a brick tetrahedron finite element interface with stable hybrid explicit implicit time stepping for maxwell s equations a new brick tetrahedron finite element interface with stable hybrid explicit implicit time stepping for maxwell s equations is described and tested the tetrahedrons are connected directly to the bricks as opposed to previous curl conforming formulations that use an intermediate layer of pyramids the electric field is expanded in linear edge elements which yields a discontinuous tangential electric field at the brick tetrahedron interface and this discontinuity is treated by nitsche s method in addition tangential continuity for an arbitrary constant electric field is imposed in the strong sense at the interface which makes it possible to avoid penalization that perturbs the frequency spectrum this hybridization preserves the null space of the curl curl operator and is free from non physical spurious modes which is confirmed by numerical tests the implicit newmark time stepping scheme is employed for the tetrahedrons which allows for local mesh refinement without reduced time step for the brick elements spatial lumping and explicit time stepping is employed which yields the standard finite difference time domain scheme furthermore we prove that the explicit implicit time stepping employed at the hybrid interface is stable for time steps up to the courant limit of the explicitly time stepped bricks second order of convergence is achieved for field solutions without singular behavior the reflection from the brick tetrahedron interface is small and scattering from a thin layer of tetrahedrons indicates levels at approximately 49db for a resolution of 14 cells per wavelength

the hp finite element method for problems in mechanics with boundary layers abstract we consider the numerical approximation of boundary layer phenomena occurring in many singularly perturbed problems in mechanics such as plate and shell problems we present guidelines for the effective resolution of such layers in the context of existing commercial p and hp finite element fe version codes we show that if high order spectral elements are available then just two elements are sufficient to approximate these layers at a near exponential rate independently of the problem parameters thickness or reynolds number we present hp mesh design principles for situations where both corner singularities and boundary layers are present

value at risk forecasts by a spatiotemporal model in chinese stock market abstract this paper generalizes a recently proposed spatial autoregressive model and introduces a spatiotemporal model for forecasting stock returns we support the view that stock returns are affected not only by the absolute values of factors such as firm size book to market ratio and momentum but also by the relative values of factors like trading volume ranking and market capitalization ranking in each period this article studies a new method for constructing stocks reference groups the method is called quartile method applying the method empirically to the shanghai stock exchange 50 index we compare the daily volatility forecasting performance and the out of sample forecasting performance of value at risk var estimated by different models the empirical results show that the spatiotemporal model performs surprisingly well in terms of capturing spatial dependences among individual stocks and it produces more accurate var forecasts than the other three models introduced in the previous literature moreover the findings indicate that both allowing for serial correlation in the disturbances and using time varying spatial weight matrices can greatly improve the predictive accuracy of a spatial autoregressive model

multivariate error components analysis of linear and nonlinear regression models by maximum likelihood abstract this paper analyses the estimation by maximum likelihood of multivariate error component models linear and nonlinear under various assumptions on the errors special attention is given to testing and imposing positivity constraints and equality and inequality restrictions also the appropriate asymptotic covariance matrices are derived enabling us inter alia to perform wald tests of various relevant hypotheses

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

energy stable and high order accurate finite difference methods on staggered grids for wave propagation over distances of many wavelengths high order finite difference methods on staggered grids are widely used due to their excellent dispersion properties however the enforceme

a novel subgridding scheme based on a combination of the finite element and finite difference time domain methods a simple and versatile local mesh refinement scheme based on the hybridization of the finite element fe and the finite difference time domain fdtd algorithms is presented the scheme achieves considerable flexibility in subgridding by using a transition region between the coarse and fine fdtd grids meshed according to an unstructured grid and solved by means of the fe method in the td an interpolation scheme in the time domain which allows the use of different time steps in the coarse and fine mesh regions is included in the paper

robust tests for heteroskedasticity in the one way error components model this paper constructs tests for heteroskedasticity in one way error components models in line with baltagi et al baltagi b h bresson g pirotte a 2006 joint lm test for homoskedasticity in a one way error component model journal of econometrics 134 401 417 our tests have two additional robustness properties first standard tests for heteroskedasticity in the individual component are shown to be negatively affected by heteroskedasticity in the remainder component we derive modified tests that are insensitive to heteroskedasticity in the component not being checked and hence help identify the source of heteroskedasticity second gaussian based lm tests are shown to reject too often in the presence of heavy tailed e g t student distributions by using a conditional moment framework we derive distribution free tests that are robust to non normalities our tests are computationally convenient since they are based on simple artificial regressions after pooled ols estimation

compact high order stencils with optimal accuracy for numerical solutions of 2 d time independent elasticity equations abstract a new approach for the increase in the order of accuracy of high order numerical techniques used for time independent elasticity is suggested on uniform square and rectangular meshes it is based on the optimization of the coefficients of the corresponding discrete stencil equations with respect to the local truncation error it is shown that the second order of accuracy of 2 d linear finite elements with 9 point stencils is optimal and cannot be improved however the order of accuracy of 25 point stencils similar to those for quadratic finite and isogeometric elements can be significantly improved we have developed new 25 point stencils for 2 d elastic problems with optimal 10th order of accuracy the numerical results are in good agreement with the theoretical findings as well as they show a big increase in accuracy of the new stencils compared with those for high order finite elements at the same number of degrees of freedom the new approach yields significantly more accurate results than those obtained by high order up to the tenth order finite elements the numerical experiments also show that the new approach with 25 point stencils yields very accurate results for nearly incompressible materials with poisson s ratio 0 4999

numerical evaluation of high order finite element time domain formulations in electromagnetics this paper compares three full wave finite element time domain fetd formulations the first is based on the vector wave equation the others on maxwell s equations viz the ebhd formulation that discretizes e rarr b rarr h rarr and drarr and the eb formulation that discretizes only e rarr and b rarr the latter two formulations use a combination of 1 and 2 form discretization to avoid an auxiliary mesh a novel method for making the ebhd formulation operational is presented conditions for finite difference time domain fdtd like explicit operation are discussed the formulations are compared numerically by solving a three dimensional cavity and a rectangular waveguide using high order field representations up to mixed fourth order the error balance between time integration and field representation is investigated difficulties in making the ebhd formulation operational which have not previously been addressed in the literature are discussed and worked around novel numerical results show that the ebhd formulation has serious performance limitations

hybrid time domain solvers for the maxwell equations in 2d numerical simulation is an important tool in understanding the electromagnetic field and how it interacts with the environment different topics for time domain finite difference fdtd and finite element fetd methods for maxwell s equations are treated in this thesis subcell models are of vital importance for the efficient modeling of small objects that are not resolved by the grid a novel model for thin sheets using shell elements is proposed this approach has the advantage of taking into account discontinuities in the normal component of the electric field unlike previous models based on impedance boundary conditions ibcs several results are presented to illustrate the capabilities of the shell element approach waveguides are of fundamental importance in many microwave applications for example in antenna feeds the key issues of excitation and truncation of waveguides are addressed a complex frequency shifted form of the uniaxial perfectly matched layer upml absorbing boundary condition abc in fetd is developed prism elements are used to promote automatic grid generation and enhance the performance results are presented where reflection errors below 70db are obtained for different types of waveguides including inhomogeneous cases excitation and analysis via the scattering parameters are achieved using waveguide modes computed by a general frequency domain mode solver for the vector helmholtz equation huygens surfaces are used in both fdtd and fetd for excitation in waveguide ports inverse problems have received an increased interest due to the availability of powerful computers an important application is non destructive evaluation of material a time domain minimization approach is presented where exact gradients are computed using the adjoint problem the approach is applied to a general form of maxwell s equations including dispersive media and upml successful reconstruction examples are presented both using synthetic and experimental measurement data parameter reduction of complex geometries using simplified models is an interesting topic that leads to an inverse problem gradients for subcell parameters are derived and a successful reconstruction example is presented for a combined dielectric sheet and slot geometry

asymptotic study of the solution for pinched cylindrical shells abstract we consider the displacement problem of a cylindrical roof under a pointwise dirac load acting in the normal direction and recognize two classes of possible responses in dependence of the boundary conditions the bending dominated and the intermediate case we theoretically analyze the local form of the solution around the load application point in both cases the latter which is equivalent to the classical pinched cylinder benchmark shows a layer of characteristic length t 1 4 in the angular direction while the first one shows a smoother solution finally we exploit the results obtained in order to derive some good numerical strategies for the problem in the last section we show the perfect correspondence between the theoretical results and the solution obtained through numerical means

introduction and study of fourth order theta schemes for linear wave equations a new class of high order implicit three time step schemes for semi discretized wave equations is introduced and studied these schemes are constructed using the modified equation approach generalizing the q scheme their stability properties are investigated via an energy analysis which enables us to design super convergent schemes and also optimal stable schemes in terms of consistency errors specific numerical algorithms for the fully discrete problem are tested and discussed showing the efficiency of our approach compared to second order q schemes

higher order hybrid implicit explicit fdtd time stepping both partially implicit fdtd methods and symplectic fdtd methods of high temporal accuracy 3rd or 4th order are well documented in the literature in this paper we combine them we construct a conservative fdtd method which is fourth order accurate in time and is partially implicit we show that the stability condition for this method depends exclusively on the explicit part which makes it suitable for use in e g modelling wave propagation in plasmas

application of stable fem fdtd hybrid to scattering problems a recently developed stable finite element method fem finite difference time domain fdtd hybrid that eliminates the staircase approximation of complex geometries is tested by convergence studies for radar cross sections for a conducting sphere 1 db accuracy in all directions is obtained with nine cells per wavelength whereas the nasa almond requires a higher resolution of about 15 cells per wavelength for scatterers with a smooth boundary the results converge quadratically with the mesh size but for a horizontally polarized wave incident on the nasa almond the order of convergence is lower because of singular fields at the tip

a hybrid method combining the multitemporal resolution time domain method of moments with the time domain geometrical theory of diffraction for thin wire antenna problems in this paper a hybrid method combining a multitemporal resolution mtr enhanced time domain method of moments td mom with the td geometrical theory of diffraction gtd is presented which allows to efficiently calculate the transient fields radiated by antennas in presence of large objects the mtr scheme tailors the time step size and thus implicitly the duration of the temporal basis function on the basis of the distance between source and test element additionally the voltage induced by source elements far away from the test element is interpolated in time the hybrid method is applied to calculate the radiation properties of thin wire antennas in presence of perfectly conducting flat scatterers to demonstrate its basic features and advantages

shell deformation states and the finite element method a benchmark study of cylindrical shells abstract we demonstrate some of the basic mathematical characteristics of shell deformation states and shell models from the point of view of finite element approximation as benchmark cases we analyze in detail three simple cylindrical shell problems these problems are seemingly similar but turn out to be quite different we 1 compute the exact displacement and strain fields in the model problems both numerically and symbolically using two variants of classical shell models 2 for comparison compute numerically the displacements and strains corresponding to certain higher order dimension reduction models derived from the energy principle 3 demonstrate the dissimilarity of the three benchmark problems as to their asymptotic behaviour in the limit of zero thickness and 4 show both theoretically and experimentally how this diversity is reflected in the accuracy of standard finite element approximations of both low and high order

tests for the error component model in the presence of local misspecification it is well known that most of the standard specification tests are not valid when the alternative hypothesis is misspecified this is particularly true in the error component model when one tests for either random effects or serial correlation without taking account of the presence of the other effect in this paper we study the size and power of the standard rao s score tests analytically and by simulation when the data are contaminated by local misspecification these tests are adversely affected under misspecification we suggest simple procedures to test for random effects or serial correlation in the presence of local serial correlation or random effects and these tests require ordinary least squares residuals only our monte carlo results demonstrate that the suggested tests have good finite sample properties for local misspecification and in some cases even for far distant misspecification our tests are also capable of detecting the right direction of the departure from the null hypothesis we also provide some empirical illustrations to highlight the usefulness of our tests

locally implicit discontinuous galerkin method for time domain electromagnetics in the recent years there has been an increasing interest in discontinuous galerkin time domain dgtd methods for the solution of the unsteady maxwell equations modeling electromagnetic wave propagation one of the main features of dgtd methods is their ability to deal with unstructured meshes which are particularly well suited to the discretization of the geometrical details and heterogeneous media that characterize realistic propagation problems such dgtd methods most often rely on explicit time integration schemes and lead to block diagonal mass matrices however explicit dgtd methods are also constrained by a stability condition that can be very restrictive on highly refined meshes and when the local approximation relies on high order polynomial interpolation an implicit time integration scheme is a natural way to obtain a time domain method which is unconditionally stable but at the expense of the inversion of a global linear system at each time step a more viable approach consists of applying an implicit time integration scheme locally in the refined regions of the mesh while preserving an explicit time scheme in the complementary part resulting in an hybrid explicit implicit or locally implicit time integration strategy in this paper we report on our recent efforts towards the development of such a hybrid explicit implicit dgtd method for solving the time domain maxwell equations on unstructured simplicial meshes numerical experiments for 3d propagation problems in homogeneous and heterogeneous media illustrate the possibilities of the method for simulations involving locally refined meshes

uniform error estimates for a class of intermediate cylindrical shell problems a uniform in thickness error estimate is obtained for a particular class of intermediate koiter shell problems solved with a classical conforming finite element method the model problem is that of a cylinder under a class of irregular loads which due to particular symmetries allow a simplified reformulation on a one dimensional domain the result is an almost hs error behavior in the h 1 dual norm were s 0 depends on the load regularity such estimate is believable to be sharp this additional claim is supported by some numerical tests

analysis of photonic crystals using the hybrid finite element finite difference time domain technique based on the discontinuous galerkin method summary two dimensional photonic crystal structures are analyzed by a recently developed hybrid technique combining the finite element time domain fetd method and the finite difference time domain fdtd method this hybrid fetd fdtd method uses the discontinuous galerkin method as framework for domain decomposition to the best of our knowledge this is the first hybrid fetd fdtd method that allows non conformal meshes between different fetd and fdtd subdomains it is also highly parallelizable these properties are very suitable for the computation of periodic structures with curved surfaces numerical examples for the computation of the scattering parameters of two dimensional photonic bandgap structures are presented as applications of the hybrid fetd fdtd method numerical results demonstrate the efficiency and accuracy of the proposed hybrid method copyright 2012 john wiley sons ltd

on the locking phenomenon for a class of elliptic problems in this paper we study the numerical behaviour of elliptic problems in which a small parameter is involved and an example concerning the computation of elastic arches is analyzed using this mathematical framework at first the statements of the problem and its galerkin approximations are defined and an asymptotic analysis is performed then we give general conditions ensuring that a numerical scheme will converge uniformly with respect to the small parameter finally we study an example in computation of arches working in linear elasticity conditions we build one finite element scheme giving a locking behaviour and another one which does not

a hybrid finite element boundary integral method for the analysis of cavity backed antennas of arbitrary shape an edge based hybrid finite element boundary integral fe bi formulation using tetrahedral elements is described for scattering and radiation analysis of arbitrarily shaped cavity backed patch antennas by virtue of the finite element method fem the cavity irregularities the dielectric super substrate inhomogeneities and the diverse excitation schemes inside the cavity may be readily modeled when tetrahedral elements are used to discretize the cavity on the aperture the volume mesh reduces to a triangular grid allowing the modeling of nonrectangular patches without special handling of the boundary integral system this formulation is typically applicable to cavity backed antenna systems with moderate aperture size to retain an o n memory requirement storage of the full matrix due to the boundary integral equation is avoided by resorting to a structured triangular aperture grid and taking advantage of the integral s convolutional property if necessary this is achieved by overlaying a structured triangular grid on the unstructured triangular grid and relating the edge field coefficients between the two grids via two narrow banded transformation matrices the combined linear system of equations is solved via the biconjugate gradient bicg method and the fft algorithm is incorporated to compute the matrix vector product efficiently with minimal storage requirements

a novel approach for the efficient computation of 1 d and 2 d summations a novel computational method is proposed to evaluate 1 d and 2 d summations and integrals which are relatively difficult to compute numerically the method is based on applying a subspace algorithm to the samples of partial sums and approximating them in terms of complex exponentials for a convergent summation the residue of the exponential term with zero complex pole of this approximation corresponds to the result of the summation since the procedure requires the evaluation of relatively small number of terms the computation time for the evaluation of the summation is reduced significantly in addition by using the proposed method very accurate and convergent results are obtained for the summations which are not even absolutely convergent the efficiency and accuracy of the method are verified by evaluating some challenging 1 d and 2 d summations and integrals

a hybrid time domain technique that combines the finite element finite difference and method of moment techniques to solve complex electromagnetic problems this paper describes a hybrid technique directly operating in time domain that combines the finite element time domain fetd the finite difference time domain fdtd and the integral equation based method of moments in the time domain momtd techniques to analyze complex electromagnetic problems involving thin wire antennas radiating in the presence of inhomogeneous dielectric bodies whose shape can be arbitrary the method brings together the ability of the fdtd scheme to deal with arbitrary material properties the versatility of the fetd to accurately model curved geometries and that of the mom to analyze thin wire structures working in the time domain provides wide band information from a single execution of the marching on in time procedure and simplifies the interfacing of the fe and mom methods with the fdtd an approach specifically designed for time domain analysis numerical results that validate the hybrid method and show its capabilities are presented in the paper

closed form green s function representations in cylindrically stratified media for method of moments applications closed form green s function cfgf representations for cylindrically stratified media which can be used as the kernel of an electric field integral equation are developed the developed cfgf representations can safely be used in a method of moments solution procedure as they are valid for almost all possible source and field points that lie on the same radial distance from the axis of the cylinder such as the air dielectric and dielectric dielectric interfaces including the axial line rho rho and phi phi which has not been available before in the course of obtaining these expressions the conventional spectral domain green s function representations are rewritten in a different form so that i we can attack the axial line problem and ii the method can handle electrically large cylinders available acceleration techniques that exist in the literature are implemented to perform the summation over the cylindrical eigenmodes efficiently lastly the resulting expressions are transformed to the spatial domain using the discrete complex image method with the help of the generalized pencil of function method where a modified two level approach is used numerical results are presented in the form of mutual coupling between two current modes to assess the accuracy of the final spatial domain cfgf representations

testing for heteroskedasticity in fixed effects models abstract we derive tests for heteroskedasticity after fixed effects estimation of linear panel models the asymptotic results are based on a large n fixed t framework where the incidental parameters problem is bypassed by utilizing a pseudo likelihood function conditional on the sufficient statistic for these parameters a simple studentization produces distribution free tests that can easily be implemented using an artificial regression based on residuals after fixed effects estimation a monte carlo exploration suggests that the tests perform well in small samples such as those encountered in practice

scale resolution locking and high order finite element modelling of shells abstract we demonstrate both by theory and experiment the benefits of using standard finite elements of relatively high degree in shell problems the difficulty of shell problems lies in their asymptotic diversity at zero thickness and in the multiple scale character of the deformation field when the thickness is small due to these characteristics standard finite elements of low degree often resolve the length scales of practical shell deformation very poorly unless extremely fine meshes are used however with standard finite elements of sufficiently high degree say cubic or quartic at least the quality of numerical scale resolution improves remarkably we show by simple error analysis that this effect is not problem specific but rather robust among the diversity of shell problems as numerical test cases we analyze two challenging problems in cylindrical shell geometry

a stable fdtd subgridding method based on finite element formulation with hanging variables the finite element time domain fetd method based on the use of hanging variables to generate nested grids is used as an interface between the coarse and fine grids in the fdtd subgridding method since the formulation for treating hanging variables is based on a galerkin type intergrid boundary operator the resulting fdtd subgridding algorithm is guaranteed to be stable numerical examples such as the computation of resonant modes of a 3 d rectangular resonant cavity and 2 d tez scattering by a pec cylinder and a naca airfoil are presented to verify the stability and accuracy of the proposed subgridding algorithm

new 25 point stencils with optimal accuracy for 2 d heat transfer problems comparison with the quadratic isogeometric elements abstract a new approach for the increase in the order of accuracy of high order elements used for the time dependent heat equation and for the time independent poisson equation has been suggested on uniform square and rectangular meshes it is based on the optimization of the coefficients of the corresponding discrete stencil equation with respect to the local truncation error by a simple modification of the coefficients of 25 point stencils the new approach exceeds the accuracy of the quadratic isogeometric elements by four orders for the heat equation and by twelve orders for the poisson equation despite the significant increase in accuracy the computational costs of the new technique are the same as those for the conventional quadratic isogeometric elements on a given mesh the numerical examples are in a good agreement with the theoretical results for the new approach and also show that the new approach is much more accurate than the conventional isogeometric elements at the same number of degrees of freedom hybrid methods that combine the new stencils with the conventional isogeometric and finite elements and can be applied to irregular domains are also presented

utilization of a unitary transform for efficient computation in the matrix pencil method to find the direction of arrival in this study we use the matrix pencil mp method to compute the direction of arrival doa of the signals using a very efficient computational procedure in which the complexity of the computation can be reduced significantly by using a unitary matrix transformation this method applies the technique directly to the data without forming a covariance matrix simulation results show that the variance of the estimate approaches to the cramer rao lower bound using real computations through the unitary transformation for the mp method leads to a very efficient computational methodology for real time implementation on a digital signal processor chip a unitary transform can convert the complex matrix to a real matrix along with their eigenvectors and thereby reducing the computational cost at least by a factor of four without sacrificing accuracy this reduction in the number of computations is achieved by using a transformation which maps centro hermitian matrices to real matrices this transformation is based on lee s work on centro hermitian matrices

comparative evaluation of absorbing boundary conditions using green s functions for layered media absorbing boundary conditions are comparatively studied using the green s functions of the vector and scalar potentials for multilayer geometries and general sources since the absorbing boundaries are introduced as additional layers with predefined reflection coefficients into the calculation of the green s functions this approach provides an absolute measure of the effectiveness of different absorbing boundaries the green s functions are calculated using different reflection coefficients corresponding to different absorbing boundaries and compared to those obtained with no absorbing boundary it is observed that the perfectly matched layer pml is by far the best among the other absorbing boundary conditions whose reflection coefficients are available

rational modeling by pencil of functions method pole zero modeling of signals such as an electromagnetic scatterer response is considered in this paper it is shown by use of the pencil of functions theorem that a the true parameters can be recovered in the ideal case where the signal is the impulse reponse of a rational function h z and b the parameters are optimal in the functional dependence sense when the observed data are corrupted by additive noise or by systematic error although the computations are more involved than in all pole modeling they are considerably less than those required in iterative schemes of pole zero modeling the advantages of the method are demonstrated by a simulation example and through application to the electromagnetic response of a scatterer the paper also includes very recent and promising results on a new approach to noise correction in contradistinction with spectral subtraction techniques where only amplitude information is emphasized and phase is ignored we propose a method that a estimates the noise spectral density for the data frame and then b performs the subtraction of the noise correlation matrix from the gram matrix of the signal

clarification of issues on the closed form green s functions in stratified media the closed form green s functions cfgf derived for the vector and scalar potentials in planar multilayer media have been revisited to clarify some issues and misunderstandings on the derivation of these green s functions in addition the range of validity of these green s functions is assessed with and without explicit evaluation of the surface wave contributions as it is well known the derivation of the cfgf begins with the approximation of the spectral domain green s functions by complex exponentials and continues with applying the sommerfeld identity to cast these approximated spectral domain green s functions into the space domain in closed forms questions and misunderstandings of this derivation which have mainly originated from the approximation process of the spectral domain green s functions in terms of complex exponentials can be categorized and discussed under the topics of 1 branch point contributions 2 surface wave pole contributions and 3 the accuracy of the obtained cfgf when these issues are clarified the region of validity of the cfgf so obtained may be defined better therefore in this paper these issues will be addressed first and then their origins and possible remedies will be provided with solid analysis and numerical demonstrations

taylor expansion based fast multipole method for 3 d helmholtz equations in layered media abstract in this paper we develop a taylor expansion te based fast multipole method fmm for low frequency 3d helmholtz green s function in layered media two forms of taylor expansions with either non symmetric or symmetric derivatives of layered media green s functions are used for the implementations of the proposed te fmm in the implementation with non symmetric derivatives an algorithm based on discrete complex image approximations and recurrence formulas is shown to be very efficient and accurate in computing the high order derivatives meanwhile the implementation based on symmetric derivatives is more robust and pre computed tables for the high order derivatives in translation operators are used numerical tests in layered media have validated the accuracy and o n complexity of the proposed algorithms

fast and accurate mom analysis of periodic arrays of multilayered stacked rectangular patches with application to the design of reflectarray antennas the scattering of plane waves by periodic arrays of stacked rectangular patches in multilayered substrates is a problem that has to be solved many times when designing reflectarray antennas made of those patches under the local periodicity assumption the solution to the periodic multilayered problem has been traditionally carried out by means of the galerkin s version of the method of moments mom in the spectral domain this approach involves the computation of double infinite summations and whereas some of these summations converge very fast some other converge very slowly in this paper the slowly convergent summations are computed by making use of an enhanced mixed potential integral equation mpie formulation of the mom in the spatial domain this enhanced formulation is based on the interpolation of the multilayered periodic green s functions and on the efficient computation of the four dimensional 4 d integrals leading to the mom matrix entries both the novel hybrid spectral spatial mom code and the standard spectral domain mom code have been used for the design of a contoured beam reflectarray antenna it has been verified that the spectral spatial mom code requires cpu times that are typically 30 times smaller than those required by the pure spectral domain mom code

generalized pencil of function method for extracting poles of an em system from its transient response a generalized pencil of function gpof method is developed for extracting the poles of an electromagnetic system from its transient response the gpof method needs the solution of a generalized eigenvalue problem to find the poles subspace decomposition is also used to optimize the performance of the gpof method the gpof method has advantages over the prony method in both computation and noise sensitivity and approaches the cramer rao bound when the signal to noise ratio snr is above threshold an application of the gpof method to a thin wire target is presented

stability of explicit implicit hybrid time stepping schemes for maxwell s equations an improved version of the stable fem fdtd hybrid method t rylander and a bondeson comput phys commun 125 75 2000 for maxwell s equations is presented the new formulation has a modified time stepping scheme and is rigorously proven to be stable for time steps up to the stability limit for the fdtd the new scheme gives less reflection at the boundary between the structured and unstructured grids than the original formulation the hybrid method is compared to the fdtd with staircasing for scattering from a conducting sphere the discretization errors of the hybrid show quadratic dependence on mesh size while the scaling is less clear for the fdtd the fdtd gives errors that are 5 60 times higher than that of the hybrid depending on resolution and staircasing strategy

a space time discretization criterion for a stable time marching solution of the electric field integral equation numerical techniques based on a time domain recursive solution of the electric field integral equation efie may exhibit instability phenomena induced by the joint space time discretization the above problem is addressed with specific reference to the evaluation of electromagnetic scattering from perfectly conducting bodies of arbitrary shape we analyze a particular formulation of the method of moments which relies on a triangular patch geometrical model of the exterior surface of the scattering body and operates according to a marching on in time scheme whereby the surface current distribution at a given time step is recursively evaluated as a function of the current distribution at previous steps a heuristic stability condition is devised which allows us to define a proper time step as well as a geometrical discretization criterion ensuring convergence of the numerical procedure and therefore eliminating insurgence of late time oscillations the stability condition is discussed and validated by means of a few working examples

an improved pencil of functions method and comparisons with traditional methods of pole extraction prony s method is usually used for the determination of poles from experimental data in the singularity expansion method sem literature it is the aim here to show that this is not the best method and that jain s pencil of functions pof method can be generalized to provide a better method an example of such a method is given

testing for heteroskedasticity and serial correlation in a random effects panel data model this paper considers a panel data regression model with heteroskedastic as well as serially correlated disturbances and derives a joint lm test for homoskedasticity and no first order serial correlation the restricted model is the standard random individual error component model it also derives a conditional lm test for homoskedasticity given serial correlation as well as a conditional lm test for no first order serial correlation given heteroskedasticity all in the context of a random effects panel data model monte carlo results show that these tests along with their likelihood ratio alternatives have good size and power under various forms of heteroskedasticity including exponential and quadratic functional forms

higher order brick tetrahedron hybrid method for maxwell s equations in time domain we present a higher order brick tetrahedron hybrid method for maxwell s equations in time domain brick shaped elements are used for large homogeneous parts of the computational domain where we exploit mass lumping and explicit time stepping in regions with complex geometry we use an unstructured mesh of tetrahedrons that share an interface with the brick shaped elements and at the interface tangential continuity of the electric field is imposed in the weak sense by means of nitsche s method implicit time stepping is used for the tetrahedrons together with the interface for cavity resonators the hybrid method reproduces the lowest non zero eigenvalues with correct multiplicity and for geometries without field singularities from sharp corners or edges the numerical eigenvalues converge towards the analytical result with an error that is approximately proportional to h 2 p where h is the cell size and p is the polynomial order of the elements for a rectangular waveguide a layer of tetrahedrons embedded in a grid of brick shaped elements yields a low reflection coefficient that scales approximately as h 2 p finally we demonstrate hybrid time stepping for a lossless closed cavity resonator where the time domain response is computed for 300 000 time steps without any signs of instabilities new hybrid fem interface between tetrahedrons and bricks for maxwell s equations nitsche s method is applied to higher order curl conforming basis functions allows for both incomplete and complete order basis functions on tetrahedrons stable hybrid explicit implicit time stepping scheme computational results up to fourth order curl conforming basis functions

correlate measurements at different test sites a new method for systematic correlation of measurements in semi anechoic and anechoic chambers is presented a signal measured in a semi anechoic chamber is first processed using the matrix pencil method which is applied sequentially on small frequency intervals on each interval the measured signal is decomposed into its propagating wave components the component corresponding to the wave reflected from the ground is identified and removed to fully retrieve the signal measured in an anechoic chamber three examples using log periodic and vivaldi antennas in different anechoic and semi anechoic chambers for varying frequency ranges illustrate the method the proposed decomposition algorithm can be utilized to characterize measurement test site imperfections

explicit and provably stable spatiotemporal fdtd refinement abstract in this paper we introduce an explicit and provably conditionally stable finite difference time domain fdtd algorithm for maxwell s equations with local refinement in both the spatial discretization length and in the time step spatiotemporal refinement this enables local spatial refinement with a locally reduced time step

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

time domain finite element methods various time domain finite element methods for the simulation of transient electromagnetic wave phenomena are discussed detailed descriptions of test trial spaces explicit and implicit formulations nodal and edge facet element basis functions are given along with the numerical stability properties of the different methods the advantages and disadvantages of mass lumping are examined finally the various formulations are compared on the basis of their numerical dispersion performance

electric and magnetic losses modeled by a stable hybrid with explicit implicit time stepping for maxwell s equations a stable hybridization of the finite element method fem and the finite difference time domain fdtd scheme for maxwell s equations with electric and magnetic losses is presented for two dimensional problems the hybrid method combines the flexibility of the fem with the efficiency of the fdtd scheme and it is based directly on ampere s and faraday s law the electric and magnetic losses can be treated implicitly by the fem on an unstructured mesh which allows for local mesh refinement in order to resolve rapid variations in the material parameters and or the electromagnetic field it is also feasible to handle larger homogeneous regions with losses by the explicit fdtd scheme connected to an implicitly time stepped and lossy fem region the hybrid method shows second order convergence for smooth scatterers the bistatic radar cross section rcs for a circular metal cylinder with a lossy coating converges to the analytical solution and an accuracy of 2 is achieved for about 20 points per wavelength the monostatic rcs for an airfoil that features sharp corners yields a lower order of convergence and it is found to agree well with what can be expected for singular fields at the sharp corners a careful convergence study with resolutions from 20 to 140 points per wavelength provides accurate extrapolated results for this non trivial test case which makes it possible to use as a reference problem for scattering codes that model both electric and magnetic losses

new oblique thin wire formalism in the fdtd method with multiwire junctions a new oblique thin wire formalism based on holland s approach is proposed in the fdtd method the principal achievement of this new formalism is to enable us to model a junction correctly between several oblique wires to this end an important criterion is proposed the continuity of the current traces in the grid must be maintained at each node of the yee cell that contains a part of one or several wires this condition prevents undamped parasite oscillations on the wire current responses in addition our approach offers versatility in its usage first the extremities of the wire can be placed freely in a yee cell second it operates in lossy medium and finally the sensitivity of the wire is minimized when inclined or shifted with regards to this last point the in cell inductance of a wire segment is formulated to take account of the segment position and its obliquity in the yee cell

a novel analysis of microstrip structures using the gaussian green s function method a novel closed form expression is derived for spatial green s functions of microstrip structures by expanding the spectral green s function into a gaussian series this innovative method is called the gaussian green s function ggf method due to the gaussian form in the closed form green s function representation the main advantage of the ggf method lies in its precision as well as rapid convergence to demonstrate the versatility of this method the current distribution of a microstrip antenna is achieved via the combination of the method of moments mom and ggf method it is shown that this method can be computationally very efficient with less than 1 error compared to the numerical integration of the spectral integral also the results of the ggf method have been compared to the results of the commercial full wave software of agilent ads

staircase free finite difference time domain formulation for general materials in complex geometries a stable cartesian grid staircase free finite difference time domain formulation for arbitrary material distributions in general geometries is introduced it is shown that the method exhibits higher accuracy than the classical yee 1966 scheme for complex geometries since the computational representation of physical structures is not of a staircased nature furthermore electromagnetic boundary conditions are correctly enforced the method significantly reduces simulation times as fewer points per wavelength are needed to accurately resolve the wave and the geometry both perfect electric conductors and dielectric structures have been investigated numerical results are presented and discussed

on the application of parametric models to the transient analysis of resonant and multiband antennas the transient responses of a resonant antenna and a fractal multiband antenna both formed by conducting surfaces are calculated the surfaces are modeled by planar triangular patches and the study is carried out by solving the time domain electric field integral equation td efie linear parametric modeling techniques are applied to considerably reduce the computation time numerical results are compared with experimental measurements

combining an extrapolation technique with the method of moments for solving large scattering problems involving bodies of revolution the purpose of this work is to combine an extrapolation technique with the method of moments mom to solve scattering problems involving large bodies it has been shown in a previous work that the current induced on the smooth parts of large scatterers may be represented as a series of complex exponential functions with a few terms based on this concept a hybrid set of basis functions is constructed using entire domain functions of complex exponential type on the smooth portion of the scatterer complemented by subdomain basis functions near edges and discontinuities an extrapolation procedure is developed in which the scattering problem is first solved for a portion of the scatterer using the conventional mom next a set of entire domain basis functions whose behaviour could be extrapolated with an increase in the size of the scatterer is extracted from this original solution the procedure outlined has the very desirable feature that the total number of basis functions remains unchanged even as the scatterer size is increased allowing for large scatterers to be handled with a relatively small number of unknowns the extrapolation technique is applied to scattering problems from bodies of revolution bors and numerical results for an open cylinder and a barrel shaped bor are presented

time domain bie analysis of large three dimensional electromagnetic scattering problems a time domain boundary integral equation bie solution of the magnetic field integral equation mfie for large electromagnetic scattering problems is presented it employs isoparametric curvilinear quadratic elements to model fields geometry and time dependence eliminating staircasing problems the approach is implicit which seems to provide both stability and permits arbitrary local mesh refinement to model geometrically difficult regions without the significant cost penalty explicit methods suffer error dependence on discretization is investigated accurate results are obtained with as few as five nodes per wavelength the performance both on large scatterers and on low radar cross section rcs scatterers is demonstrated including the six wavelength nasa almond two spheres a thirteen wavelength missile and a high q cavity

wavelet based testing for serial correlation of unknown form in panel models wavelet analysis is a new mathematical method developed as a unified field of science over the last decade or so as a spatially adaptive analytic tool wavelets are useful for capturing serial correlation where the spectrum has peaks or kinks as can arise from persistent dependence seasonality and other kinds of periodicity this paper proposes a new class of generally applicable wavelet based tests for serial correlation of unknown form in the estimated residuals of a panel regression model where error components can be one way or two way individual and time effects can be fixed or random and regressors may contain lagged dependent variables or deterministic stochastic trending variables our tests are applicable to unbalanced heterogenous panel data they have a convenient null limit n 0 1 distribution no formulation of an alternative model is required and our tests are consistent against serial correlation of unknown form even in the presence of substantial in homogeneity in serial correlation across individuals this is in contrast to existing serial correlation tests for panel models which ignore inhomogeneity in serial correlation across individuals by assuming a common alternative and thus have no power against the alternatives where the average of serial correlations among individuals is close to zero we propose and justify a data driven method to choose the smoothing parameter the finest scale in wavelet spectral estimation making the tests completely operational in practice the data driven finest scale automatically converges to zero under the null hypothesis of no serial correlation and diverges to infinity as the sample size increases under the alternative ensuring the consistency of our tests simulation shows that our tests perform well in small and finite samples relative to some existing tests

moment based tests for individual and time effects in panel data models abstract this paper proposes two hausman type tests respectively for individual and time effects in a two way error component regression model by comparing estimators of the variance of the idiosyncratic error at different robust levels they are both robust to the presence of the other effect and the test for the individual effect has a larger asymptotic power than the corresponding anova f test when the effects are correlated with covariates tests jointly for both effects are also discussed monte carlo evidence shows their good size properties and better power properties than competing tests and the application to the crime rate study gives further support

block pseudospectral methods for maxwell s equations ii two dimensional discontinuous coefficient case block pseudospectral bps methods are examined for maxwell s equations in two dimensional inhomogeneous media for the case of a rectangular strip with a straight line interface blocks may be coupled via fictitious points or a generalization of characteristic outflow conditions the bps methods generalize to curvilinear strips described by a change of variables such strips can conform to interfaces while overlapping with a high order free space grid to form a composite grid method numerical experiments on strips with dielectrics lossy materials perfect conductors and absorbing layers indicate that the two coupling methods are comparable and accurate with just 3 4 points per wavelength full composite examples are included to demonstrate high accuracy and geometric flexibility

a note on mass lumping in the finite element time domain method mass lumping has been used to produce explicit time integration schemes for the finite element time domain method in this paper we show that a specific choice in the lumping procedure can produce a scheme that is equivalent to the finite difference time domain method if lumping is done in the time integration process one can show that it can be equivalent to the newmark beta method

evaluation of efficient closed form green s function in a cylindrically stratified medium an efficient technique is proposed for the removal of the spatial singularity for a z directed current source in a cylindrically layered structure by decomposing the spectral domain green s function into the particular and homogeneous parts the particular part with the singularity is converted into the spatial domain using sommerfeld s identity while the dcim with general pencil of function technique is applied on the spectral domain homogeneous part the use of the ratio form of the reflection transmission matrices the debye approximation and the subsequent envelope extraction for the treatment of the spatial domain singularity is thus avoided in addition a very significant reduction in the number of modes required for convergence is also achieved the technique is applied for evaluating the input impedance of several antennas in the cylindrical multilayer structure together with a coupling configuration for the excitation of the multilayer structure

fourth order energy preserving locally implicit time discretization for linear wave equations a family of fourth order coupled implicit explicit time schemes is presented as a special case of fourth order coupled implicit schemes for linear wave equations the domain of interest is decomposed into several regions where different fourth order time discretization are used chosen among a family of implicit or explicit fourth order schemes the coupling is based on a lagrangian formulation on the boundaries between the several non conforming meshes of the regions a global discrete energy is shown to be preserved and leads to global fourth order consistency in time numerical results in 1d and 2d for the acoustic and elastodynamics equations illustrate the good behavior of the schemes and their potential for the simulation of realistic highly heterogeneous media or strongly refined geometries for which using everywhere an explicit scheme can be extremely penalizing accuracy up to fourth order reduces the numerical dispersion inherent to implicit methods used with a large time step and makes this family of schemes attractive compared to second order accurate methods

the problem of membrane locking in finite element analysis of cylindrical shells we analyse the problem of membrane locking in h p finite element models of a thin hemicylindrical shell roof loaded by a smoothly varying normal pressure distribution we show that in the standard finite element method locking occurs especially at low values ofp and when the finite element grid is not aligned with the axis of the cylinder a general strategy of avoiding locking by using modified bilinear forms is introduced and a special implementation of this strategy on aligned rectangular grids is considered

element free galerkin method for static and dynamic analysis of spatial shell structures the implementation of the element free galerkin method efg for static and free vibration analysis of general shell structures is presented in this paper the formulation of the discrete system equations is derived from the governing equations of stress resultant geometrically exact shell theory based on the cosserat surface a discrete singularity free mapping between the five and the six degrees of freedom formulation is constructed by exploiting the geometry connection between the orthogonal group and the unit sphere moving least squares approximation is used in both the construction of shape functions based on arbitrarily distributed nodes as well as in the surface approximation of general spatial shell geometry discrete system equations are obtained by incorporating these interpolations into the galerkin weak form the formulation is verified through numerical examples of static stress analysis and frequency analysis of spatial shell structures the phenomena of shear locking and membrane locking are illustrated by showing the membrane and shear energy as fractions of the total energy essential boundary conditions are efficiently imposed through a penalty technique for both static analysis and frequency analysis the formulation is tested on several benchmark problems and the results compare favorably with closed form solutions and that of finite element analyses

an in depth stability analysis of nonuniform fdtd combined with novel local implicitization techniques this work focuses on efficient full wave solutions of multiscale electromagnetic problems in the time domain three local implicitization techniques are proposed and carefully analyzed in order to relax the traditional time step limit of the finite difference time domain fdtd method on a nonuniform staggered tensor product grid newmark cranknicolson cn and alternating direction implicit adi implicitization all of them are applied in preferable directions alike hybrid implicitexplicit hie methods as to limit the rank of the sparse linear systems both exponential and linear stability are rigorously investigated for arbitrary grid spacings and arbitrary inhomogeneous possibly lossy isotropic media numerical examples confirm the conservation of energy inside a cavity for a million iterations if the time step is chosen below the proposed relaxed limit apart from the theoretical contributions new accomplishments such as the development of the leapfrog alternating direction hybrid implicit explicit adhie fdtd method and a less stringent courant like time step limit for the conventional fully explicit fdtd method on a nonuniform grid have immediate practical applications a novel newmark beta fdtd method is proposed in 3d the leapfrog adhie fdtd method is for the first time proposed a courant like time step limit less stringent than the currently known limits is found for conventional nonuniform fdtd the stability of three local implicitization techniques is rigorously analyzed in the algebraic sense the stability of the proposed implicitization techniques is numerically validated by a cavity example

testing ar 1 against ma 1 disturbances in an error component model this paper derives three lm statistics for an error component model with first order serially correlated errors the first lm statistic jointly tests for zero first order serial correlation and random individual effects the second lm statistic tests for zero first order serial correlation assuming fixed individual effects and the third lm statistic tests for zero first order serial correlation assuming random individual effects in all three cases the corresponding lm statistic is the same whether the alternative is ar 1 or ma 1 this paper also derives two extensions of the burke godfrey and termayne 1990 test from the time series to the panel data literature the first tests the null of ar 1 disturbances against ma 1 disturbances and the second tests the null of ma 1 disturbances against ar 1 disturbances in an error component model these tests are computationally simple requiring only ols or within residuals the small sample performance of these tests are studied using monte carlo experiments

transforming the error components model for estimation with general arma disturbances abstract baltagi and li 1991 give a transformation which may be applied to certain autocorrelated disturbances in an error components model to yield spherical disturbances they derive the transformation for ar 1 and ar 2 cases we show that the results of galbraith and zinde walsh 1992 on the general arma form of the transformation matrix can be applied to allow estimation of the error components model with disturbances which follow any arma p q process we also show that for models with a cross sectional dimension which is large relative to the time dimension it is possible to use this method to perform a general autocorrelation transformation without specifying a particular arma process or estimating arma parameters

locating all the modes of green s function for a three layered medium based on the path tracking algorithm through a mathematical analysis on the relationship between the characteristic equations of the microstrip geometry and a configuration with a three layered medium a method based on the path tracking algorithm is proposed for precisely locating all the modes for a three layered medium with moderate thickness including surface wave modes leaky wave modes and improper real modes with this method the difficulty caused by branch points and cuts in the contour integral method could be avoided this method can be applied not only in the discrete complex image method dcim but also in the steepest descent path sdp method the proposed method can be extended to more complicated configurations

application of the matrix pencil method for estimating the sem singularity expansion method poles of source free transient responses from multiple look directions the matrix pencil method has been utilized for estimating the natural resonances from different transient responses recorded along multiple look directions as a function of time after the incident field has passed the structure the novelty of this article is that a single estimate for all the poles are done utilizing multiple transient waveforms emanating from the structure along multiple look directions the sem poles are independent of the angle at which the transient response is recorded the only difference between the various waveforms are that the residues at the various poles are of different magnitudes some of the residues may even be zero for some of the poles indicating that the contribution from certain sem poles may not be significant along that look direction here all the waveforms are utilized providing a single estimate for the poles without performing an arithmetic mean of the various waveforms

wave oriented signal processing of dispersive time domain scattering data phase space data processing is receiving increased attention because or its potential for furnishing new discriminants relating to classification and identification of targets and other scattering environments primary emphasis has been on time frequency processing because of its impact on transient especially wideband short pulse excitations here we investigate the windowed fourier transform the wavelet transform and model based superresolution algorithms within the context of a fully quantified and calibrated test problem investigated by us previously two dimensional 2 d short pulse plane wave scattering by a finite periodic array of perfectly conducting coplanar flat strips because the forward problem has been fully calibrated and parametrized some quantitative measures can be assigned with respect to the tradeoffs of these time frequency algorithms yielding tentative performance assessments of the tested processing algorithms

application of dcim on marine controlled source electromagnetic survey the discrete complex image method dcim is used to calculate the mixed potential electric field integral equation the dcim has been used broadly in high frequency domain and now is successfully introduced to the extremely low frequency situation of marine controlled source electromagnetic mcsem survey the integral path in high frequency situation does not hold valid for extremely low frequency situation the reason can be ascribed to the change of wave number formulas a new integral path suitable for the extremely low frequency situation is proposed the appropriate ranges of the parameters used in dcim are given the computation is stable at these considerably large ranges the results of a five layer model calculated with dcim are compared with those with the filter method and the direct integral method the computation time with dcim is comparable to the time with filter method the effects of water depth upper sediment thickness and oil layer thickness are studied with dcim the results show that electric field varies with the change of thickness the effects accord to the physical meanings of mcsem survey it is safe to conclude that the dcim with the new path is valid in mcsem survey

finite element analysis of complex antennas and arrays various technical issues are addressed in the frequency and time domain finite element analysis of complex antennas and arrays that may consist of fine structures and composite materials the paper starts with the finite element formulation of a generic antenna problem formulation for the modeling of general electrically and magnetically dispersive lossy and anisotropic materials in the time domain finite element analysis is presented for the first time this is followed by discussion of three typical techniques for truncation of the finite element computational domain via the use of absorbing boundary conditions perfectly matched layers and boundary integral equations it then describes the modeling of antenna feeds using a current probe including an improved model a voltage gap and a waveguide port boundary condition after that numerical approaches to modeling infinite phased arrays large finite arrays and antenna platform interaction are presented including two novel domain decomposition algorithms in both the frequency and time domains numerical examples are given to demonstrate the capability and application of the finite element analysis of a variety of complex antennas and arrays

hybrid finite difference time domain modeling of curved surfaces using tetrahedral edge elements a hybrid finite difference time domain fdtd method is proposed for solving transient electromagnetic problems associated with structures of curved surfaces the method employs the conventional fdtd method for most of the regular region but introduces the tetrahedral edge based finite element scheme to model the region near the curved surfaces without any interpolation for the fields on the curved surface nor any additional stability constraint due to the finer division near the curved surfaces the novel finite element scheme is found to have second order accuracy unconditional stability programming ease and computational efficiency the hybrid method is applied to solve the electromagnetic scattering of three dimensional 3 d arbitrarily shaped dielectric objects to demonstrate its superior performance