libraries are used to facilitate the parallel dense kernel operations at the fine grained level we appply our new solvers for discretized helmholtz equations for multifrequency seismic imaging and iteratively solve time harmonic seismic inverse boundary value problems in particular we use the hss algorithms to solve the dense schur complement systems associated with the root separator of the separator tree obtained from nested dissection of the graph of discretized helmholtz equations we

two numerical solutions for the parallel plate fed slot antenna an integrodifferential equation for the electric field in the aperture of a parallel plate waveguide fed slot antenna is numerically solved using galerkin s method with a basis of edge condition weighted chebyshev polynomials and pulse expansion with point matching efficient algorithms are obtained for the elements of the reduced matrix equations for both moment methods the numerical convergence of the techniques is demonstrated by the resultant aperture field distributions and input reflection coefficients for the case of dominant transverse electromagnetic mode excitation

multi core parallel robust structured multifrontal factorization method for large discretized pdes in this paper based on the current mainstream multi core architecture of parallel computer and the robust structured multifrontal factorization in brief rsmf method we propose a multi core parallelization of rsmf in brief mrsmf method mrsmf method parallelizes the nested dissection ordering symbolic decomposition and numerical decomposition of rsmf method which aims to implement these operations on the multi core parallel machine the multi core parallelization of symbolic decomposition and numerical decomposition are based on the binary elimination tree numerical experiments show that the mrsmf method is effective

calculation of electromagnetic scattering from a dielectric cylinder using the conjugate gradient method and fft the scattering problem of an axially uniform dielectric cylinder is formulated in terms of the electric field integral equation where the cylinder is of general cross sectional shape inhomogeneity and anisotropy and the incident field is arbitrary using the pulse function expansion and the point matching technique the integral equation is reduced to a system of simultaneous equations then a published procedure for solving the system using the conjugate gradient method and the fast fourier transform fft is generalized to the case of oblique incidence scattering

the wiener hopf solution of the isotropic penetrable wedge problem diffraction and total field the diffraction of an incident plane wave by an isotropic penetrable wedge is studied using generalized wiener hopf equations and the solution is obtained using analytical and numerical analytical approaches that reduce the wiener hopf factorization to fredholm integral equations of second kind mathematical aspects are described in a unified and consistent theory for angular region problems the formulation is presented in the general case of skew incidence and several numerical tests at normal incidence are reported to validate the new technique the solutions consider engineering applications in terms of gtd utd diffraction coefficients and total fields

diffraction of an electric polarized wave by a dielectric wedge the problems of diffraction of an e polarized plane wave by an inhomogeneous imperfectly conducting dielectric wedge or a homogeneous dielectric wedge with vanishing conductivity are formulated as integral equations conditions for existence and uniqueness of the solutions of the integral equations are found the integral equations are solved by iterative methods an explicit expression for the far field is found the series expansion of the far field near the edge of a homogeneous wedge converges very fast for relative permittivities in the interval from one to ten the physical optical approximation of the far field is poor