a fast combined field volume integral equation solution to em scattering by 3 d dielectric objects of arbitrary permittivity and permeability a fast solution to the combined field volume integral equation cfvie for electromagnetic scattering by large three dimensional dielectric bodies of arbitrary permittivity and permeability is presented the cfvie is formulated in the region of the scatterers by expressing the total fields as the sum of the incident wave and the radiated wave due to both the electric and magnetic polarization currents the resultant integral equation is solved using the method of moments mom then the precorrected fast fourier transform p fft method is applied to reduce the memory requirement and accelerate the matrix vector multiplication in the mom solution in the implementation of the p fft method two sets of projection operators are constructed respectively for the projections of the electric sources and magnetic sources in addition two sets of interpolation operators are also applied respectively for the computation of the vector scalar potentials and the curl of the vector potentials in the support of the testing functions the resultant method has a memory requirement of o n and a computational complexity of o nlogn respectively where n denotes the number of unknowns

reduced rank approximations to the far field transform in the gridded fast multipole method the fast multipole method fmm has been shown to have a reduced computational dependence on the size of finest level groups of elements when the elements are positioned on a regular grid and fft convolution is used to represent neighboring interactions however transformations between plane wave expansions used for fmm interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of fmm computations when finest level groups are large the transformation operators which are forward and inverse fourier transforms with the wave space confined to the unit sphere are smooth and well approximated using reduced rank decompositions that further reduce the computational dependence of the fmm on finest level group size the adaptive cross approximation aca is selected to represent the forward and adjoint far field transformation operators required by the fmm however the actual error of the aca is found to be greater than that predicted using traditional estimates and the aca generally performs worse than the approximation resulting from a truncated singular value decomposition svd to overcome these issues while avoiding the cost of a full scale svd the aca is employed with more stringent accuracy demands and recompressed using a reduced truncated svd the results show a greatly reduced approximation error that performs comparably to the full scale truncated svd without degrading the asymptotic computational efficiency associated with aca matrix assembly

a highly accurate fgg fg fft for the combined field integral equation in this paper a novel realization of the integral equation in combination with the fast fourier transform for the cfie is established by fitting both the green s function and its gradient onto the nodes of a uniform cartesian grid the new method has been compared with several existing popular fft based methods including the aim the ie fft and the p fft the accuracy of the proposed method is significantly higher than other fft based methods and the method is not sensitive to both the grid spacing and the expansion order the outstanding merit of the proposed method is that the fitting procedure is independent of the basis functions therefore when the higher order basis functions would be adopted in the method of moments only one fitting procedure for the green s function and its gradient on a basis function support is needed to meet all of basis functions defined on this support some numerical examples are provided in this paper to demonstrate the accuracy and efficiency of the proposed method

an efficient hybrid mlfma fft solver for the volume integral equation in case of sparse 3d inhomogeneous dielectric scatterers electromagnetic scattering problems involving inhomogeneous objects can be numerically solved by applying a method of moments discretization to the volume integral equation for electrically large problems the iterative solution of the resulting linear system is expensive both computationally and in memory use in this paper a hybrid mlfma fft method is presented which combines the fast fourier transform fft method and the high frequency multilevel fast multipole algorithm mlfma in order to reduce the cost of the matrix vector multiplications needed in the iterative solver the method represents the scatterers within a set of possibly disjoint identical cubic subdomains which are meshed using a uniform cubic grid this specific mesh allows for the application of ffts to calculate the near interactions in the mlfma and reduces the memory cost considerably since the aggregation and disaggregation matrices of the mlfma can be reused additional improvements to the general mlfma framework such as an extention of the fft interpolation scheme of sarvas et al from the scalar to the vectorial case in combination with a more economical representation of the radiation patterns on the lowest level in vector spherical harmonics are proposed and the choice of the subdomain size is discussed the hybrid method performs better in terms of speed and memory use on large sparse configurations than both the fft method and the hf mlfma separately and it has lower memory requirements on general large problems this is illustrated on a number of representative numerical test cases

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

correction to the application of the conjugate gradient method for the solution of electromagnetic scattering from arbitrarily oriented wire antennas the method of conjugate gradients is applied to the analysis of radiation from thin wire antennas with this iterative technique it is possible to solve electrically large arbitrarily oriented wire structures without storing any matrices as is conventionally done in the method of moments the basic difference between the proposed method and galerkin s method for the same expansion functions is that for the iterative technique we are solving a least squares problem hence as the order of the approximation is increased the proposed technique guarantees a monotonic decrease of the least squared error parallel ai y parallel 2 whereas galerkin s method does not even though the method converges for any initial guess a good one may significantly reduce the time of computation also explicit error formulas are given for the rate of convergence of this method hence any problem can be solved to a prespecified degree of accuracy it is shown that the method has the advantage of a direct solution as the final solution is obtained in a finite number of steps the method is also suitable for solving singular operator equations in which case the method monotonically converges to the least squares solution with minimum norm numerical results are presented for the thin wire antennas and are compared with the solution obtained by the method of moments

a new value picking regularization strategy application to the 3 d electromagnetic inverse scattering problem the nonlinear electromagnetic inverse scattering problem of reconstructing a possibly quasi piecewise constant inhomogeneous complex permittivity profile is solved by iterative minimization of a pixel based data fit cost function because of the ill posedness it is necessary to introduce some form of regularization many authors apply a smoothing constraint on the reconstructed permittivity profile but such regularization smooths away sharp edges in this paper a simple yet effective regularization strategy the value picking vp regularization is proposed this new technique is capable of reconstructing piecewise constant permittivity profiles without degrading the edges it is based on the knowledge that only a few different permittivity values occur in such profiles the values of which need not be known in advance vp regularization does not impose this a priori information in a strict sense such that it can be applied also to profiles that are only approximately piecewise constant the vp regularization is introduced in the solution of the inverse problem by adding a choice function to the data fit cost function for every permittivity unknown in the discretized problem when minimized the choice function forces the corresponding permittivity unknown to be close to one member of a set of auxiliary variables the vp values which are continuously updated throughout the iterations to minimize the regularized cost function a half quadratic gauss newton optimization technique is presented finally a stepwise relaxed vp regularization scheme is proposed in which the number of vp values is gradually increased this scheme is tested with synthetic and measured scattering data obtained from inhomogeneous 3d targets and is shown to achieve high reconstruction quality

an iterative method for solving electrostatic problems the method of steepest descent is applied to the solution of electrostatic problems the relation between this method and the rayleigh ritz galerkin s and the method of least squares is outlined also explicit error formulas are given for the rate of convergence for this method it is shown that this method is also suitable for solving singular operator equations in that case this method monotonically converges to the solution with minimum norm finally it is shown that the technique yields as a by product the smallest eigenvalue of the operator in the finite dimensional space in which the problem is solved numerical results are presented only for the electrostatic case to illustrate the validity of this procedure which show excellent agreement with other available data

acceleration of fast multipole method for large scale periodic structures with finite sizes using sub entire domain basis functions an acceleration technique to the fast multipole method fmm has been proposed to handle large scale problems of periodic structures in free space with finite sizes based on the accurate sub entire domain basis functions in the proposed algorithm only nine or 27 elements in the whole impedance matrix are required to be computed and stored for a two dimensional or three dimensional periodic structure and the matrix vector multiply can be performed efficiently using the combination of fast fourier transform and fmm the theoretical analysis and numerical results show that both the memory requirement and computational complexity are only of the order of o n with small constants where n is the total number of unknowns

electromagnetic scattering by finite periodic arrays using the characteristic basis function and adaptive integral methods we introduce a novel technique that combines the aim algorithm with the characteristic basis function method cbfm to solve the problem of electromagnetic scattering by large but finite periodic arrays an important advantage of using the cbfm for this problem is that we only need to analyze a single unit cell to construct the characteristic basis functions cbfs for the entire array the cbfs are generated by illuminating a single unit cell with a plane wave incident from different angles for both the and polarizations the initial set of cbfs generated in the manner described above are then downselected by applying a singular value decomposition svd procedure and retaining only the left singular vectors whose corresponding singular values fall above a threshold next in the conventional cbfm we derive a reduced matrix by applying the galerkin procedure and solve it directly if its size is manageable however when solving an array problem which precludes the direct solve option we can utilize the adaptive integral method aim algorithm detailed below not only to accelerate the solution but to reduce memory requirements as well numerical examples are included in this communication to demonstrate the accuracy and the numerical efficiency of the proposed technique

a fast volume integral equation method for elastic wave propagation in a half space abstract a fast method for solving the volume integral equation is developed for scattering analysis of elastic wave propagation in a half space the proposed method applies the fast generalized fourier transform and inverse transform formulated in the present study to the krylov subspace method the amount of calculations required for the proposed method is o nlogn where n is the number of grid points used to model the elastic half space furthermore the mpi parallel algorithm for the generalized fourier transform is presented for further reduction of the cpu time numerical calculations are performed in order to examine the effects of the number of sampling grid points as well as their intervals on the solutions of the volume integral equation and the cpu time required for the analysis in addition comparisons of the proposed method with the previous method based on the trapezoidal approach touhei 2009 are also performed in order to discuss the properties of the solution of the present method

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

investigation of scattering properties of large scale aperiodic tilings using a combination of the characteristic basis function and adaptive integral methods this paper presents a hybrid approach for efficient analysis of electromagnetic em scattering from large scale aperiodic structures e g aperiodic penrose and danzer tilings which integrates the characteristic basis function method cbfm and the adaptive integral method aim by performing a domain decomposition a series of characteristic basis functions cbfs that are defined on a macro block and comprised of a relatively large number of sub domain basis functions facilitate a substantial reduction in the method of moments mom matrix size enabling the use of a direct solver for large problems the aim is applied to accelerate the calculation of cbfm reduced mom matrices significantly decreasing the cpu time and memory required for solving large scale problems as the size of one block becomes electrically large the original cbfm combined with the aim is employed to generate the initial cbfs by solving a large problem with multiple excitations which results in efficiently constructing the final cbfs afforded by the singular value decomposition svd procedure this methodology produces a two level cbfm aim hybrid algorithm for efficiently characterizing large scale objects the numerical results presented demonstrate the accuracy and efficiency of the proposed hybrid algorithm then the developed solver is applied to investigate em scattering properties of large scale aperiodic tilings the numerical results show that penrose danzer tilings exhibit significantly improved grating lobe suppression as compared to their periodic counterparts

sphere plate casimir interaction in d 1 dimensional spacetime in this paper we derive the formula for the casimir interaction energy between a sphere and a plate in d 1 dimensional minkowski spacetime it is assumed that the scalar field satisfies the dirichlet or neumann boundary conditions on the sphere and the plate as in the d 3 case the formula is of tgtg type one of our main contributions is deriving the translation matrices which express the change of bases between plane waves and spherical waves for general d using orthogonality of gegenbauer polynomials it turns out that the final tgtg formula for the casimir interaction energy can be simplified to one that is similar to the d 3 case to illustrate the application of the formula both large separation and small separation asymptotic behaviors of the casimir interaction energy are computed the large separation leading term is proportional to l d 1 if the sphere is imposed with dirichlet boundary condition and to l d 1 if the sphere is imposed with neumann boundary condition where l is distan

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

improved impedance matrix localization method em problems moment method calculations have the well known limitations of requiring excessive storage and execution times for even modestly large electromagnetics problems the impedance matrix localization iml method was introduced as a modification to standard moment method calculations to ease these limitations it utilizes a matrix transformation which effectively changes the basis testing functions into ones resembling traveling waves an improved method that uses an orthogonal transformation to generate standing wave like basis functions is presented here remarkable improvements are achieved in the numerical stability of the method and in its compatibility with iterative solvers furthermore the correspondence of the large elements in this matrix to geometrical theory of diffraction gtd terms is strengthened as is the possibility of further increasing the speed of iterative solutions by constructing preconditioners based on the pattern of nonzero matrix elements

a faster aggregation for 3d fast evanescent wave solvers using rotations a novel technique to accelerate the aggregation and disaggregation stages in evanescent plane wave methods is presented the new method calculates the six plane wave radiation patterns from a multipole expansion aggregation and calculates the multipole expansion of an incoming field from the six plane wave incoming field patterns it is faster than the direct approach for multipole orders larger than one and becomes six times faster for large multipole orders the method relies on a connection between the discretizations of the six integral representations and on the fact that the wigner d matrices become diagonal for rotations around the z axis the proposed technique can also be extended to the vectorial case in two different ways one of which is very similar to the scalar case the other method relies on a beltrami decomposition of the fields and is faster than the direct approach for any multipole order this decomposition is also not limited to evanescent wave solvers but can be used in any vectorial multilevel fast multipole algorithm

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

planar near field to far field transformation using an equivalent magnetic current approach an alternative method is presented for computing far field antenna patterns from near field measurements the method utilizes the near field data to determine equivalent magnetic current sources over a fictitious planar surface that encompasses the antenna and these currents are used to ascertain the far fields under certain approximations the currents should produce the correct far fields in all regions in front of the antenna regardless of the geometry over which the near field measurements are made an electric field integral equation efie is developed to relate the near fields to the equivalent magnetic currents the method of moments is used to transform the integral equation into a matrix one the matrix equation is solved with the conjugate gradient method and in the case of a rectangular matrix a least squares solution for the currents is found without explicitly computing the normal form of the equation near field to far field transformation for planar scanning may be efficiently performed under certain conditions numerical results are presented for several antenna configurations

full wave three dimensional microwave imaging with a regularized gauss newton method theory and experiment a reconstruction algorithm is detailed for three dimensional full vectorial microwave imaging based on newton type optimization the goal is to reconstruct the three dimensional complex permittivity of a scatterer in a homogeneous background from a number of time harmonic scattered field measurements the algorithm combines a modified gauss newton optimization method with a computationally efficient forward solver based on the fast fourier transform method and the marching on in source position extrapolation procedure a regularized cost function is proposed by applying a multiplicative additive regularization to the least squares datafit this approach mitigates the effect of measurement noise on the reconstruction and effectively deals with the non linearity of the optimization problem it is furthermore shown that the modified gauss newton method converges much faster than the broyden fletcher goldfarb shanno quasi newton method promising quantitative reconstructions from both simulated and experimental data are presented the latter data are bi static polarimetric free space measurements provided by institut fresnel marseille france

analysis of arbitrarily shaped dielectric radomes using adaptive integral method based on volume integral equation the adaptive integral method aim is employed to solve the volume integral equation vie for analyzing the radiation of the antenna with an arbitrarily shaped radome small dipoles are used as exciting sources modeling the radomes by tetrahedron cells the induced volume current is determined by the aim based on vie the application of aim significantly reduces cpu time and computer memory requirement hence the method presented in the paper can be applied to simulate electrically large sized radomes finally the radiation patterns of small dipole arrays in the presence of spherical and conical radomes are calculated

a fast volume integral equation method for the direct inverse problem in elastic wave scattering phenomena a fast method for solving the volume integral equation is introduced for the solution of forward and inverse multiple scattering problems in an elastic 3 d full space for both forward and inverse scattering analysis the volume integral equation in the wavenumber domain is used by means of the discrete fourier transform the volume integral equation in the wavenumber domain can be dealt with as a fredholm equation of the 2nd kind with respect to a non hermitian operator on a finite dimensional vector space the bi cgstab method is employed to construct the krylov subspace in the wavenumber domain the current procedure establishes a fast and simplified method without requiring the derivation of a coefficient matrix several numerical results validate the accuracy and effectiveness of the current method for both forward and inverse scattering analysis according to the numerical results the reconstruction of inhomogeneities of the wave field is successful even for multiple scattering of several cubes

solution of arbitrarily dimensional matrix equation in computational electromagnetics by fast lifting wavelet like transform a new wavelet matrix transform wmt operated by lifting wavelet like transform lwlt is applied to the solution of matrix equations in computational electromagnetics the method can speedup the wmt without allocating auxiliary memory for transform matrices and can be implemented with the absence of the fast fourier transform furthermore to handle the matrix equation of arbitrarily dimension a new in space preprocessing technique based on lwlt is constructed to eliminate the limitation in matrix dimension complexity analysis and numerical simulation show the superiority of the proposed algorithm in saving cpu time numerical simulations for scattering analysis of differently shaped objects are considered to validate the effectiveness of the proposed method in particular due to its generality the proposed preprocessing technique can be extended to other engineering areas and therefore can pave a broad way for the application of the wmt

polylog time and near linear work approximation scheme for undirected shortest paths shortest paths computations constitute one of the most fundamental network problems nonetheless known parallel shortest paths algorithms are generally inefficient they perform significantly more work product of time and processors than their sequential counterparts this gap known in the literature as the transitive closure bottleneck poses a long standing open problem our main result is an o mn e 0 s m n1 e 0 work polylog time randomized algorithm that computes paths within 1 o 1 polylog n of shortest from s source nodes to all other nodes in weighted undirected networks with n nodes and m edges for any fixed e 0 0 this work bound nearly matches the o d sm sequential time in contrast previous polylog time algorithms required nearly min o d n3 o d m2 work even when s 1 and previous near linear work algorithms required near o n time we also present faster sequential algorithms that provide good approximate distances only between distant vertices we obtain an o m sn n e 0 time algorithm that computes paths of weight 1 o 1 polylog n dist o w max polylog n where dist is the corresponding distance and w max is the maximum edge weight our chief instrument which is of independent interest are efficient constructions of sparse hop sets a d e hop set of a network g v e is a set e of new weighted edges such that mimimum weight d edge paths in v e e have weight within 1 e of the respective distances in g we construct hop sets of size o n1 e 0 where e o 1 polylog n and d o polylog n

2 d validation of a formulation for the analysis of 3 d bodies that are periodic in one direction and finite sized in the others a numerical scheme to analyze three dimensional bodies that are periodic in one direction z and finite sized in the other ones x y is presented the geometry and material composition of the body can be arbitrary a new formulation using the conjugate gradient fast fourier transform method cg fft has been developed the formulation is based on the discretization and resolution of the electric field integral equation efie in both the real and spectral domains and leads to an efficient and accurate numerical procedure results are presented for rcs equivalent currents and fields inside 3 d periodic structures infinitely long cylinders with arbitrary shape and material composition these results are compared with analytical solutions and the agreement is found to be good

the receiving antenna as a linear differential operator application to spherical near field scanning the general receiving antenna is represented as a linear differential operator converting the incident field and its spatial derivatives at a single point in space to an output voltage the differential operator is specified explicitly in terms of the multipole coefficients of the antenna s complex receiving pattern when the linear operator representation is applied to the special probes used in spherical near field measurements a probe corrected spherical transmission formula is revealed that retains the form applicability and simplicity of the nonprobe corrected equations the new spherical transmission formula is shown to be consistent with the previous transmission formula derived from the rotational and translational addition theorems for spherical waves

spherical wave operators and the translation formulas translational formulas for both scalar and vector spherical wave solutions of the helmholtz equation are developed in a straightforward manner using differential operator representations for the modal functions and well known expressions for the scalar and dyadic free space green s functions the expansion coefficients are given in compact integral or differential operator forms useful for analytic investigation

fast solution of mixed dielectric conducting scattering problem using volume surface adaptive integral method this paper presents the adaptive integral method utilized to solve scattering problems of mixed dielectric and conducting objects using volume surface integral equation the scattering problem is formulated using volume integral equation and surface integral equation for dielectric material object and conducting object respectively the combined field integral equation is formulated to treat closed conducting surfaces the method of moments is applied to discretize the integral equations the resultant matrix system is solved by an iterative solver where the adaptive integral method is employed to accelerate the matrix vector multiplication the block diagonal preconditioner is implemented to further accelerate the convergence of the present solution numerical results are presented to demonstrate the accuracy and efficiency of the technique

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

a weak form of the conjugate gradient fft method for plate problems a number of electromagnetic field problems for planar structures can be formulated in terms of a hypersingular integral equation in which a grad div operator acts on a vector potential the vector potential is a convolution of the free space green s function and some surface current density over the domain of interest a weak form of this integral equation is obtained by testing it with subdomain basis functions defined over the plate domain only as a next step the vector potential is expanded in a sequence of subdomain basis functions and the grad div operator is integrated analytically over the plate domain only for the problem of electromagnetic scattering by a plate the method shows excellent numerical performance the numerical difficulties encountered in some previous conjugate gradient fast fourier transform cgfft methods have been eliminated

application of the discrete fourier transform method to nonorthogonal dihedral reflectors the discrete fourier transform method dftm is used to calculate the radar cross section rcs or orthogonal or nonorthogonal dihedral reflectors in order to accurately model the mutual interactions between the two plates a four point bivariate lagrange interpolation is incorporated into the dftm the resulting algorithm is simple and efficient results obtained with it compare favorably with measurements and predictions computed using the method of moments

fast algorithms for constructing t spanners and paths with stretch t the distance between two vertices in a weighted graph is the weight of a minimum weight path between them where the weight of a path is the sum of the weights of the edges in the path a path has stretch t if its weight is at most t times the distance between its end points we present algorithms that compute paths of stretch 2 leq t leq log n on undirected graphs g v e with nonnegative weights the stretch t is of the form t beta 2 epsilon where beta is integral and epsilon 0 is at least as large as some fixed epsilon 0 we present an tilde o m k n 2 epsilon t time randomized algorithm that finds paths between k specified pairs of vertices and an tilde o m ns n 2 1 log n m epsilon t deterministic algorithm that finds paths from s specified sources to all other vertices for any fixed epsilon 0 where n v and m e this improves significantly over the slower tilde o min k n m exact shortest paths algorithms and a previous tilde o mn 64 t kn 32 t time algorithm by awerbuch et al proc 34th ieee annual symposium on foundations of computer science ieee piscataway nj 1993 pp 638 647 a t spanner of a graph g is a set of weighted edges on the vertices of g such that distances in the spanner are not smaller and within a factor of t from the corresponding distances in g previous work was concerned with bounding the size and efficiently constructing t spanners we construct t spanners of size tilde o n 1 2 epsilon t in tilde o mn 2 epsilon t expected time for any fixed epsilon 0 which constitutes a faster construction by a factor of n3 2 t m of sparser spanners than was previously attainable we also provide efficient parallel constructions our algorithms are based on pairwise covers and a novel approach to construct them efficiently

a nondirective plane wave mlfma stable at low frequencies a novel method called the nondirective stable plane wave multilevel fast multipole algorithm nspwmlfma is presented to evaluate the low frequency lf interactions that cannot be handled by the multilevel fast multipole algorithm mlfma it is well known that the mlfma cannot be used for lf interactions since it suffers from numerical instability contrary to current techniques the proposed technique is not based on the spectral representation of the green function instead the addition theorem of the mlfma is manipulated into a form that allows numerically stable translations along the z axis the translation operator for these translations is derived in closed form a qr based method is devised to allow stable translations in all the other directions interpolations and anterpolations are also provided allowing a full multilevel algorithm since the nspwmlfma is based on the same mathematical foundations as the mlfma it requires limited adaptations to existing mlfma codes the fact that a qr is needed limits this algorithm to lf interactions however a coupling with the mlfma is straightforward allowing the easy construction of a broadband algorithm the dc limit of the algorithm is also presented and it is shown that the algorithm remains valid for static problems finally it is shown that the error introduced in the different steps of the algorithm is controllable and a single level vectorial version of the algorithm is applied to a generic scattering application to demonstrate its validity

a full wave 2 5d volume integral equation solver for 3d millimeter wave scattering by large inhomogeneous 2d objects a two and a half dimensional full wave forward solver to compute the three dimensional 3d electromagnetic field scattered by an infinitely long inhomogeneous lossy dielectric cylinder with arbitrary cross sectional shape under a given 3d time harmonic illumination is presented the relevant set of linear equations obtained after performing a spatial fourier transform of the fields along the axial direction and applying a method of moments discretization to the two dimensional contrast source volume integral equation is solved iteratively with a stabilized biconjugate gradient fast fourier transform method in this way objects with cross sectional dimensions of several to many wavelengths can be handled in a very fast way furthermore a vectorial 3d gaussian beam illumination usually employed in active millimeter wave mm wave imaging systems is implemented using a complex source gaussian beam formulation the validity of the method is proved by comparison with analytic results and with the results from a full wave 3d solver finally the method is applied to a millimeter wave imaging example showing the scattering from an object hidden under clothing on a human body

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

a fast solver for the helmholtz equation on long thin structures we present a fast solver for the helmholtz equation on long thin structures it operates on an integral equation formulation of the problem in which the solution is represented as a superposition of fields generated by sources on the structure usually on the boundary or boundaries of the structure it uses a standard iterative solver for linear equations in conjunction with a novel method for applying the forward matrix whose computational complexity is o n where n is the number of points on which the integral equation is solved the algorithm is suitable for structures in either two dimensions 2 d or three dimensions it does not depend in any great detail on the specifics of the helmholtz equation and thus is also suitable for similar equations we demonstrate the algorithm by using it to simulate scattering in 2 d from dielectric structures using an integral equation formulation constructed using a combination of single layer and double layer potentials yielding a second kind integral equation numerical results show the algorithm to be efficient and accurate

finite element analysis of saint venant torsion problem with exact integration of the elastic plastic constitutive equations abstract in this paper torsion of prismatic bars considering elastic plastic material behaviour is studied based on the presented variational formulation associated isoparametric finite elements are developed the unknown warping function is approximated using an isoparametric concept the elastic plastic stresses are obtained by an exact integration of the rate equations thus the ultimate torque can be calculated in one single load step this quantity describes the plastic reserve of a bar subjected to torsion furthermore for linear isotropic hardening no local iterations are necessary to compute the stresses at the integration points the numerical results are in very good agreement with available analytical solutions for simple geometric shapes the arbitrary shaped domains may be simply or multiple connected

a survey of conjugate gradient algorithms for solution of extreme eigen problems of a symmetric matrix a survey of various conjugate gradient cg algorithms is presented for the minimum maximum eigen problems of a fixed symmetric matrix the cg algorithms are compared to a commonly used conventional method found in imsl it is concluded that the cg algorithms are more flexible and efficient than some of the conventional methods used in adaptive spectrum analysis and signal processing

simultaneous microwave imaging and parameter estimation using modified level set method a modified level set method mlsm is proposed to simultaneously reconstruct the shape and electrical properties of 2 d objects as a numerical technique the formal level set method lsm can retrieve the shape and position of objects using synthetic measurement data in general the constitutive parameters of an object e g its relative complex permittivity are among the a priori information needed for the lsm for mlsm an evolution strategy is proposed to simultaneously calculate both the shape and complex permittivity of a 2 d object the initial guesses in respect of the complex permittivity and shape of the target object converge on their real values as the cost function is minimized the cost function is regularized with two penalty terms to prevent sudden change in the shape of the object a curvature based regularization is used also laplacian regularizer is used to reduce fluctuations in the object s constitutive parameters during the process using different synthetic data sets the capabilities of mlsm in microwave imaging and parameter estimation are evaluated it is found that using mlsm it is possible to completely separate two adjacent objects separated by a distance of one fifteenth of a wavelength the proposed method can retrieve targets of different relative permittivities with less than 10 error one interesting feature of this method is its high fidelity in retrieving the immersed one tenth wavelength targets in highly contrasting up to as high as 8 1 domains in the case of targets with little contrast 10 the proposed method with more iterations can converge on a value which is 57 more than the actual value these features are valuable in distinguishing malignant tissue from normal tissue

multiple scattering by multiple spheres a new proof of the lloyd berry formula for the effective wavenumber we provide the first classical derivation of the lloyd berry formula for the effective wavenumber of an acoustic medium filled with a sparse random array of identical small scatterers our approach clarifies the assumptions under which the lloyd berry formula is valid more precisely we derive an expression for the effective wavenumber which assumes the validity of lax s quasi crystalline approximation but makes no further assumptions about scatterer size and then we show that the lloyd berry formula is obtained in the limit as the scatterer size tends to zero

adaptive spectral estimation by the conjugate gradient method this paper proposes an alternative technique for adaptive spectral estimation the new technique applies the method of conjugate gradient which is used for iteratively finding the generalized eigenvector corresponding to the minimum generalized eigenvalue of a semidefinite hermitian matrix to the adaptive spectral analysis problem computer simulations have been performed to compare the new method to existing ones from the limited examples presented it is seen that the new method is computationally more efficient at the expense of more core storage also this method is effective for small data records and can implement noise correction to yield unbiased spectral estimates if an estimate of the noise covariance matrix is available the technique performs well for both narrow band and wide band signals

improving the convergence rate of the conjugate gradient fft method using subdomain basis functions a technique to improve the convergence rate of the conjugate gradient fast fourier transform cg fft method is presented the procedure involves the incorporation of subdomain basis functions associated with the current representation of linear and planar radiating elements it is shown that significant improvements are achieved in the convergence of the cg fft when using sinusoidal basis functions numerical results are presented for thin cylindrical dipoles conducting strips and material plates of various sizes in all cases an increase in the rate of convergence by a factor of two or better was observed

a saim faffa method for efficient computation of electromagnetic scattering problems a novel method is proposed through an effective combination of the subdomain adaptive integral method saim with the fast far field approximation faffa for efficient computation of electromagnetic scattering problems in the saim technique the whole perfectly electrically conducting structure is decomposed into subdomains and each subdomain is properly handled by the aim with its local cartesian grid individually a current continuity boundary condition is introduced on the interface between contiguous subdomains to guarantee the accuracy moreover the faffa technique is utilized to speed up the process of updating the modified excitation vectors numerical results show that the present hybrid method can not only significantly decrease the number of auxiliary grid points and the memory requirement of green s function matrix but also improve the convergence of the iterative process compared to the conventional aim

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

roots of bivariate polynomial systems via determinantal representations we give two determinantal representations for a bivariate polynomial they may be used to compute the zeros of a system of two of these polynomials via the eigenvalues of a two parameter eigenvalue problem the first determinantal representation is suitable for polynomials with scalar or matrix coefficients and consists of matrices with asymptotic order n 2 4 where n is the degree of the polynomial the second representation is useful for scalar polynomials and has asymptotic order n 2 6 the resulting method to compute the roots of a system of two bivariate polynomials is very competitive with some existing methods for polynomials up to degree 10 as well as for polynomials with a small number of terms

application of a conjugate gradient fft method to scattering from thin planar material plates the backscatter cross section is calculated for thin material plates with finite electric permittivity conductivity and magnetic permeability illuminated by a plane wave the plates are assumed to be planar with an arbitrary perimeter the integral equations are formed and solved by a combined conjugate gradient fast fourier transform cg fft method the cg fft method was tested for several geometrics and materials measured and computed backscatter results are compared for a perfectly conducting equilateral triangle plate a square dielectric and magnetic plate and a circular dielectric plate the agreement between measured and computed data is generally good except toward edge on incidence where several factors cause discrepancies accurate approximations to the geometry and far field integrals become critical near edge on incidence and it is postulated that as the incidence angle approaches edge on the sampling interval and tolerance should be decreased

meshless methods for the inverse problem related to the determination of elastoplastic properties from the torsional experiment abstract the problem of determining the elastoplastic properties of a prismatic bar from the given experimental relation between the torsional moment m and the angle of twist per unit length of the rod s length is investigated as an inverse problem the proposed method to solve the inverse problem is based on the solution of some sequences of the direct problem by applying the levenberg marquardt iteration method in the direct problem these properties are known and the torsional moment is calculated as a function of the angle of twist from the solution of a non linear boundary value problem this non linear problem results from the saint venant displacement assumption the ramberg osgood constitutive equation and the deformation theory of plasticity for the stress strain relation to solve the direct problem in each iteration step the kansa method is used for the circular cross section of the rod or the method of fundamental solutions mfs and the method of particular solutions mps are used for the prismatic cross section of the rod the non linear torsion problem in the plastic region is solved using the picard iteration

precorrected fft solution of the volume integral equation for 3 d inhomogeneous dielectric objects this work presents a fast solution to the volume integral equation for electromagnetic scattering from three dimensional inhomogeneous dielectric bodies by using the precorrected fast fourier transform fft method the object is modeled using tetrahedral volume elements and the basis functions proposed by schaubert et al are employed to expand the unknown electric flux density the basis functions are then projected onto a fictitious uniform grid surrounding the nonuniform mesh enabling the fft to be used to speed up the matrix vector multiplies in the iterative solution of the matrix equation the resultant method greatly reduces the memory requirement to o n and the computational complexity to o nlogn where n is the number of unknowns as a result this method is capable of computing electromagnetic scattering from large complex dielectric objects

potential integrals for uniform and linear source distributions on polygonal and polyhedral domains formulas for the potentials due to uniform and linearly varying source distributions defined on simply shaped domains are systematically developed and presented domains considered are infinite planar strips infinite cylinders of polygonal cross sections planar surfaces with polygonal boundaries and volumetric regions with polyhedral boundaries the expressions obtained are compact in form and their application in the numerical solution of electromagnetics problems by the method of moments is illustrated

a trade off between space and efficiency for routing tables two conflicting goals play a crucial role in the design of routing schemes for communication networks a routing scheme should use paths that are as short as possible for routing messages in the network while keeping the routing information stored in the processors local memory as succinct as possible the efficiency of a routing scheme is measured in terms of its stretch factor the maximum ratio between the length of a route computed by the scheme and that of a shortest path connecting the same pair of vertices most previous work has concentrated on finding good routing schemes with a small fixed stretch factor for special classes of network topologies in this paper the problem for general networks is studied and the entire range of possible stretch factors is examined the results exhibit a trade off between the efficiency of a routing scheme and its space requirements almost tight upper and lower bounds for this trade off are presented specifically it is proved that any routing scheme for general n vertex networks that achieves a stretch factor k 1 must use a total of o n 1 1 2 k 4 bits of routing information in the networks this lower bound is complemented by a family k k of hierarchical routing schemes for every k l for unit cost general networks which guarantee a stretch factor of o k require storing a total of o k 3 n 1 1 h log n bits of routing information in the network name the vertices with o log 2 n bit names and use o log n bit headers

a combined finite element boundary integral formulation for solution of two dimensional scattering problems via cgfft a novel technique is presented for computing the scattering by two dimensional structures of arbitrary inhomogeneity the proposed approach combines the usual finite element fe method with the boundary integral equation to formulate a discrete system this is subsequently solved via the conjugate gradient cg algorithm a particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer several of the resulting boundary integrals are then convolutions and can be evaluated via the fast fourier transform fft in the implementation of the cg algorithm the solution approach presented here offers the principal advantage of having o n memory demand and employs a one dimensional fft as against the two dimensional fft required in a traditional implementation of the proposed cg fft algorithm the speed of the proposed solution method is compared with that of the traditional cg fft algorithm results are presented for several rectangular composite cylinders and one perfectly conducting cylinder these are shown to be in excellent agreement with the moment method

sums of spherical waves for lattices layers and lines we consider the connections between sums of spherical wave functions over lattices layers and lines the differences between sums over lattices and those over a doubly periodic constituent layer are expressed in terms of series with exponential convergence correspondingly sums over the layer can be regarded as composed of a sum over a central line and another sum over displaced lines exhibiting exponential convergence we exhibit formulas which can be used to calculate accurately and efficiently sums of spherical waves over lattices layers and lines which in turn may be used to construct quasiperiodic green s functions for the helmholtz equation of use in scattering problems for layers and lines of spheres and for finding the bloch modes of lattices of spheres we illustrate the numerical accuracy of our expressions

plastic analysis of torsion of a prismatic beam finite element formulation for stress analysis of a twisting beam is developed the formulation is effective for a prismatic beam with solid section as well as a thin walled beam and can be applied both to a pure torsion problem and a warping torsion problem the formulation is of a great advantage to an elastic plastic torsion problem the formulation does not stand on the assumption of a thin walled structure and therefore torsional rigidity of the section can be evaluated exactly without using the so called saint venant s torsional constant torsional rigidity is in this paper evaluated directly by a warping function of the section warping function is evaluated numerically due to shape of the section due to progress of plastic region and due to effect of finite displacement finite rotation small strain pure torsion and warping torsion of a rectangular beam and an h beam which have an elastic plastic material property are analysed and the extension to the finite displacement problem is discussed many numerical examples are provided in order to check the accuracy of the formulation

error and convergence in numerical implementations of the conjugate gradient method em problems the conjugate gradient method has previously been applied in electromagnetics in two ways to moment method matrices and directly to continuous operator equations numerical implementations of these two methods are shown here to be equivalent it is concluded that the advantage of the conjugate gradient method is therefore its potential computational efficiency as a solution procedure not its ability to achieve a more exact solution than the moment method

a fast volume surface integral equation solver for scattering from composite conducting dielectric objects this paper presents a fast hybrid volume surface integral equation approach for the computation of electromagnetic scattering from objects comprising both conductors and dielectric materials the volume electric field integral equation is applied to the material region and the surface electric field integral equation is applied on the conducting surface the method of moments mom is used to convert the integral equation into a matrix equation and the precorrected fft p fft method is employed to reduce the memory requirement and cpu time for the matrix solution the present approach is sufficiently versatile in handling problems with either open or closed conductors and dielectric materials of arbitrary inhomogeneity due to the combination of the surface and volume electric field integral equations the application of the precorrected fft method facilitates the solving of much larger problems than can be handled by the conventional mom

te scattering by a two dimensional groove in a ground plane using higher order boundary conditions an application of a third order generalized boundary condition to scattering by a filled rectangular groove is presented deficiencies of such higher order boundary conditions are addressed and a correction for the present case is proposed as part of the process of examining and correcting the accuracy of the proposed generalized boundary conditions an exact solution is developed and a comparison is provided with a solution based on the standard impedance boundary condition

approximation algorithms for spanner problems and directed steiner forest we present an o nlogn approximation algorithm for the problem of finding the sparsest spanner of a given directed graph g on n vertices a spanner of a graph is a sparse subgraph that approximately preserves distances in the original graph more precisely given a graph g v e with nonnegative edge lengths d e r 0 and a stretchk 1 a subgraph h v e h is a k spanner of g if for every edge s t e the graph h contains a path from s to t of length at most email protected d s t the previous best approximation ratio was email protected n 2 3 due to dinitz and krauthgamer stoc 11 we also improve the approximation ratio for the important special case of directed 3 spanners with unit edge lengths from email protected n to o n 1 3logn the best previously known algorithms for this problem are due to berman raskhodnikova and ruan fsttcs 10 and dinitz and krauthgamer the approximation ratio of our algorithm almost matches dinitz and email protected s lower bound for the integrality gap of a natural linear programming relaxation our algorithm directly implies an o n 1 3logn approximation for the 3 spanner problem on undirected graphs with unit lengths an easy o n approximation algorithm for this problem has been the best known for decades finally we consider the directed steiner forest problem given a directed graph with edge costs and a collection of ordered vertex pairs find a minimum cost subgraph that contains a path between every prescribed pair we obtain an approximation ratio of o n 2 3 e for any constant e 0 which improves the o n email protected min n 4 5 m 2 3 ratio due to feldman kortsarz and nutov email protected 12

performing interpolation and anterpolation entirely by fast fourier transform in the 3 d multilevel fast multipole algorithm the fast multipole methods are used for solving a scalar acoustic or vector electromagnetic wave equation by integral equation methods with a large number of unknowns in this paper a new method is presented for performing interpolation and anterpolation in both spherical coordinates theta and phi by fft in the three dimensional 3 d multilevel fast multipole algorithm mlfma the key idea is to approximate functions on the unit sphere by truncated fourier series in two variables rather than by the usual spherical harmonics the proposed method is exact in interpolating and anterpolating and has the high numerical efficiency of fft the method is numerically compared to the method of performing interpolation and anterpolation using lagrangian interpolation which presently is probably the fastest method for those operations and the results suggest that the proposed new method is equally or more efficient depending on the desired accuracy

approximating k spanner problems for k 2 given a graph g v e a subgraph g v h h e is a k spanner of g if for any pair of vertices u w v it satisfies dh u w kdg u w the basic k spanner problem is to find a k spanner of a given graph g with the smallest possible number of edges this paper considers approximation algorithms for this and some related problems for k 2 known to be 2log1 n inapproximable the basic k spanner problem over undirected graphs with k 2 has been given a sublinear ratio approximation algorithm with ratio roughly o n2 k 1 but no such algorithms were known for other variants of the problem including the directed and the client server variants as well as for the related k dss problem we present the first approximation algorithms for these problems with sublinear approximation ratio the second contribution of this paper is in characterizing some wide families of graphs on which the problems do admit a logarithmic and a polylogarithmic approximation ratios these families are characterized as containing graphs that have optimal or near optimal spanners with certain desirable properties such as being a tree having low arboricity or having low girth all our results generalize to the directed and the client server variants of the problems as a simple corollary we present an algorithm that given a graph g builds a subgraph with o n edges and stretch bounded by the tree stretch of g namely the minimum maximal stretch of a spanning tree for g the analysis of our algorithms involves the novel notion of edge dominating systems developed in the paper the technique introduced in the paper reduces the studied algorithmic approximability questions on k spanners to purely graph theoretical questions concerning the existence of certain combinatorial objects in families of graphs

optimal interpolation of radiated fields over a sphere an optimal sampling interpolation algorithm is developed that allows the accurate recovery of scattered or radiated fields over a sphere from a minimum number of samples using the concept of the field equivalent spatial bandwidth a central interpolation scheme is developed to compute the field in theta phi coordinates starting from its samples the maximum allowable sample spacing and error upper bounds are also rigorously derived several simulated examples of pattern reconstruction are presented for both the cases of field and power pattern interpolation the interpolation error as a function of the retained sample number has been also evaluated and compared with the theoretical upper bounds the algorithm stability versus randomly distributed errors added to the exact samples is demonstrated

graph distances in the data stream model we explore problems related to computing graph distances in the data stream model the goal is to design algorithms that can process the edges of a graph in an arbitrary order given only a limited amount of working memory we are motivated by both the practical challenge of processing massive graphs such as the web graph and the desire for a better theoretical understanding of the data stream model in particular we are interested in the trade offs between model parameters such as per data item processing time total space and the number of passes that may be taken over the stream these trade offs are more apparent when considering graph problems than they were in previous streaming work that solved problems of a statistical nature our results include the following 1 spanner construction there exists a single pass tilde o tn 1 1 t space tilde o t 2n 1 t time per edge algorithm that constructs a 2t 1 spanner for t omega log n log log n the algorithm satisfies the semistreaming space restriction of o n operatorname polylog n and has per edge processing time o operatorname polylog n this resolves an open question from j feigenbaum et al theoret comput sci 348 2005 pp 207 216 2 breadth first search bfs trees for any even constant k we show that any algorithm that computes the first k layers of a bfs tree from a prescribed node with probability at least 2 3 requires either greater than k 2 passes or tilde omega n 1 1 k space since constructing bfs trees is an important subroutine in many traditional graph algorithms this demonstrates the need for new algorithmic techniques when processing graphs in the data stream model 3 graph distance lower bounds any t approximation of the distance between two nodes requires omega n 1 1 t space we also prove lower bounds for determining the length of the shortest cycle and other graph properties 4 techniques for decreasing per edge processing we discuss two general techniques for speeding up the per edge computation time of streaming algorithms while increasing the space by only a small factor

a conjugate gradient procedure for the analysis of planar conductors with alternating patch and aperture formulations em scattering the formulation of an electromagnetic scattering problem by an operator equation can be done in different ways leading to different rates of convergence when the conjugate gradient algorithm is used the convergence can tend to slow down at certain stages depending on the formulation used thus whenever the error tends to level off in one formulation it is advisable to switch to another one to this end a procedure that alternates repeatedly between formulations is presented it is shown to accelerate the convergence rate during the earlier stages of the iterative process making it possible to arrive at a prescribed practical error criterion faster a substantial saving in storage allocation is attained

scattering from planar structures containing small features using the adaptive integral method aim fast integral equation algorithms such as the adaptive integral method aim have been demonstrated to reduce memory and execution time associated with moment method solutions for arbitrarily shaped three dimensional 3 d geometries in this paper we examine the efficiency of aim in modeling planar structures that contain small and intricate details as is the case with spirals and slot antennas such geometries require high tessellation due to the inclusion of very small features resulting in a large number of unknowns aim with its capability to translate the original grid to an equivalent sparser uniform grid is uniquely suited for the analysis of such geometries in the latter part of the paper we demonstrate the application of aim in connection with a finite element boundary integral formulation for cavity backed antennas

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

generating low degree 2 spanners a k spanner of a connected undirected unweighted graph g v e is a subgraph g consisting of all the vertices of v and a subset of the edges with the additional property that the distance between any two vertices in g is larger than that distance in g by no more than a factor of k this paper is concerned with approximating the problem of finding a 2 spanner in a given graph with minimum maximum degree we first show that the problem is at least as hard to approximate as set cover then a randomized approximation algorithm is provided for this problem with approximation ratio of tilde o delta 1 4 we then present a probabilistic algorithm that is more efficient for sparse graphs our algorithms are converted into deterministic ones using derandomization

broadband multilevel fast multipole algorithm for electric magnetic current volume integral equation a volume integral equation method given in terms of the equivalent electric and magnetic volume currents and discretized using non conforming element wise constant approximations is applied to electromagnetic scattering analysis of inhomogeneous and anisotropic objects a broadband version of the multilevel fast multipole algorithm mlfma combining low frequency stable planewave expansion technique with the high frequency mlfma and utilizing global interpolators based on trigonometric polynomials is used to accelerate the computations

the fast multipole method and fourier convolution for the solution of acoustic scattering on regular volumetric grids the fast multipole method fmm is applied to the solution of large scale three dimensional acoustic scattering problems involving inhomogeneous objects defined on a regular grid the grid arrangement is especially well suited to applications in which the scattering geometry is not known a priori and is reconstructed on a regular grid using iterative inverse scattering algorithms or other imaging techniques the regular structure of unknown scattering elements facilitates a dramatic reduction in the amount of storage and computation required for the fmm both of which scale linearly with the number of scattering elements in particular the use of fast fourier transforms to compute green s function convolutions required for neighboring interactions lowers the often significant cost of finest level fmm computations and helps mitigate the dependence of fmm cost on finest level box size numerical results demonstrate the efficiency of the composite method as the number of scattering elements in each finest level box is increased

plastic instability of beam structures using co rotational elements in a previous paper comput methods appl mech engrg 191 2002 1755 the authors have presented a 3d co rotational elastic beam element including warping effects this formulation is now further developed in order to incorporate elasto plastic deformations the element possesses seven degrees of freedom at each node and can be used to model beams with arbitrary cross sections thus within the present approach the centroid and shear center of the cross section are not necessarily coincident the main purpose of this element is to model elasto plastic instability problems in this context two methods of branch switching are tested and discussed in the first one the bifurcation point is isolated by successive bisections and the branch switching is operated by using the eigenvector associated to the negative eigenvalue in the second one introduced by petryk an energy approach is used to select automatically the stable post bifurcation path six examples including large displacement and stability problems are used in order to assess the performances of the element

a diagonalized multilevel fast multipole method with spherical harmonics expansion of the k space integrals diagonalization of the fast multipole method fmm for the helmholtz equation is usually achieved by expanding the multipole representation in propagating plane waves the resulting k space integral over the ewald sphere is numerically evaluated storing the k space quadrature samples of the method of moments mom basis functions constitutes a large portion of the overall memory requirements of the resulting algorithm for solving the integral equations of scattering and radiation problems in this paper it is proposed to expand the k space representation of the basis functions by spherical harmonics in order to reduce the sampling redundancy introduced by numerical quadrature rules aggregations plane wave translations and disaggregations in the realized multilevel fast multipole method mlfmm are carried out using the k space samples of a numerical quadrature rule however the incoming plane waves on the finest mlfmm level are expanded in spherical harmonics again thus due to the orthonormality of spherical harmonics the testing integrals for the individual testing functions are simplified into series over products of spherical harmonics expansion coefficients overall the resulting mlfmm can save a considerable amount of memory without compromising accuracy and numerical speed

approximate distance oracles let g v e be an undirected weighted graph with vvv n and vev m let k 1 be an integer we show that g v e can be preprocessed in o kmn1 k expected time constructing a data structure of size o kn1p1 k such that any subsequent distance query can be answered approximately in o k time the approximate distance returned is of stretch at most 2k 1 that is the quotient obtained by dividing the estimated distance by the actual distance lies between 1 and 2k 1 a 1963 girth conjecture of erdos implies that n1p1 k space is needed in the worst case for any real stretch strictly smaller than 2kp1 the space requirement of our algorithm is therefore essentially optimal the most impressive feature of our data structure is its constant query time hence the name oracle previously data structures that used only o n1p1 k space had a query time of n1 k our algorithms are extremely simple and easy to implement efficiently they also provide faster constructions of sparse spanners of weighted graphs and improved tree covers and distance labelings of weighted or unweighted graphs

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

a scheme to analyze conducting plates of resonant size using the conjugate gradient method and the fast fourier transform a scheme for analyzing electrodynamic problems involving conducting plates of resonant size using the conjugate gradient cg method and the fast fourier transform fft is presented in detail the problems are analyzed by solving their corresponding electric field integral equation the procedure is made easy and systematic by using a sampling process with rooftop functions to represent the induced current and pulses to average the fields these functions have been widely used in moment method mm applications the scheme is an efficient numerical tool benefiting from the good convergence and low memory requirements of the cg and the low cpu time consumed in performing convolutions with the fft in comparison with the mm the scheme avoids the storage of large matrices and reduces the computer time by an order of magnitude several results are presented and compared with analytical numerical or measured values that appear in the literature