discontinuous galerkin volume integral equation solution of scattering from inhomogeneous dielectric objects by using the swg basis function a discontinuous galerkin volume integral equation dgvie method that uses the schaubert wilton glisson swg basis function is proposed for the analysis of scattering from inhomogeneous dielectric objects the main advantages of the proposed dgvie method are 1 no hypersingular integrals need to be calculated or compared with other methods that use nonconformal meshes and swg basis functions 2 the number of unknowns in the dgvie method that uses the swg basis function is less than that in the scheme that uses the piecewise constant vector basis function for the same mesh and 3 the code of the proposed dgvie can be easily obtained by a minor modification of the conventional method of moments code a trial explanation is presented for the fact that the explicit enforcement of the continuity condition at the interface between two elements is not required in the dgvie the numerical results are presented to validate the accuracy and efficiency of the proposed method

solution of 3d inverse scattering problems by combined inverse equivalent current and finite element methods an approach combining boundary integral and finite element methods is introduced for the solution of three dimensional inverse electromagnetic medium scattering problems based on the equivalence principle unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts a linear radiation problem and a nonlinear cavity problem the first problem is formulated by a boundary integral equation the computational burden of which is reduced by employing the multilevel fast multipole method mlfmm reconstructed cauchy data on the surface allows the utilization of the lorentz reciprocity and the poynting s theorems exploiting these theorems the noise level and an initial guess are estimated for the cavity problem moreover it is possible to determine whether the material is lossy or not in the second problem the estimated surface currents form inhomogeneous boundary conditions of the cavity problem the cavity problem is formulated by the finite element technique and solved iteratively by the gauss newton method to reconstruct the properties of the object regularization for both the first and the second problems is achieved by a krylov subspace method the proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained

extension of brzozowski s derivation calculus of rational expressions to series over the free partially commutative monoids we introduce an extension of the derivatives of rational expressions to expressions denoting formal power series over partially commuting variables the expressions are purely noncommutative however they denote partially commuting power series the derivations which are so called f derivations are shown to satisfy the commutation relations our main result states that for every so called rigid rational expression there exists a stable finitely generated submodule containing it moreover this submodule is generated by what we call words that is by products of letters and of pure stars consequently this submodule is free and it follows that every rigid rational expression represents a recognizable series in k this generalizes the previously known property where the star was restricted to mono alphabetic and connected series

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

a wide band equivalent source reconstruction method exploiting the stoer bulirsch algorithm with the adaptive frequency sampling conventional equivalent source reconstruction methods are only operating at a single frequency point each time however for wide band radiators their computation cost of the source reconstruction increases with the number of frequency points in this communication a wide band equivalent source reconstruction method wb srm based on the neville type stoer bulirsch sb algorithm is developed since the sb algorithm is a recursive tabular method it can perform the interpolation over a broadband using a single rational function without any singularity issue supported by the adaptive frequency sampling afs scheme the number of required sampling data is significantly reduced which leads to much better computational efficiency during the afs process three fitting models fm are considered two are triangle rules and another one is rhombus rule in this communication a bisection searching strategy is performed furthermore to achieve high order accuracy the nystrom method is implemented numerical examples are presented to validate the proposed wb srm and demonstrate its accuracy and applications

efficient reconstruction of dielectric objects based on integral equation approach with gauss newton minimization reconstruction of unknown objects by microwave illumination requires efficient inversion for measured electromagnetic scattering data in the integral equation approach for reconstructing dielectric objects based on the born iterative method or its variations the volume integral equations are involved because the imaging domain is fully inhomogeneous when solving the forward scattering integral equation the nystrom method is used because the traditional method of moments may be inconvenient due to the inhomogeneity of the imaging domain the benefits of the nystrom method include the simple implementation without using any basis and testing functions and low requirement on geometrical discretization when solving the inverse scattering integral equation the gauss newton minimization approach with a line search method lsm and multiplicative regularization method mrm is employed the lsm can optimize the search of step size in each iteration whereas the mrm may reduce the number of numerical experiments for choosing the regularization parameter numerical examples for reconstructing typical dielectric objects under limited observation angles are presented to illustrate the inversion approach

a faffa mlfma algorithm for electromagnetic scattering based on the multilevel fast multipole algorithm mlfma an efficient method is proposed to accelerate the solution of the combined field integral equation in electromagnetic scattering and radiation where the fast far field approximation faffa is combined with mlfma the translation between groups in mlfma is expensive because spherical hankel functions and legendre polynomials are involved and the translator is defined on an eward sphere with many k spl circ directions when two groups are in the far field region however the translation can be greatly simplified by faffa where only a single k spl circ direction is involved in the translator the condition for using faffa and the way to efficiently incorporate faffa with mlfma are discussed complexity analysis illustrates that the computational cost in faffa mlfma can be asymptotically cut by half compared to the conventional mlfma numerical results are given to verify the efficiency of the algorithm

multilevel plane wave based near field far field transformation for electrically large antennas in free space or above material halfspace a recently presented fully probe corrected near field far field transformation employing plane wave expansion and diagonal translation operators enables near field far field transformation for arbitrary measurement contours and arbitrary antennas a multilevel extension inspired by the multilevel fast multipole method is presented that is suitable for the efficient transformation of electrically large antennas with a size of tens or even hundreds of wavelengths the measurement points are grouped in a multilevel fashion and translations are carried out to the box centers on the highest level only the plane waves are processed through the different levels to the measurement points using a disaggregation and anterpolation procedure resulting in a reduced overall complexity in the second part of this paper the influence of perfectly conducting ground planes and dielectric halfspaces as an approximation for ground effects in a real measurement setup is investigated as such ground reflected waves are assumed which propagate from the investigated antenna to the field probe and add to the direct wave contributions the far field conditions required for these assumptions are achieved by a source box grouping scheme by this extension ground effects are directly considered within the near field far field transformation transformation results using simulated and measured near field data are shown

application of the tikhonov regularization technique to the equivalent magnetic currents near field technique the equivalent magnetic currents method can be used to characterize radiating structures and to obtain information about the current distribution on the radiating device under test dut in order to do so the system is assumed to be linear and inversion from near field measurements can be carried out using numerical techniques such as the singular value decomposition however this approach is very sensitive to modeling and measurement errors which is a consequence of the ill conditioned nature of the inversion process here we propose to account for the ill conditioning by using a tikhonov regularization technique to perform the inversion this technique requires a regularization parameter to be set to an appropriate value and we show that a generalized cross validation approach yields adequate determination of the regularization parameter directly from the measured data the proposed method can be tailored to account for specific characteristics of the dut this point is illustrated by the estimation of the current distribution of a bidimensional radiating structure for which prior information about the orientation of radiating edges is incorporated into the inversion method

stable solution of time domain combined field integral equations for transient electromagnetic scattering by composite structures based on nystrom scheme and laguerre function transient electromagnetic scattering by composite structures is formulated by time domain combined field integral equations tdcfies traditionally the tdcfies are solved by combining the method of moments moms in space domain and march on intime mot scheme in time domain the space domain mom requires two basic functions to represent the electric and magnetic current densities on material interfaces respectively and the conventional choice of hat n times mathrm rwg basis function for representing the magnetic current density may not be good in the tdcfies in addition the mot scheme has a well known late time instability problem which will aggravate in the surface integral equations with penetrable media in this communication the tdcfies for composite structures are solved by a different approach in which the nystrom method is used to discretize the space domain while the galerkin method with laguerre basis and testing functions is employed to discretize the time domain the proposed approach can fully overcome the drawbacks of the traditional approach as demonstrated by numerical examples

an inverse fast multipole method for geometry reconstruction using scattered field information a novel inverse fast multipole method fmm application for accelerating inverse problem solution is presented the idea is based on the multipole expansion properties of the scattered fields and reconstructed equivalent currents which allow an easy inversion of the fmm operators resulting in a forward solution of the inverse problem i e without matrix inversion or cost function minimization in addition this technique allows the use of reconstruction domain discretization larger than half a wavelength and overcomes the restriction of having the entire target enclosed by a reconstruction domain features that also contribute to the reduction of calculation time two 3d application examples are presented highlighting the achieved inverse fmm speed up with respect to previous inverse scattering methods for geometry reconstruction

knowledge based antenna pattern interpolation we examine the problem of interpolating antenna radiation patterns from a small number of measurements and propose an algorithm to perform the interpolation when naive methods fail often due to multipath corruption of the pattern this algorithm exploits constraints on the antenna s underlying design to avoid ambiguities but is sufficiently general to address many different antenna types a theoretical basis for the robustness of this algorithm is developed and its performance is verified in simulation using a number of popular antenna designs and with a controlled laboratory experiment

confidence and conflict in multivariate calibration summary multivariate calibration involves using an estimated relationship between a multivariate response y and an explanatory vector x to predict unknown x in future from further observed responses in controlled calibration with multivariate normal errors the profile likelihood function for the unknown x denoted 4 displays a term which measures the mutual inconsistency of the given response vector denoted z in predicting 4 this inconsistency diagnostic fundamentally differentiates the behaviour of likelihood based and bayes confidence regions from those of the unconditional sampling approach in addition the diagnostic serves to pinpoint an inadequate response vector z

solving the volume integral equations of electromagnetic scattering time harmonic electromagnetic scattering by inhomogeneous three dimensional structures within a free space environment can be described by electric and magnetic field volume integral equations involving the free space green function a comprehensive set of galerkin projection formulations also known as moment methods for the numerical solution of these equations is presented together with comparative numerical results such formulations are widely used for particle scattering analysis optical near field calculation etc results are obtained with higher order divergence and curl conforming basis functions on iso parametric tetrahedral meshes the results demonstrate that all formulations converge with similar accuracy in the case of an analytically solvable test problem when modeling flux densities as solution variables it is argued that solenoidal function spaces should be used rather than the standard divergence conforming function spaces this assertion is supported by the results some of the formulations involve solving for curl conforming fields such fields can be discretized with fewer unknowns than divergence conforming ones implying lower computational costs additionally some formulations yield system matrices which are approximately halfway sparse meaning that computational costs will be down by a factor of 2 when iterative solvers are employed which is the case for the widely used fast methods

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

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

prediction diagnostics and updating in multivariate calibration summary in multivariate calibration the relationship between a q variate response vector y and p explanatory variables x are estimated from training data in order to predict an unknown x denoted by e from further observed responses when q p both the profile likelihood for e and bayesian inference for e depend on a prediction inconsistency diagnostic which highlights those response vectors used for prediction which are internally inconsistent in the prediction of e when several further response vectors together display systematic anomalies one is led to questioning the estimated model the information in prediction data about changes in parameters is investigated under various assumptions the results indicate systematic anomalies in prediction data may be detected in a variety of ways but corrected only under strong assumptions so that recalibration might be needed

on the calculation of potential integrals for linear source distributions on triangular domains present analytical formulas for the singular field contributions of linear source distributions on triangular domains the formulas can be used for near field calculations of electric and magnetic source currents especially for the calculation of method of moments mom matrix elements due to the solution of surface integral equations for mom self coupling terms involving the scalar green function of free space the authors present expressions comprising analytical solutions of both the source integrals and the testing integrals

estimating fetal age by ultrasound measurements an example of multivariate calibration a problem in the estimation of gestational age by ultrasound measurement of fetal bone lengths the femur length f and the biparietal diameter bpd is described by means of multivariate calibration techniques f and bpd are combined to give an index of gestational age which is significantly more accurate than existing indices based on f or bpd alone a detailed description of the statistical analysis is given ranging from the initial steps of data analysis and model choice to the final step of determining the index and its accuracy a number of interesting aspects of multivariate calibration theory are illustrated

planar near field to far field transformation using an array of dipole probes a method is presented for computing far field antenna patterns from measured near field data measured by an array of planar dipole probes the method utilizes the near field data to determine some equivalent magnetic current sources over a fictitious planar surface which encompasses the antenna these currents are then used to find the far fields the near field measurement is carried out by terminating each dipole with 50 spl omega load impedances and measuring the complex voltages across the loads an electric field integral equation efie is developed to relate the measured complex voltages to the equivalent magnetic currents the mutual coupling between the array of probes and the test antenna modeled by magnetic dipoles is taken into account the method of moments with galerkin s type solution procedure is used to transform the integral equation into a matrix one the matrix equation is solved with the conjugate gradient fast fourier transformation cg fft method exploiting the block toeplitz structure of the matrix numerical results are presented for several antenna configurations to show the validity of the method

weighted asynchronous cellular automata we study weighted systems whose behavior is described as a formal power series over a free partially commutative or trace monoid it is shown that the interleaving approach and the distributed approach are equivalent in this setting this holds both in the deterministic and in the nondeterministic case consequently we obtain a particularly simple class of sequential weighted automata that already have full expressive power

efficient nystrom solutions of electromagnetic scattering by composite objects with inhomogeneous anisotropic media analysis of electromagnetic em scattering by composite objects with inhomogeneous or anisotropic media requires an efficient solution of volume integral equations vies or volume surface integral equations vsies in the integral equation approach the traditional method of moments mom with the rao wilton glisson rwg basis function and the schaubert wilton glisson swg basis function may not be convenient because the basis functions are defined over a triangular or tetrahedral element pairs and the swg basis function could cause a surface charge density on the common faces separating dissimilar media in this work we develop an efficient nystrom scheme as an alternative to solve the vies or vsies for those objects the advantages of nystrom method include the simple mechanism of implementation allowance of nonconforming meshes and removal of basis or testing function making the method more suitable for solving such problems numerical examples for em scattering by typical objects are presented to demonstrate the method

phaseless near field far field transformation utilizing combinations of probe signals phaseless near field far field transformations based on nonconvex optimization suffer from local stationary points in order to avoid the corresponding suboptimal solutions the incorporation of combinations of probe signals into the cost functional is proposed and investigated the nonconvex optimization based on the wirtinger calculus relies on forward and adjoint radiation operator evaluations via the fast irregular antenna field transformation algorithm fiafta and is performed by a memory limited quasi newton method this allows the solution of large scale problems with utilization of the full flexibility of the fiafta in terms of measurement probe correction and arbitrary sample locations results for synthetic and measured near field data reveal significant improvements when the knowledge of probe signal combinations is utilized especially in applications with a large number of unknowns

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

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

confidence regions in multivariate calibration on propose une methode alternative qui donne une region a bon comportement correspondant a la region invariante par translation uniformement la plus precise

numerical solution of time domain volume integral equations for transient electromagnetic scattering by dielectric objects electromagnetic em interaction with penetrable objects can be described by volume integral equations vies in integral equation approach and time domain vies tdvies are required for formulating transient em problems with such objects the tdvies are usually solved by combining the method of moments mom with well designed basis function in space domain and a march on in time mot scheme in time domain the space domain mom requires conforming meshes in geometric discretization and twofold numerical integrations in matrix generation while the mot in time domain suffers from a late time instability problem in this communication we propose an alternative approach that uses the nystrom method to discretize the vies in space domain while employing the mom with laguerre basis and testing functions to discretize the equations in time domain the proposed approach can simplify the numerical implementation and produce a march on in degree procedure similar to that in frequency domain approaches numerical examples are presented to illustrate the approach and good results have been observed

combining independent studies in a calibration problem abstract the problem of calibration in which the response variable is measured by k different methods or using different instruments is considered it is well known that the usual classical estimator for the unknown explanatory variable has infinite mean and mean squared error when k 1 in this article a linear combination of the classical estimators is proposed it is shown that the combined estimator has finite mean provided that k 2 and finite mean squared error provided that k 3 expressions for asymptotic bias and mean squared error are given also two confidence sets for the unknown exploratory variable are developed sufficient conditions under which they will be finite intervals are given the results are illustrated by a practical example

analyte identification in multivariate calibration in calibration experiments an estimated relationship between covariate information for a sample and an observed response is used to infer the covariate information for unknown samples from their responses in some situations this covariate information comprises a nominal variable e g identity of a chemical sex of an animal and a real valued variable e g concentration of the chemical age of animal if the calibrating relationship can be estimated separately for each candidate identity the first step in analyzing unknown samples is to correctly determine their identity a discrimination statistic is suggested for use in this situation and its asymptotic distribution is derived the investigation is motivated by the possibility of using multiple immunoassays in environmental monitoring to identify and quantitate contaminated samples in situations where there are several candidate pollutants that cross react significantly to single assays an example is given of the use of a four antibody assay for the simultaneous monitoring of the levels in water samples of several of the commonly used triazine herbicides and their derivatives

reconstruction of equivalent currents distribution over arbitrary three dimensional surfaces based on integral equation algorithms a technique for the determination of the equivalent currents distribution from a known radiated field is described this inverse radiation problem is solved through an integral equation algorithm that allows the characterization of antennas of complex geometry both for near field to far field nf ff transformation purposes as well as for diagnostic tasks the algorithm is based on the representation of the radiating structure by means of a set of equivalent currents over a three dimensional 3d surface that can be fitted to the arbitrary geometry of the antenna the innovative formulation uses an integral equation involving the electric field due to the currents tangential components to the represented antenna 3d surface for that purpose both the magnetic and electric equivalent currents are considered in the integral equations regularization techniques are also introduced to improve the convergence of the proposed iterative solution the paper concludes with several results related to the practical verification of the equivalence principle and the characterization of a horn antenna

theory of traces abstract the theory of traces originated by a mazurkiewicz in 1977 is an attempt to provide a mathematical description of the behavior of concurrent systems its aim is to reconcile the sequential nature of observations of the system behavior on the one hand and the nonsequential nature of causality between the actions of the system on the other hand one can see the theory of traces to be rooted in formal string language theory with the notion of partial commutativity playing the central role alternatively one can see the theory of traces to be rooted in the theory of labeled acyclic directed graphs or even in the theory of labeled partial orders this paper attempts to present a major portion of the theory of traces in a unified way however it is not a survey in the sense that a number of new notions are introduced and a number of new results are proved although traditionally most of the development in the theory of traces follows the string language theoretic line we try to demonstrate to the reader that the graph theoretic point of view may be more appropriate the paper essentially consists of two parts the first one sections 1 through 4 is concerned with the basic theory of traces the second one section 5 presents applications of the theory of traces to the theory of the behavior of concurrent systems where the basic system model we have chosen is the condition event system introduced by c a petri

recognizable languages in concurrency monoids automata with concurrency relations a are labelled transition systems with a collection of binary relations indicating when two actions in a given state of the automaton are concurrent we investigate concurrency monoids m a comprising all finite computation sequences of a modulo a canonical congruence induced by the concurrency relations with composition as monoid operation under suitable assumptions on a we obtain a kleene type characterization of the recognizable languages of m a this generalizes results of cori metivier perrin and ochmanski in trace theory

quadrature over a pyramid or cube of integrands with a singularity at a vertex a simple transformation is introduced which facilitates the evaluation of integrals over certain square based pyramids or cubes in cases where the integrand has a singularity at a vertex

multilevel fast multipole accelerated inverse equivalent current method employing rao wilton glisson discretization of electric and magnetic surface currents the radiation of any object in a homogeneous environment can be described by a set of equivalent sources different types of equivalent sources are feasible and all of them have their own benefits equivalent current methods are especially advantageous for irregular measurement grids of arbitrary shape and if a priori information about the object shall be used also they can immediately provide diagnostic information about the object in this paper a very flexible equivalent current method is presented which has been derived from a general purpose boundary integral equation solver as such the method works with arbitrary triangular surface meshes and rao wilton glisson basis functions where electric and or magnetic surface current densities can be assumed high efficiency is achieved since the multilevel fast multipole method has been adapted to speed up the inverse solution process results obtained from simulations and measurements are presented where large scale problems with dimensions up to 75 wavelengths are considered

dgtd analysis of electromagnetic scattering from penetrable conductive objects with ibc to avoid straightforward volumetric discretization a discontinuous galerkin time domain dgtd method integrated with the impedance boundary condition ibc is presented in this paper to analyze the scattering from objects with finite conductivity two situations are considered 1 the skin depth is smaller than the thickness of the conductive volume 2 the skin depth is larger than the thickness of a thin conductive sheet for the first situation a surface impedance boundary condition sibc is employed wherein the surface impedance usually exhibits a complex relation with the frequency to incorporate the sibc into dgtd the surface impedance is first approximated by rational functions in the laplace domain using the fast relaxation vector fitting frvf technique via inverse laplace transform the time domain dgtd matrix equations can be obtained conveniently in integral form with respect to time t for the second situation a transmission ibc tibc is used to include the transparent effects of the fields in the tibc the tangential magnetic field jump is related with the tangential electric field via the surface conductivity in this work a specifically designed dgtd algorithm with tibc is developed to model the graphene up to the terahertz thz band in order to incorporate the tibc into dgtd without involving the time domain convolution an auxiliary surface polarization current governed by a first order differential equation is introduced over the graphene for open region scattering problems the dgtd algorithm is further hybridized with the time domain boundary integral tdbi method to rigorously truncate the computational domain to demonstrate the accuracy and applicability of the proposed algorithm several representative examples are provided

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

near field to near far field transformation for arbitrary near field geometry utilizing an equivalent electric current and mom presented here is a method for computing near and far field patterns of an antenna from its near field measurements taken over an arbitrarily shaped geometry this method utilizes near field data to determine an equivalent electric current source over a fictitious surface which encompasses the antenna this electric current once determined can be used to ascertain the near and the far field this method demonstrates the concept of analytic continuity i e once the value of the electric field is known for one region in space from a theoretical perspective its value for any other region can be extrapolated it is shown that the equivalent electric current produces the correct fields in the regions in front of the antenna regardless of the geometry over which the near field measurements are made in this approach the measured data need not satisfy the nyquist sampling criteria an electric field integral equation is developed to relate the near field to the equivalent electric current a moment method procedure is employed to solve the integral equation by transforming it into a matrix equation a least squares solution via singular value decomposition is used to solve the matrix equation computations with both synthetic and experimental data where the near field of several antenna configurations are measured over various geometrical surfaces illustrate the accuracy of this method

fast antenna diagnosis algorithm using oblate spheroidal nonuniform grids a fast algorithm for the diagnosis of large antennas is developed the algorithm is based on the rayleigh sommerfeld rs backpropagation method accelerated by a multilevel nonuniform grid algorithm comparison between the field distributions reconstructed from measurements and the desired ones can be used for the localization of antenna defects and geometrical distortions the optimal performance is obtained by using oblate spheroidal grids which are tailored to both the measurement and antenna surfaces further acceleration can be achieved for particular cases via optimal sampling on the antenna surface the algorithm s performance is demonstrated for the example of a parabolic reflector with a number of surface distortions and compared to that achieved with spherical grids the accuracy and error controllability are studied in comparison to the direct rs integral computation

reconstruction of the field distribution on slot array antennas using the gerchberg papoulis algorithm a method to reconstruct the field distribution on slot array antennas is presented the field on each slot is reconstructed with high spatial resolution by extrapolating the invisible region of the plane wave spectrum pws using the gerchberg papoulis g p algorithm the information of the slot positions angles and lengths is exploited in the g p algorithm to enhance the accuracy and resolution of the reconstructed field the proposed algorithm is validated through the source reconstruction of a k band radial line slot antenna rlsa from the near field on planar and spherical scanning surfaces

multivariate calibration when the error covariance matrix is structured this article concerns multivariate calibration in linear models the error covariance matrix is assumed to have linear factor structure a new approach to calibration incorporating distributional properties of the observations of the calibration set is proposed the proposed predictor is based on estimating the parameters in the best linear predictor in the assumed model the predictor is tested on two data sets meat data and fish data

a new method for avoiding the truncation error in near field antennas measurements a new method to avoid the truncation error in antenna near field measurements is presented the approach relies on the concept of information content of the field according to this point of view the truncation problem is solved by picking up the information that is lost due to the finite size of scanning area in points of the space reachable by the measurement system the method can be applied to any scanning geometry including the planar and cylindrical ones whenever the set up allows to vary the distance between the antenna under test and the probe during the scanning procedure application of the method to cylindrical near field scanning is numerically investigated assessing the effectiveness of the proposed technique

methods for noise reduction in far field patterns obtained from cylindrical near field antenna measurements two different methods to reduce the noise power in the far field pattern of an antenna as measured in cylindrical near field cnf are proposed both methods are based on the same principle the data recorded in the cnf measurement assumed to be corrupted by white gaussian and space stationary noise are transformed into a new domain where it is possible to filter out a portion of noise those filtered data are then used to calculate a far field pattern with less noise power than that one obtained from the measured data without applying any filtering statistical analyses are carried out to deduce the expressions of the signal to noise ratio improvement achieved with each method although the idea of the two alternatives is the same there are important differences between them the first one applies a modal filtering requires an oversampling and improves the far field pattern in all directions the second method employs a spatial filtering on the antenna plane does not require oversampling and the far field pattern is only improved in the forward hemisphere several examples are presented using both simulated and measured near field data to verify the effectiveness of the methods

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

nystrom method solution of volume integral equations for electromagnetic scattering by 3d penetrable objects the volume integral equations vies for electromagnetic em scattering by three dimensional 3d penetrable objects are solved by nystrom method the vies are essential and cannot be replaced by surface integral equations sies for inhomogeneous problems but they are usually solved by the method of moments mom the nystrom method as an alternative for the mom has shown much promise and has been widely used to solve the sies but it is less frequently applied to the vies especially for 3d em problems in this work we implement the nystrom method for 3d vies by developing an efficient local correction scheme for singular and near singular integrals over tetrahedral elements the scheme first interpolates the unknown functions within the tetrahedral elements and then derives analytical solutions for the resultant singular or near singular integrals after singularity subtraction the scheme is simpler and more efficient in implementation compared with those based on the redesign of quadrature rules for the singular or near singular integrands numerical examples are presented to demonstrate the effectiveness of the proposed scheme and its convergence feature is also studied

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

antenna generalized scattering matrix in terms of equivalent infinitesimal dipoles application to finite array problems a full wave antenna modeling method by means of elementary sources described in terms of colocalized infinitesimal dipoles is presented in this paper the procedure provides a generalized scattering matrix gsm in terms of equivalent infinitesimal dipoles from the gsm of the antenna by using rotation and translation of spherical modes the number of equivalent infinitesimal dipoles and their positions are optimized by using a genetic algorithm the application to the full wave analysis of arrays is also presented providing very accurate results even when the minimum spheres of the antennas in the array environment overlap considerably which cannot be solved by the direct coupling of generalized scattering matrices in terms of spherical waves some examples of antenna modeling and their application to the analysis of arrays of antennas on a metallic plane will be shown

the sources reconstruction method for amplitude only field measurements an extension of the sources reconstruction method srm for antenna diagnostics using amplitude only field measurements is presented while previous works limit the application to canonical domain cases the combination of the srm capabilities for handling with arbitrary geometry domains jointly with phase retrieval techniques allows antenna diagnostics extension to complex geometry antenna and field acquisition domains the consideration of the radiation inverse problem with a general integral equation formulation using arbitrary geometry field and currents domains and field phaseless information supposes a challenging ill posed problem that is solved using iterative minimization techniques for non linear problems different examples are presented from simple to general antenna diagnostics cases

inverse estimates from a multiresponse model summary in a multiresponse model a multivariate y is modelled as a nonlinear function of the independent variable x the inverse estimate of x for a given observation on y is the object of study in this paper a straightforward method is proposed for estimating x and setting confidence limits to the estimate an example of determining age from the lengths of horns of a rhinoceros is given animal based on horn lengths only we specifically deal with the situation in which the response functions are nonlinear in the unknown parameters the method proposed is to augment the original data set with the additional measure ments lag and vpg of the extra animal whose age is needed and a guessed age xi varying values of xg will generate varying values of the maximized likelihood conditional on xg and these define the profile likelihood kalbfleisch and sprott 1970 for xg this profile likelihood can be used and interpreted in a number of ways all basically intended to illustrate the reliability of the age estimate a cautionary word is required the step of associating the profile likelihood with classical confidence limits for the true value of xg is difficult and only approximate solutions are available to that extent this paper should not be regarded as proposing a definitive answer there are open questions raised in particular it would be valuable to quantify more precisely the sampling distribution of the profile likelihood function the problem posed here is a version of the multivariate calibration problem the literature although sometimes couched in more general terms invariably deals in detail only with response models that are linear in the unknown parameters 0 brown 1982 gives a broad review of the linear multivariate calibration problem and outlines both bayesian and non bayesian solutions hunter and lamboy 1981 review the linear problem from a bayesian viewpoint brown and sundberg 1987 1989 propose using the profile likelihood of x minder and whitney 1975 derived a marginal likelihood approach the classic paper on univariate linear calibration is that of fieller 1940 and many modern ideas can be related back to the fieller fiducial limits oman and wax 1984 give an interesting application of linear multivariate calibration in estimating fetal age given two

source identification in time domain electromagnetics in this paper we introduce two numerical methods to get an electric source that gives a specified electromagnetic field some time after the source starts emitting the first one is called the time reversal method trm and originates from acoustics and the second one is called linear combination of configuration fields lccf and consists in constructing and solving a linear problem in order to find a possible required source in this paper we show on 1d and 2d examples that the last method gives lower relative errors when compared with the time reversal method

accurate and efficient nystrom volume integral equation method for the maxwell equations for multiple 3 d scatterers in this paper we develop an accurate and efficient nystrom volume integral equation vie method for the maxwell equations for a large number of 3 d scatterers the cauchy principal values that arise from the vie are computed accurately using a finite size exclusion volume together with explicit correction integrals consisting of removable singularities also the hyper singular integrals are computed using interpolated quadrature formulae with tensor product quadrature nodes for cubes spheres and cylinders that are frequently encountered in the design of meta materials the resulting nystrom vie method is shown to have high accuracy with a small number of collocation points and demonstrates p convergence for computing the electromagnetic scattering of these objects numerical calculations of multiple scatterers of cubic spherical and cylindrical shapes validate the efficiency and accuracy of the proposed method

radial field retrieval in spherical scanning for current reconstruction and nf ff transformation a near field to far field nf ff transformation is addressed for the case of spherical scanning using equivalent magnetic currents emcs and matrix methods it is based on the decoupling of the field components and the iterative retrieval of the radial component of the electric field the technique is applied for far field calculation as well as for the estimation of the current distribution of the antenna under test aut using spherical near field facilities results from measured near field data of several antennas are presented and compared to those of the analytical solution via a spherical wave mode expansion method

the kleene schutzenberger theorem for formal power series in partially commuting variables kleene s theorem on the coincidence of regular and rational languages in free monoids has been generalized by schutzenberger to a description of the recognizable formal power series in noncommuting variables over arbitrary semirings and by ochmanski to a characterization of the recognizable languages in trace monoids we will describe the recognizable formal power series over arbitrary semirings and in partially commuting variables i e over trace monoids we prove that the recognizable series are certain rational power series which can be constructed from the polynomials by using the operations sum product and a restricted star which is applied only to series for which the elements in the support all have the same connected alphabet the converse is true if the underlying semiring is commutative moreover if in addition the semiring is idempotent then the same result holds with a star restricted to series for which the elements in the support have connected possibly different alphabets it is shown that these assumptions over the semiring are necessary this provides a joint generalization of kleene s schutzenberger s and ochmanski s theorems

a hybrid scheme with nystrom discretization for solving transient electromagnetic scattering by conducting objects the interaction of transient electromagnetic em waves with objects can be formulated by the integral equation approach in time domain for conducting objects or homogeneous penetrable objects the time domain surface integral equations tdsies can be applied traditionally the tdsies are solved by combining the method of moments mom in spatial domain and a march on in time mot scheme in temporal domain the mom usually requires conforming meshes with a well designed basis function and the mot may suffer from a stability problem in this work we propose a hybrid scheme in which the nystrom method is used in spatial domain while the mom with laguerre function as basis and testing functions is employed with a march on in degree mod manner in the temporal domain the nystrom method does not require any basis and testing functions and can use nonconforming meshes in spatial domain whereas the mom with laguerre function as basis and testing functions can fully eliminate the stability problem in temporal domain numerical examples for em scattering by typical conducting objects are presented to demonstrate the scheme and its merits have been verified

on the condition number of a normal matrix in near field to far field transformations in near field scanning the model parameters for the antenna under test can be determined from measured probe outputs by solving a linear system of equations in the least squares sense the model parameters are far field pattern values cylindrical or spherical wave expansion coefficients or equivalent surface source values the normal matrix of this linear system of equations is sometimes extremely ill conditioned this occurs when certain sets of model parameters lie outside the spatial bandwidth of the operator that computes the probe output one remedy is to restrict the sets of model parameters allowed and perform upsampling if needed to achieve the desired accuracy these ideas are illustrated through analysis and examples that involve both 2 d and 3 d scanning geometries

nonconformal discretization of electric current volume integral equation with higher order hierarchical vector basis functions a nonconformal discretization of the electric current volume integral equation jvie is presented for the electromagnetic scattering analysis of inhomogeneous dielectric objects this jvie is based on higher order geometrical and current modeling where curved tetrahedral elements and higher order hierarchical vector hohv basis functions are adopted in order to implement the nonconformal discretization the half face based hohv basis function is introduced to address the nonconformal volumetric elements compared to the conventional low order conformal nonconformal vie our nonconformal hohv based jvie has the advantage of improving the computational efficiency and accuracy compared to the previous vie discretized by other higher order functions our nonconformal jvie is based on the higher order geometric modeling and the hohv bases in order to improve the efficiency the basis expansion and recombination technique is introduced to significantly accelerate the matrix filling moreover the flexibility of basis order selection is further enhanced by the mixed order schemes numerical results are given to demonstrate its accuracy efficiency and flexibility

efficient near field far field transformation for nonredundant sampling representation on arbitrary surfaces in near field antenna measurements a nonredundant sampling representation on arbitrary surfaces in near field antenna measurements together with a direct near field far field transformation is described the utilized sampling criterion depends on the electrical size of the antenna under test aut along with the separation between the aut and the measurement surface the minimum number of samples required is directly linked with the number of unknowns in the linear system of equations derived considering spherical expansion of radiated aut fields equivalent plane wave sources are used to represent the aut fields plane wave translations can be directly performed for any arbitrary measurement grid with the same efficiency thus nonredundant sampling representations can be utilized on any scan surface in contrast other fast field transformation techniques would lose their efficiency the proposed sampling is applied to near field measurements and synthetic data using a variety of antennas and the results are compared to the case of standard sampling remarkable decrease in the number of measurement points is observed with a negligible change in the accuracy of the transformed pattern thereby greatly reducing the measurement time and the computational effort