an upgraded aca algorithm in complex field and its statistical analysis an upgraded adaptive cross approximation u aca algorithm in complex field is proposed including detailed discussion about both relative error estimator and pivoting threshold two new relative error estimators are constructed and the range of the pivoting threshold is determined theoretically besides a statistical analysis of the u aca algorithm for computational electromagnetics is provided to identify the credibility of existing relative error estimators and new ones the statistical experiments show that the u aca algorithm with either of the two new relative error estimators is a more robust algorithm at present for applications in computational electromagnetics compared with the previous aca algorithm

fast factorization acceleration of mom compressive domain decomposition domain decomposition dd for integral equation can be achieved by aggregating standard basis functions into specialized basis functions on each sub domain this results in a strong compression of the mom matrix which allows an iteration free e g lu decomposition solution also for electrically large problems fast matrix vector product algorithms can be used in the matrix filling and compression process of the employed aggregate functions approach this hybrid approach has received considerable attention in recent literature in order to quantitatively assess the performance advantages and limitations of this class of methods we start by proposing and demonstrating the use of the adaptive integral method aim fast factorization to accelerate the synthetic function expansion sfx dd approach the method remains iteration free with a significant boost in memory and time performances with analytical predictions of complexity scalings confirmed by numerical results then we address the complexity scaling of both stand alone dd and its combined use with fast mom this is done analytically and discussed with respect to known literature accounts of various implementations of the dd paradigm with nonobvious results that highlight needs and limitations and yielding practical indications

refined boundary conditions on the free surface of an elastic half space taking into account non local effects the dynamic response of a homogeneous half space with a traction free surface is considered within the framework of non local elasticity the focus is on the dominant effect of the boundary layer on overall behaviour a typical wavelength is assumed to considerably exceed the associated internal lengthscale the leading order long wave approximation is shown to coincide formally with the local problem for a half space with a vertical inhomogeneity localized near the surface subsequent asymptotic analysis of the inhomogeneity results in an explicit correction to the classical boundary conditions on the surface the order of the correction is greater than the order of the better known correction to the governing differential equations the refined boundary conditions enable us to evaluate the interior solution outside a narrow boundary layer localized near the surface as an illustration the effect of non local elastic phenomena on the rayleigh wave speed is investigated

an asymptotic analysis of initial value problems for thin elastic plates an asymptotic technique is developed to analyse initial value problems in application to the three dimensional theory of thin elastic plates various sets of long wave initial data are considered with arbitrary distribution along the plate thickness to account for the initial data composite asymptotic expansions are employed utilizing both two dimensional low frequency and high frequency models the former correspond to the classical theories of plate bending and extension and their refinements whereas the latter are associated with the long wave motions occurring in the vicinities of thickness stretch and shear resonance frequencies six cases of iteration process are revealed depending on the symmetry of the initial data and their thickness variation for each case approximate two dimensional initial conditions are derived including higher order corrections for the two dimensional low frequency refined plate theories the validity of the proposed approach is justified by comparison with the exact solution of the model plane problem for initial data with uniform distribution along the thickness and sinusoidal distribution along the mid plane the methodology of the paper has potential for more general initial value problems specified over a narrow domain including many of those commonly met in physical applied mathematics

on the treatment of arbitrary boundary conditions using a fast direct mathcal h matrix solver in mom this communication adapts the formalism of hierarchical mathcal h matrices to the direct solution process lu decomposition of the method of moments mom in the frequency domain a novel clustering approach based on physical constraints is presented and extended to treat dielectric bodies as well as arbitrary boundary conditions comparisons with other numerical methods are provided the analyses show a considerable speedup of the computation times and a significant reduction of required memory compared with the traditional mom solution process especially for highly resonant structures where iterative solvers like the multilevel fast multipole algorithm show poor convergence

fast iterative solution of integral equations with method of moments and matrix decomposition algorithm singular value decomposition the multilevel matrix decomposition algorithm mlmda was originally developed by michielsen and boag for 2d tmz scattering problems and later implemented in 3d by rius et al the 3d mlmda was particularly efficient and accurate for piece wise planar objects such as printed antennas however for arbitrary 3d problems it was not as efficient as the multilevel fast multipole algorithm mlfma and the matrix compression error was too large for practical applications this paper will introduce some improvements in 3d mlmda like new placement of equivalent functions and svd postcompression the first is crucial to have a matrix compression error that converges to zero as the compressed matrix size increases as a result the new mda svd algorithm is comparable with the mlfma and the adaptive cross approximation aca in terms of computation time and memory requirements remarkably in high accuracy computations the mda svd approach obtains a matrix compression error one order of magnitude smaller than aca or mlfma in less computation time like the aca the mda svd algorithm can be implemented on top of an existing mom code with most commonly used green s functions but the mda svd is much more efficient in the analysis of planar or piece wise planar objects like printed antennas

accelerated direct solution of electromagnetic scattering via characteristic basis function method with sherman morrison woodbury formula based algorithm the characteristic basis function method has been proposed to accelerate the direct solution of the method of moments by reducing the number of unknowns however with the increase in the target size the reduced matrix will still become too large to directly solve and store in this communication the algorithm based on the sherman morrison woodbury smw formula is employed to address this problem for the first time it compresses the reduced matrix into a product of block diagonal matrices with the aid of the smw formula and the adaptive cross approximation subsequently the inverse of the reduced matrix can be easily obtained by the inverses of these block diagonal matrices the numerical results about the electromagnetic scattering are shown to demonstrate the performance of the proposed method

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples it is shown that the electromagnetic em field radiated or scattered by bounded sources can be accurately represented over a substantially arbitrary surface by a finite number of samples even when the observation domain is unbounded the number of required samples is nonredundant and essentially coincident with the number of degrees of freedom of the field this result relies on the extraction of a proper phase factor from the field expression and on the use of appropriate coordinates to parameterize the domain it is demonstrated that the number of degrees of freedom is independent of the observation domain and depends only on the source geometry the case of spheroidal sources and observation domains with rotational symmetry is analyzed in detail and the particular cases of spherical and planar sources are explicitly considered for these geometries precise and fast sampling algorithms of central type are presented which allow an efficient recovery of em fields from a nonredundant finite number of samples such algorithms are stable with respect to random errors affecting the data

performance analysis of music type high resolution estimators for direction finding in correlated and coherent scenes an asymptotic analysis is presented of a class of high resolution estimators for resolving correlated and coherent plane waves in noise these estimators are in turn constructed from certain eigenvectors associated with spatially smoothed or unsmoothed covariance matrices generated from a uniform array the analysis is first carried out for the smoothed case and from this the conventional i e unsmoothed multiple signal classification music scheme follows as a special case independent of the total number of sources present in the scene the variance of the conventional music estimator along the true arrival angles is shown to be zero within a first order approximation the bias expressions in the smoothed case are used to obtain a resolution threshold for two coherent equipowered plane waves in white noise and the result is compared to the one derived by kaveh et al 1986 for two uncorrelated equipowered plane waves

a generalized approach to direction finding with reference to the recently developed estimation of signal parameters using a rotational invariance techniques esprit it is pointed out that other operators can be used to generate the matrix pencil by way of example the moving window operator is discussed

comments on fast direct solution of method of moments linear system in the above named work a new algorithm is presented for direct non iterative frequency domain method of moments mom calculations based on block wise compression of the impedance matrix the storage requirements and computational complexity of the algorithm are claimed to be n3 2 and n2 respectively if n is the number of unknowns for a mom surface discretization that is fixed with respect to the wavelength a more rigorous analysis explicitly using the asymptotic expression for the number of degrees of freedom dof in the interaction between groups of scatterers is presented here showing that this should be n3 2log n and n2log2 n respectively the complexity analysis applies to problems that can be formulated as a surface integral equation sie on surfaces in or between homogeneous media such as a ship or an airplane it does not apply to volume discretization mom or multilayer problems the results presented here are also relevant for block wise compression methods using iterative solvers since the compressed impedance matrix is the same consequently the above complexity analysis applies to very large problems well beyond the reach of even the largest existent computers for moderate size problems the measured complexity is lower

edge bending wave on a thin elastic plate resting on a winkler foundation this paper is concerned with elucidation of the general properties of the bending edge wave in a thin linearly elastic plate that is supported by a winkler foundation a homogeneous wave of arbitrary profile is considered and represented in terms of a single harmonic function this serves as the basis for derivation of an explicit asymptotic model containing an elliptic equation governing the decay away from the edge together with a parabolic equation at the edge corresponding to beam like behaviour the model extracts the contribution of the edge wave from the overall dynamic response of the plate providing significant simplification for analysis of the localized near edge wave field

prony pisarenko and the matrix pencil a unified presentation in the past the prony and pisarenko algorithms have been widely used in the pole zero identification of linear systems as well as in the problem of extracting harmonics embedded in noise these techniques have also been applied successfully to the direction of arrival doa problem it is shown that these algorithms are equivalent to a recently proposed doa estimation technique called the matrix pencil approach

axisymmetric vibration of circular plates and its analog in elliptical plates using characteristic orthogonal polynomials the axisymmetric vibration of circular plates and its analog in elliptic plates with clamped simply supported and free boundary conditions are investigated using boundary characteristic orthogonal polynomials in the rayleigh ritz method modified polar coordinates are employed to analyze the vibration of elliptical plates with circular plates as a special case axisymmetric vibration of circular plates and its analog in elliptical plates with concentric nodal elipses require only one dimensional shape functions in the rayleigh ritz method the first six natural frequencies and the parameters associated with nodal ellipses are tabulated

reconstructing polygons from moments with connections to array processing we establish a set of results showing that the vertices of any simply connected planar polygonal region can be reconstructed from a finite number of its complex moments these results find applications in a variety of apparently disparate areas such as computerized tomography and inverse potential theory where in the former it is of interest to estimate the shape of an object from a finite number of its projections whereas in the latter the objective is to extract the shape of a gravitating body from measurements of its exterior logarithmic potentials at a finite number of points we show that the problem of polygonal vertex reconstruction from moments can in fact be posed as an array processing problem and taking advantage of this relationship we derive and illustrate several new algorithms for the reconstruction of the vertices of simply connected polygons from moments

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

fast direct solution of method of moments linear system a novel algorithm the compressed block decomposition cbd is presented for highly accelerated direct noniterative method of moments mom solution of electromagnetic scattering and radiation problems the algorithm is based on a block wise subdivision of the mom impedance matrix impedance matrix subblocks corresponding to distant subregions of the problem geometry are not calculated directly but approximated in a compressed form subsequently the matrix is decomposed preserving the compression examples are presented of typical problems in the range of 5000 to 70000 unknowns the total execution time for the largest problem is about 1 h and 20 min for a single excitation vector the main strength of the method is for problems with multiple excitation vectors monostatic rcs computations due to the negligible extra cost for each new excitation for radiation and scattering problems in free space the numerical complexity of the algorithm is shown to be n 2 and the storage requirements scale with n 3 2

on the convergence of the aca algorithm for radiation and scattering problems the adaptive cross approximation aca algorithm when used to accelerate the numerical solution of integral equations for radiation and scattering problems sometimes suffers from inaccuracies these inaccuracies occur when the aca convergence criterion which is based on an approximation of the residual relative error is prematurely satisfied this paper identifies the two sources of this problem and proposes adaptations of the algorithm that remedy them

the statistical performance of the music and the minimum norm algorithms in resolving plane waves in noise this paper presents an asymptotic statistical analysis of the null spectra of two eigen assisted methods music 1 and minimum norm 2 for resolving independent closely spaced plane waves in noise particular attention is paid to the average deviation of the null spectra from zero at the true angles of arrival for the plane waves these deviations are expressed as functions of signal to noise ratios number of array elements angular separation of emitters and the number of snapshots in the case of music an approximate expression is derived for the resolution threshold of two plane waves with equal power in noise this result is validated by monte carlo simulations

hierarchical matrix techniques based on matrix decomposition algorithm for the fast analysis of planar layered structures the matrix decomposition algorithm mda provides an efficient matrix vector product for the iterative solution of the integral equation ie by a blockwise compression of the impedance matrix the mda with a singular value decomposition svd recompression scheme i e so called mda svd method shows strong ability for the analysis of planar layered structures however iterative solution faces the problem of convergence rate an efficient hierarchical h lu decomposition algorithm based on the h matrix techniques is proposed to handle this problem exploiting the data sparse representation of the mda svd compressed impedance matrix h lu decomposition can be efficiently implemented by h matrix arithmetic h matrix techniques provide a flexible way to control the accuracy of the approximate h lu factors h lu decomposition with low accuracy can be used as an efficient preconditioner for the iterative solver due to its low computational cost while h lu decomposition with high accuracy can be used as a direct solver for dealing with multiple right hand side rhs vector problems particularly numerical examples demonstrate that the proposed method is very robust for the analysis of various planar layered structures

a low frequency model for dynamic motion in pre stressed incompressible elastic structures an asymptotic one dimensional theory with minimal essential parameters is constructed to help elucidate two dimensional low frequency dynamic motion in a pre stressed incompressible elastic plate in contrast with the classical theory the long wave limit of the fundamental mode of antisymmetric motion is non zero the occurrence of an associated quasi front therefore offers considerable deviation from the classical case moreover the presence of pre stress makes the plate stiffer and thus may preclude bending in the classical sense discontinuities on the associated leading order wavefronts are smoothed by deriving higher order theories both quasi fronts are shown to be either receding or advancing but of differing type the problems of surface and edge loading are considered and in the latter case a specific problem is formulated and solved to illustrate the theory in the case of antisymmetric motion and an appropriate form of pre stress it is shown that the leading order governing equation for the mid surface deflection is essentially that of waves propagating along an infinite string a higher order equation for which is derived

on timoshenko reissner type theories of plates and shells abstract linear tr theories timoshenko reissner theories of isotropic plates and shells are discussed these theories take into account the transversal shear deformation and rotation inertia the main subject under consideration is the construction of these theories by the asymptotic method and the related error estimates for static and dynamic problems in the dynamic case a method is suggested for the extension of the range of applicability of the tr theory

analysis of the acoustical edge flexural mode in a plate using refined asymptotics the dispersion properties of bending wave localized near the stress free edge of a thin isotropic plate are investigated for relatively high frequency in order to clarify the nature of the wave attention is focused to the sensibility to the improved boundary conditions and to the iterations of the main differential operator when describing by two dimensional 2 d approximate plate theories as shown the boundary conditions of next asymptotic order do not change too much the leading part of the desired wave but the corrections of the main operator lead to dramatical changes finally beginning with its simplest kirchooff s plate model only the leading part of wave may be subjected to asymptotic correction for applications the wave speed calculation is reduced to two simple analytical formulas the results agree well with experiments and finite element testing the alternative approach related to the timoshenko reissner mindlin theory is discussed

sub domain decomposition iterative method combined with aca an efficient technique for the scattering from a large highly conducting rough sea surface the sub domain decomposition iterative method sdim is presented to solve efficiently a large linear system obtained by sampling the boundary integral equations from the method of moments then this new technique is tested on the electromagnetic scattering problem from a large highly conducting one dimensional rough sea surface the diagonal blocks are the local impedance matrices corresponding to the geometry sub domains while the off diagonal blocks are the coupling matrices describing the interaction between two different sub domains the principle of sdim is to invert the impedance matrix by blocks reducing significantly the complexity in comparison to a direct lu inversion of the whole impedance matrix in addition to accelerate the matrix vector products and to reduce the memory requirement the adaptive cross approximation aca is applied to compress the sub domain coupling matrices for microwave frequencies the results show that sdim converges rapidly and faster for the tm polarization moreover the mean compression ratio of aca is of the order of 98 which makes this method very efficient

high order approximate low frequency theory of elastic anisotropic lining and coating a problem of the dynamic behavior of an elastic layer coupled to one or two thick elastic solids is considered all the materials may possess a general anisotropy and the layer is assumed to be thin enough with respect to the characteristic wavelength introducing the asymptotic power series with respect to the thickness over wavelength ratio for the main quantities and using the asymptotic integration method the displacements and stresses on the layer surfaces are related thus the so called impedance boundary conditions ibc are deduced for three cases for a coated substrate with given displacements or with given stresses on the surface and for two substrates with a layer in between in contrast to previous papers these ibc are obtained for the most general situation with the asymptotic accuracy up to the sixth order uniform with respect to the representation of the displacements and stresses presented theory can be used for studying the surface and interface phenomena as well as for calculating fie

approximate boundary conditions for a fluid loaded elastic plate approximate boundary conditions for an infinite elastic layer immersed in a fluid are derived by using series expansions in the thickness coordinate of the plate fields the displacements fields are eliminated adopting the three dimensional equations of motion the sums and differences of the boundary pressure fields and their normal derivatives are related through a set of approximate boundary conditions one symmetric and one antisymmetric these equations involve powers in the layer thickness together with partial derivatives with respect to time as well as the spatial variables in the plate plane the approximate boundary conditions can be truncated to an arbitrary order and explicit relations are presented including terms of order five comparisons are made with effective boundary conditions using classical plate theories the numerical examples involve reflection and transmission of plane waves incident on the plate at different angles as well as the pressure fields due to a line force three fluid loading cases are studied modest heavy and light loadings the results using truncated approximate boundary conditions are compared to exact and classical plate solutions the examples show that the accuracies of the power series approximations of order three and higher are very good in the frequency interval considered

approximation of boundary element matrices this article considers the problem of approximating a general asymptotically smooth function in two variables typically arising in integral formulations of boundary value problems by a sum of products of two functions in one variable from these results an iterative algorithm for the low rank approximation of blocks of large unstructured matrices generated by asymptotically smooth functions is developed this algorithm uses only few entries from the original block and since it has a natural stopping criterion the approximative rank is not needed in advance

asymptotic equivalence of homogenisation procedures and fine tuning of continuum theories abstract long wave models obtained in the process of asymptotic homogenisation of structures with a characteristic length scale are known to be non unique the term non uniqueness is used here in the sense that various homogenisation strategies may lead to distinct governing equations that usually for a given order of the governing equation approximate the original problem with the same asymptotic accuracy a constructive procedure presented in this paper generates a class of asymptotically equivalent long wave models from an original homogenised theory the described non uniqueness manifests itself in the occurrence of additional parameters characterising the model a simple problem of long wave propagation in a regular one dimensional lattice structure is used to illustrate important criteria for selecting these parameters the procedure is then applied to derive a class of continuum theories for a two dimensional square array of particles applications to asymptotic structural theories are also discussed in particular we demonstrate how to improve the governing equation for the rayleigh love rod and explain the reasons for the well known numerical accuracy of the mindlin plate theory

higher order effective modeling of periodic heterogeneous beams ii derivation of the proper boundary conditions for the interior asymptotic solution abstract this paper constitutes the second part of a study devoted to the 1d modeling of beam like structures of arbitrary cross section with periodic properties along the axis in the first part the asymptotic expansion method has been described and the equations involving the successive terms of the outer solution have been given in particular it has been shown that neither the leading term nor the full outer solution are able to satisfy arbitrary prescribed edge data a specific study is thus necessary and it is presented in this paper the method used is the decay analysis initially proposed for homogeneous plates by gregory and wan j elast 14 1984 27 this approach consists in deriving the appropriate set of boundary conditions for the outer expansion solution for any arbitrary edge data stress displacement or mixed data these boundary conditions are obtained from the solution of canonical beam problems without computing any inner solution the method is illustrated through numerical examples on a lattice structure the results obtained prove the importance of a correct treatment of the edge effects in order that the inclusion of higher order terms in the beam model serves actually to increase the accuracy of the outer expansion solution

a perturbation approach for evaluating natural frequencies of moderately thick elliptic plates natural frequencies for moderately thick elliptic plates are calculated by perturbing initial values corresponding to the kirchhoff classical theory of plate bending the proposed approach utilizes a universal algebraic equation for perturbed eigenvalues previously derived by the authors for elliptic plates of a small eccentricity a dual procedure is developed to evaluate the sought for natural frequencies starting from those for a circular thin plate a comparison with finite element computations is presented an importance of the perturbation techniques in question for interpreting of finite element data is emphasized

perturbation analysis of tk method for harmonic retrieval problems the authors present a first order perturbation analysis of the tufts kumaresan tk 1980 method used to estimate frequencies of complex sinusoids in small additive noise several fundamental properties are presented and proved further illustrations are provided through numerical examples

using spectral low rank preconditioners for large electromagnetic calculations for solving large dense complex linear systems that arise in electromagnetic calculations we perform experiments using a general purpose spectral low rank update preconditioner in the context of the gmres method preconditioned by an approximate inverse preconditioner the goal of the spectral preconditioner is to improve the convergence properties by shifting by one the smallest eigenvalues of the original preconditioned system numerical experiments on parallel distributed memory computers are presented to illustrate the efficiency of this technique on large and challenging real life industrial problems copyright 2004 john wiley sons ltd

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

equivalence principle algorithm with body of revolution equivalence surface for the modeling of large multiscale structures we propose a multiscale solver of equivalence principle algorithm with a body of revolution bor equivalence surface es first the whole object is decomposed into subdomains the ess are defined as proper bors e g spheres in this work to enclose each subdomain the rao wilton glisson rwg and bor basis functions are defined on each sphere respectively second the octree is constructed in each nonzero subdomain the multilevel fast multipole algorithm mlfma is employed to solve the equivalent currents on the es individually and then the equivalent currents are projected from rwg onto the bor basis functions the couplings between neighboring subdomains are evaluated directly using mlfma and the separated subdomains are substituted by the es to es couplings and are evaluated efficiently by the bor method of moments bor mom to solve the equation system a hybrid inner and outer iterative solver is employed where the inner iteration is used to solve each local subdomains and the outer iteration is used to update the global solutions by collecting all the local solutions numerical results and discussions demonstrate the validity of the proposed work

optimization of block size for cbfm in mom the optimum number of blocks of the cbfm is derived theoretically and demonstrated numerically the minimum order of cpu time for the cbfm is shown to be o n7 3 where n is the number of unknowns in addition the optimum size of overlapping region of the blocks also is investigated numerically

a multilevel matrix decomposition algorithm for analyzing scattering from large structures a multilevel algorithm is presented for analyzing scattering from electrically large surfaces the algorithm accelerates the iterative solution of integral equations that arise in computational electromagnetics the algorithm permits a fast matrix vector multiplication by decomposing the traditional method of moment matrix into a large number of blocks with each describing the interaction between distant scatterers the multiplication of each block by a trial solution vector is executed using a multilevel scheme that resembles a fast fourier transform fft and that only relies on well known algebraic techniques the computational complexity and the memory requirements of the proposed algorithm are o n log sup 2 n

a modified prony algorithm for exponential function fitting a modification of the classical technique of prony for fitting sums of exponential functions to data is considered the method maximizes the likelihood for the problem unlike the usual implementation of prony s method which is not even consistent for transient signals proves to be remarkably effective in practice and is supported by an asymptotic stability result novel features include a discussion of the problem parametrization and its implications for consistency the asymptotic convergence proofs are made possible by an expression for the algorithm in terms of circulant divided difference operators

solving overdetermined eigenvalue problems we propose a new interpretation of the generalized overdetermined eigenvalue problem left bf a lambda bf b right bf v approx 0 for two m times n m n matrices bf a and bf b its stability analysis and an efficient algorithm for solving it usually the matrix pencil bf a lambda bf b does not have any rank deficient member therefore we aim to compute lambda for which bf a lambda bf b is as close as possible to rank deficient i e we search for lambda that locally minimize the smallest singular value over the matrix pencil bf a lambda bf b practically the proposed algorithm requires cal o mn 2 operations for computing all the eigenpairs we also describe a method to compute practical starting eigenpairs the effectiveness of the new approach is demonstrated with numerical experiments a matlab based implementation of the proposed algorithm can be found at http www mat univie ac at neum software oeig

degrees of freedom in multiple antenna channels a signal space approach multiple antenna systems that are limited by the area and geometry of antenna arrays are considered given these physical constraints the limit on the available number of spatial degrees of freedom is derived the commonly used statistical multiple input multiple output mimo model is inadequate antenna theory is applied to take into account the area and geometry constraints and to define the spatial signal space so as to interpret experimental channel measurements in an array independent but manageable description of the physical environment based on these modeling strategies for a spherical array of effective aperture a in a physical environment of angular spread spl omega in solid angle the number of spatial degrees of freedom is shown to be a spl omega for uni polarized antennas and 2a spl omega for tri polarized antennas together with the 2wt degrees of freedom for a system of bandwidth w transmitting in an interval t the total degrees of freedom of a multiple antenna channel is therefore 4wta spl omega

multilevel fast adaptive cross approximation algorithm with characteristic basis functions this paper presents a multilevel fast adaptive cross approximation mlfaca algorithm for accelerated iterative solution of the method of moments mom matrix equation for electrically large targets the mlfaca compresses the impedance submatrices between well separated blocks into products of sparse matrices constructed with the aid of the fast adaptive cross sampling facs scheme and the butterfly algorithm as a result the mlfaca can reduce both the computational time and the storage of the mom to mathbf o mathbf n mathbf log mathbf 2 text n where mathbf n is the number of the rao wilton glisson rwg basis functions in the analyzed target meanwhile the mlfaca maintains the adaptive and kernel independent properties furthermore the characteristic basis function method cbfm is employed to decrease the size of the outer matrices of the mlfaca to further reduce the storage and iteration time numerical results are presented to demonstrate the advantages of the proposed method including a successful solution of a scattering problem involving 10 861 668 rwg basis functions

a non local asymptotic theory for thin elastic plates the three dimensional dynamic non local elasticity equations for a thin plate are subject to asymptotic analysis assuming the plate thickness to be much greater than a typical microscale size the integral constitutive relations incorporating the variation of an exponential non local kernel across the thickness are adopted long wave low frequency approximations are derived for both bending and extensional motions boundary layers specific for non local behaviour are revealed near the plate faces it is established that the effect of the boundary layers leads to the first order corrections to the bending and extensional stiffness in the classical two dimensional plate equations

approximation of the flexural velocity branch in plates the fitting of the flexural velocity branch by means of the pade approximation is examined its use for free isotropic plates is elaborated and compared to other approaches the flexural velocity expansion into power series which underlies the pade implementation is detailed the generalization for fluid loaded plates and inhomogeneous plates is outlined and the impact of anisotropy is discussed in some detail

transverse vibrations of a clamped elliptical plate carrying a concentrated mass at an arbitrary position free vibrations of clamped thin elliptical plates carrying a concentrated mass at an arbitrary position are studied in order to analyze the mass effect on the natural frequencies and mode shapes of the plate a variational approach the well known ritz method is used where the displacement amplitude is approximated by polynomial expressions in the cartesian coordinates the present proposal exhibits excellent agreement with particular cases of the problem available in the literature and also with an independent solution obtained by means of the finite element method some new results are presented for the natural frequencies and modes of clamped elliptical plates with a concentrated mass

a refined nonlinear theory of plates with transverse shear deformation abstract a higher order shear deformation theory of plates accounting for the von karman strains is presented the theory contains the same dependent unknowns as in the hencky mindlin type first order shear deformation theory and accounts for parabolic distribution of the transverse shear strains through the thickness of the plate exact solutions of simply supported plates are obtained using the linear theory and the results are compared with the exact solutions of 3 d elasticity theory the first order shear deformation theory and the classical plate theory the present theory predicts the deflections stresses and frequencies more accurately when compared to the first order theory and the classical plate theory

error bound of the multilevel adaptive cross approximation mlaca an error bound of the multilevel adaptive cross approximation mlaca which is a multilevel version of the adaptive cross approximation singular value decomposition aca svd is rigorously derived for compressing an off diagonal submatrix of the method of moments mom impedance matrix with a binary tree the l level mlaca includes l 1 steps and each step includes 2 l aca svd decompositions if the relative frobenius norm error of the aca svd used in the mlaca is smaller than varepsilon the rigorous proof in this communication shows that the relative frobenius norm error of the l level mlaca is smaller than 1 varepsilon l 1 1 in practical applications the error bound of the mlaca can be approximated as varepsilon l 1 because varepsilon is always ll 1 the error upper bound can be used to control the accuracy of the mlaca to ensure an error of the l level mlaca smaller than varepsilon for different l the aca svd threshold can be set to 1 varepsilon tfrac 1 l 1 1 which approximately equals varepsilon l 1 for practical applications

on plate theories and saint venant s principle abstract it is generally known hat the classical germain kirchhoff plate theory is the leading term of the outer asymptotic expansion or interior solution in a small thickness parameter for the linear elastostatics of thin flat isotropic bodies this leading term or the actual outer solution alone cannot satisfy arbitrarily prescribed admissible edge data on the other hand the complementary inner asymptotic expansion or boundary layer solution is determined by a sequence of boundary value problems which are nearly as difficult to solve as the original problem for stress edge data saint venant s principle has been invoked to generate a set of stress boundary conditions for the classical plate theory as well as for higher order terms in the outer expansion giving various thick plate theories without any reference to the inner solution attempts to derive the corresponding boundary conditions for displacement and other types of edge data in the literature for general shape plates have not been successful the present study applies a general method developed by the authors to derive the correct set of boundary conditions for arbitrarily prescribed admissible edge data without an explicit solution of the inner or boundary layer solution for a number of special cases of general interest including cases with displacement edge data our general results also show that to be strictly correct saint venant s principle should be applied only to the leading term outer solution i e the classical plate theory

multiscale compressed block decomposition for fast direct solution of method of moments linear system the multiscale compressed block decomposition algorithm ms cbd is presented for highly accelerated direct non iterative solution of electromagnetic scattering and radiation problems with the method of moments mom the algorithm is demonstrated to exhibit n2 computational complexity and storage requirements scaling with n1 5 for electrically large objects several numerical examples illustrate the efficiency of the method in particular for problems with multiple excitation vectors the largest problem presented in this paper is the monostatic rcs of the nasa almond at 50 ghz for one thousand incidence angles discretized using 442 089 rwg basis functions being entirely algebraic ms cbd is independent of the greens function of the problem

a long wave model for the surface elastic wave in a coated half space the paper deals with the three dimensional problem in linear isotropic elasticity for a coated half space the coating is modelled via the effective boundary conditions on the surface of the substrate initially established on the basis of an ad hoc approach and justified in the paper at a long wave limit an explicit model is derived for the surface wave using the perturbation technique along with the theory of harmonic functions and radon transform the model consists of three dimensional quasi static elliptic equations over the interior subject to the boundary conditions on the surface which involve relations expressing wave potentials through each other as well as a two dimensional hyperbolic equation singularly perturbed by a pseudo differential or integro differential operator the latter equation governs dispersive surface wave propagation whereas the elliptic equations describe spatial decay of displacements and stresses as an illustration the dynamic response is calculated for impulse and moving surface loads the explicit analytical solutions obtained for these cases may be used for the non destructive testing of the thickness of the coating and the elastic moduli of the substrate