fully hierarchical divergence conforming basis functions on tetrahedral cells with applications a new set of hierarchical divergence conforming vector basis functions on curvilinear tetrahedrons is presented the basis can model both mixed and full order polynomial spaces to arbitrary order as defined by raviart and thomas and nedelec solenoidal and non solenoidal components are separately represented on the element except in the case of the mixed first order space for which a decomposition procedure on the global mesh wide level is presented therefore the hierarchical aspect of the basis can be made to extend down to zero polynomial order the basis can be used to model divergence conforming quantities such as electromagnetic flux and current density fluid velocity etc within numerical methods such as the finite element method fem or integral equation based methods the basis is ideally suited to p adaptive analysis the paper concludes with two example applications the first is the fem based solution of the linearized acoustic vector wave equation where it is shown how the decomposition into solenoidal components and their complements can be used to stabilize the method at low frequencies the second is the solution of the electric field volume integral equation for electromagnetic scattering analysis where the benefits of the decomposition are again demonstrated

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

global stability and chaos in a population model with piecewise constant arguments sufficient conditions are obtained for the global stability of the positive equilibrium of dx dt rx t 1 ax t b j 0 c jx t j it is shown that for certain special cases solutions of the equation can have chaotic behaviour through period doubling bifurcations

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

maximally orthogonalized higher order bases over generalized wires quadrilaterals and hexahedra this paper presents a general theory of maximally orthogonalized div and curl conforming higher order basis functions hobfs over generalized wires quadrilaterals and hexahedra in particular all elements of such bases necessary for fast and easy implementation are listed up to order n 8 numerical results given for div conforming bases applied in an iterative method of moments solution of integral equations show that the condition number and the number of iterations are a much lower than in the case of other hobfs of polynomial type and b practically not dependent on the applied expansion order

integral equation formulations for characteristic modes of dielectric and magnetic bodies five types of surface integral equation ie formulations are presented to determine the characteristic modes of dielectric and magnetic bodies it should be noted that these five formulations are derived in a unified manner instead of directly using the ie coefficient matrices of scattering problems this paper presents the formulations in a more natural and rigorous way the ie formulations result in the generalized real symmetric eigenvalue equations for the characteristic modes it is found that the eigenvalues of the first four formulations indicate the negative or positive imaginary part of the complex power of the characteristic modes which are zero at resonance the first two ie formulations result in two new generalized eigenvalue equations while the last three ie formulations lead to the same generalized eigenvalue equations as in the references moreover the first two formulations can be immune from spurious modes from which the third and fourth formulations suffer

electromagnetic analysis of large scale periodic arrays using a two level cbfs method accelerated with fmm fft to realize efficient analysis of large scale planar periodic arrays a two level characteristic basis functions method accelerated with fast multipole method fast fourier transform fmm fft is developed in this paper the characteristic basis functions cbfs for each element are constructed in a two level framework in which the cbfs construction based on plane wave derivation for single element at child level and the cbfs construction based on local interaction between array elements at father level are combined the number of unknowns is reduced significantly by the two level cbfs further fmm fft is applied to expedite the computation of interaction between elements numerical results of large scale planar periodic arrays are given to demonstrate the validity and efficiency of the present method

hierarchical divergence conforming nedelec elements for volumetric cells a new family of hierarchical divergence conforming vector bases is proposed for tetrahedral prism and brick cells these functions span the divergence conforming reduced curl spaces of nedelec the bases are constructed from orthogonal scalar polynomials to enhance their linear independence which is a simpler process than an orthogonalization applied to the final vector functions specific functions are tabulated to order 6 5 these basis are intended for use with numerical solutions of volume integral equations or differential equations containing divergence operators

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

comparison theorems and oscillation criteria for difference equations abstract first we establish the equivalence of the oscillation of the delay difference equation x n p n x n k 0 and the second order difference equation 2 y n 1 2 k 1 k k k 1 p n k k k 1 k 1 y n 0 where pn is a sequence of nonnegative real numbers and k is a positive integer next we obtain some sharp conditions for oscillations and nonoscillations of the first equation

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

the persistence and global attractivity in general nonautonomous discrete single species kolmogorov model with delays in this paper general nonautonomous discrete time single species kolmogorov model with delays is studied some sufficient conditions on the boundedness persistence permanence and global attractivity of solutions are established as application the discrete time nonautonomous delayed allee effect model is discussed the sufficient conditions on the permanence and global attractivity are obtained

a fast analysis of scattering and radiation of large microstrip antenna arrays an accurate and efficient method that combines the precorrected fast fourier transform fft method and the discrete complex image method dcim is presented to characterize the scattering and radiation properties of arbitrarily shaped microstrip patch antennas in this method the mixed potential integral equation mpie is discretized in the spatial domain by means of the discrete complex image method the resultant system is solved iteratively using the generalized conjugate residual method gcr and the precorrected fft technique is used to speed up the matrix vector multiplication the precorrected fft eliminates the need to generate and store the usual square impedance matrix and thus leads to a significant reduction in memory requirement and computational cost numerical results are presented for arbitrarily shaped microstrip antenna arrays to demonstrate the accuracy and efficiency of this technique

an efficient hybrid go pws algorithm to analyze conformal serrated edge reflectors for millimeter wave compact range a method to analyze parabolic reflectors with arbitrary piecewise rim is presented in this communication this kind of reflectors when operating as collimators in compact range facilities needs to be large in terms of wavelength their analysis is very inefficient when it is carried out with fullwave mom techniques and it is not very appropriate for designing with po techniques also fast go formulations do not offer enough accuracy to reach performance results the proposed algorithm is based on a go pws hybrid scheme using analytical as well as non analytical formulations on one side an analytical treatment of the polygonal rim reflectors is carried out on the other side non analytical calculi are based on efficient operations such as m2 order 2 dimensional fft a combination of these two techniques in the algorithm ensures real ad hoc design capabilities reached through analysis speedup the purpose of the algorithm is to obtain an optimal conformal serrated edge reflector design through the analysis of the field quality within the quiet zone that it is able to generate in its forward half space

a more scalable and efficient parallelization of the adaptive integral method part i algorithm a more effective parallelization of the adaptive integral method aim is proposed for solving the 3 d volume electric field integral equation the aim computations are distributed among processes by employing two workload decomposition strategies 1 a novel 2 d pencil decomposition of the auxiliary regular grid is used to parallelize the anterpolation interpolation and 3 d fft accelerated propagation steps and 2 a balanced 3 d block decomposition of the scattering volume is used to parallelize the correction step the scalability of the proposed parallelization method is investigated theoretically to compare it with competing methods the concepts of resource constraints parallel efficiency constraints scalability limits and acceptable parallelization regions are introduced by using n p plots where n and p denote the number of unknowns and processes respectively using these concepts it is shown that the proposed parallelization of aim has better weak and strong scalability compared to the traditional ones i e it enables not only larger problems to be solved but also faster solution of a given problem by increasing p

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

mom volume integral equation solution for an isolated metal dielectric resonator with the edge based basis functions the objective of the present study is to show that the method of volume integral used in conjunction with the zeroth order edge based basis functions de carvalho and de souza mendes 1999 gives an accurate and stable solution for a metal dielectric resonator when the number of the basis functions remains relatively small special attention is paid to the resonator in the form of a thin dielectric layer backed by two metal sheets the metal surface is described in terms of the rao wilton glisson rwg basis functions

volume surface integral equation method based on higher order hierarchical vector basis functions for em scattering and radiation from composite metallic and dielectric structures this paper presents a novel galerkin type method of moments solution of the volume surface integral equation vsie which is developed for the analysis of electromagnetic scattering and radiation from composite metallic and dielectric structures our new scheme utilizes curved tetrahedral elements and curved triangular patches for geometric modeling and the associated higher order hierarchical vector hohv basis functions for volume surface current modeling in contrast to the previous studies on higher order vsie our scheme which is reported for the first time in vsie is much more flexible in comparison with the conventional low order scheme our scheme requires much less memory and computational time for the same accuracy level numerical results are provided to demonstrate the accuracy efficiency and flexibility of our scheme

on the determination of resonant modes of dielectric objects using surface integral equations although surface integral equations have been extensively used for solving the scattering problem of arbitrarily shaped dielectric objects when applied to the resonance problem there are still some issues not fully addressed by the literature in this paper the method of moments with rao wilton glisson basis functions is applied to the electric field integral equation efie for solving the resonance problem of dielectric objects the resonant frequency is obtained by searching for the minimum of the reciprocal of the condition number of the impedance matrix in the complex frequency plane and the modal field distribution is obtained through singular value decomposition svd the determinant of the impedance matrix is not used since it is difficult to find its roots for the exterior efie the original basis functions are used as testing functions for the interior efie the basis functions rotated by 90 spl deg are used as testing functions to obtain an accurate modal field solution the impedance matrix needs to be reduced by half before svd is applied to it numerical results are given and compared with those obtained by using the volume integral equation

existence of positive periodic solutions of nonlinear discrete model exhibiting the allee effect in this paper we shall consider the discrete nonlinear delay population model with allee effectx n 1 x n exp a n b n x p n w c n x q n w where a n b n and c n are positive sequences of period w and p and q are positive integers by using the coincidence degree theorem as well as some priori estimates we will establish a sufficient condition for the existence of positive periodic solution x n

a novel grid robust higher order vector basis function for the method of moments a set of novel grid robust higher order vector basis functions is proposed for the method of moments mom solution of integral equations for three dimensional 3 d electromagnetic em problems these basis functions are defined over curvilinear triangular patches and represent the unknown electric current density within each patch using the lagrange interpolation polynomials the highlight of these basis functions is that the lagrange interpolation points are chosen to be the same as the nodes of the well developed gaussian quadratures as a result the evaluation of the integrals in the mom is greatly simplified additionally the surface of an object to be analyzed can be easily meshed because the new basis functions do not require the side of a triangular patch to be entirely shared by another triangular patch which is a very stringent requirement for traditional vector basis functions the proposed basis functions are implemented with point matching for the mom solution of the electric field integral equation the magnetic field integral equation and the combined field integral equation numerical examples are presented to demonstrate the higher order convergence and the grid robustness for defective meshes using the new basis functions

on the formulation of hybrid finite element and boundary integral methods for 3 d scattering this paper studies in detail a variety of formulations for the hybrid finite element and boundary integral fe bi method for three dimensional 3 d electromagnetic scattering by inhomogeneous objects it is shown that the efficiency and accuracy of the fe bi method depends highly on the formulation and discretization of the boundary integral equation bie used a simple analysis of the matrix condition number identifies the efficiency of the different fe bi formulations and an analysis of weighting functions shows that the traditional fe bi formulations cannot produce accurate solutions a new formulation is then proposed and numerical results show that the resulting solution has a good efficiency and accuracy and is completely immune to the problem of interior resonance finally the multilevel fast multipole algorithm mlfma is employed to significantly reduce the memory requirement and computational complexity of the proposed fe bi method

efficient simulation of rectangular dielectric resonators using volume mpie mom formulation with combined entire domain and subdomain basis functions an efficient method of moments mom formulation using combined entire domain and subdomain basis functions is proposed for simulating the resonant modes of a rectangular dielectric resonator in free space an approximate analytical solution for the resonant mode of the dr is used as the entire domain basis function while a set of tetrahedral basis functions are used as subdomain basis functions since the main profile of the resonant mode can be well represented by the entire domain basis function only small number of subdomain basis functions are needed for further refinement of the representation compared with the mom formulations using only subdomain or entire domain basis functions this method is much faster for the same accuracy numerical results are given and compared with other methods

method of moments solution for a printed patch slot antenna on a thin finite dielectric substrate using the volume integral equation in this paper a volume integral equation vie based modeling method suitable for a patch or slot antenna on a thin finite dielectric substrate is developed and tested two new key features of the method are the use of proper dielectric basis functions and proper vie conditioning close to the metal surface where the surface boundary condition of the zero tangential e component must be extended into adjacent tetrahedra the extended boundary condition is the exact result for the piecewise constant dielectric basis functions the latter operation allows one to achieve a good accuracy with one layer of tetrahedra for a thin dielectric substrate and thereby greatly reduces computational cost the use of low order basis functions also implies the use of low order integration schemes and faster filling of the impedance matrix for some common patch slot antennas the vie based modeling approach is found to give an error of about 1 or less in the resonant frequency for one layer tetrahedral meshes with a relatively small number of unknowns this error is obtained by comparison with fine finite element method fem simulations or with measurements or with the analytical mode matching approach hence it is competitive with both the method of moments surface integral equation approach and with the fem approach for the printed antennas on thin dielectric substrates

an efficient volume integral equation solution to em scattering by complex bodies with inhomogeneous bi isotropy a generalized volume integral equation method is formulated for electromagnetic scattering by arbitrarily shaped complex bodies with inhomogeneous bi isotropy based on the volume equivalence principle the integral equations are represented in terms of a pair of coupled bi isotropic polarized volume electric and magnetic flux densities reduction of the integral equations into the corresponding matrix equations is obtained using the method of moments mom combined with the tetrahedral mesh in the mom solution the three dimensional solenoidal function is incorporated as the basis function defined over each tetrahedral element and the details of implementation particularly the treatment of integral singularities will be elucidated the efficiency and accuracy of the proposed method are validated by illustratively supported examples

oscillations of delay difference equations consider the delay difference equation n 1 n pn n k 0 n 0 1 2 where pn is a sequence of real numbers and k is a positive integer new oscillation criteria for this equation are established an extension of the results to difference equations with several delays is also presented

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

determination of resonant modes of dielectric resonators using mom sie with combined entire domain and subdomain basis functions method of moments mom combined with surface integral equation sie is a favorable approach for determining resonant modes of dielectric resonators to decrease the number of unknowns the subdomain basis functions are combined with an entire domain basis function which is an approximate solution of the resonant mode since the main profile of the current distribution can be represented by the entire domain basis function only small refinements are needed for better depiction of the current distribution as an example the te sub 11 spl delta mode of a rectangular dielectric resonator is simulated and compared with other methods

multilayered media green s functions in integral equation formulations a compact representation is given of the electric and magnetic type dyadic green s functions for plane stratified multilayered uniaxial media based on the transmission line network analog along the aids normal to the stratification furthermore mixed potential integral equations are derived within the framework of this transmission line formalism for arbitrarily shaped conducting or penetrable objects embedded in the multilayered medium the development emphasizes laterally unbounded environments but an extension to the case of a medium enclosed by a rectangular shield is also included

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

optimal modeling parameters for higher order mom sie and fem mom electromagnetic simulations general guidelines and quantitative recipes for adoptions of optimal higher order parameters for computational electromagnetics cem modeling using the method of moments and the finite element method are established and validated based on an exhaustive series of numerical experiments and comprehensive case studies on higher order hierarchical cem models of metallic and dielectric scatterers the modeling parameters considered are electrical dimensions of elements h refinement polynomial orders of basis functions p refinement orders of gauss legendre integration formulas integration accuracy and geometrical curvature orders of elements in the model the goal of the study which is the first such study of higher order parameters in cem is to reduce the dilemmas and uncertainties associated with the great modeling flexibility of higher order elements basis and testing functions and integration procedures this flexibility is the principal advantage but also the greatest shortcoming of the higher order cem and to ease and facilitate the decisions to be made on how to actually use them by both cem developers and practitioners

hierarchical curl conforming nedelec elements for quadrilateral and brick cells new curl conforming hierarchical vector basis functions are developed for quadrilateral and hexahedral cells these bases are constructed from orthogonal polynomials and are shown to maintain superior linear independence as their polynomial order is increased the procedure for constructing these basis functions is described and general expressions are provided for an arbitrary order

higher order hybrid fem mom technique for analysis of antennas and scatterers a novel higher order large domain hybrid computational electromagnetic technique based on the finite element method fem and method of moments mom is proposed for three dimensional analysis of antennas and scatterers in the frequency domain the geometry of the structure is modeled using generalized curved parametric hexahedral and quadrilateral elements of arbitrary geometrical orders the fields and currents on elements are modeled using curl and divergence conforming hierarchical polynomial vector basis functions of arbitrary approximation orders and the galerkin method is used for testing the elements can be as large as about two wavelengths in each dimension as multiple mom objects are possible in a global exterior region the mom part provides much greater modeling versatility and potential for applications especially in antenna problems than just as a boundary integral closure to the fem part the examples demonstrate excellent accuracy convergence efficiency and versatility of the new fem mom technique and very effective large domain meshes that consist of a very small number of large flat and curved fem and mom elements with p refined field and current distributions of high approximation orders the reduction in the number of unknowns is by two orders of magnitude when compared to available data for low order fem mom modeling

double higher order large domain volume surface integral equation method for analysis of composite wire plate dielectric antennas and scatterers a novel double higher order large domain galerkin type method of moments based on higher order geometrical modeling and higher order current modeling is proposed for analysis of composite dielectric and metallic radiation scattering structures combining the volume integral equation vie approach for dielectric parts and the surface integral equation sie approach for metallic parts of the structure the technique employs lagrange type interpolation generalized hexahedra and quadrilaterals of arbitrary geometrical mapping orders for the approximation of geometry and hierarchical divergence conforming polynomial vector basis functions of arbitrary expansion orders for the approximation of currents within the elements the double higher order vsie vie sie method is extensively validated and evaluated against the analytical solutions and the numerical results obtained by alternative higher order methods

oscillation and global attractivity in hematopoiesis model with periodic coefficients in this paper we shall consider the nonlinear delay differential equation p t email protected t p m email protected 1 p n email protected email protected t p t where k is a positive integer b t and c t are positive periodic functions of period w in the nondelay case we shall show that has a unique positive periodic solution email protected t and we will study the global attractivity of email protected t in the delay case we shall establish some sufficient conditions for oscillation of all positive solutions of about email protected t and establish some sufficient conditions for the global attractivity of email protected t our results in this paper extend as well as improve the results in the autonomous case

scattering from 3 d inhomogeneous chiral bodies of arbitrary shape by the method of moments a method of moments mom solution is presented for the problem of electromagnetic scattering by a three dimensional 3d inhomogeneous chiral scatterer illuminated by an arbitrary incident field the volume equivalence principle was used to obtain coupled integral equations for equivalent volume currents these integral equations were then solved numerically using mom the volume of the scatterer was modeled by tetrahedral cells and face based expansion functions were used to approximate the equivalent currents computed results are in very good agreement with exact data or other published data

fast fourier transform based iterative method for electromagnetic scattering from 1d flat surfaces an efficient iterative method is proposed for computing the electromagnetic fields scattered from a one dimensional 1d flat surface the new iterative method is based on a similar implementation to the conjugate gradient fast fourier transform cg fft where acceleration of the matrix vector multiplications is achieved using fast fourier transforms fft however the iterative method proposed is not based on krylov subspace expansions and is shown to converge faster than gmres fft and cgne fft while maintaining the computational complexity and memory usage of those methods analysis is presented deriving an explicit convergence criterion

higher order frequency domain computational electromagnetics a review of the higher order computational electromagnetics cem for antenna wireless and microwave engineering applications is presented higher order cem techniques use current field basis functions of higher orders defined on large e g on the order of a wavelength in each dimension curvilinear geometrical elements which greatly reduces the number of unknowns for a given problem the paper reviews all major surface volume integral and differential equation electromagnetic formulations within a higher order computational framework focusing on frequency domain solutions with a systematic and unified review of generalized curved parametric quadrilateral triangular hexahedral and tetrahedral elements and various types of higher order hierarchical and interpolatory vector basis functions in both divergence and curl conforming arrangements a large number of actual higher order techniques representing various combinations of formulations elements bases and solution procedures are identified and discussed the examples demonstrate the accuracy efficiency and versatility of higher order techniques and their advantages over low order discretizations the most important one being a much faster higher order convergence of the solution it is demonstrated that both components of the higher order modeling namely higher order geometrical modeling and higher order current field modeling are essential for accurate and efficient cem analysis of general antenna scattering and microwave structures

oscillatory and asymptotic behavior of positive periodic solutions of nonlinear discrete model exhibiting the allee effect in this paper we shall consider the discrete nonlinear delay population model with allee effectx n 1 x n exp a n b n x p email protected c n x q email protected where a n b n and c n are positive sequences of period w and p and q are positive integers we will establish some sufficient conditions for the oscillation of all positive solutions about its positive periodic solution x n and prove that every nonoscillatory solution converges to x n monotonically as n

separation of horizontal and vertical dependencies in a surface volume integral equation approach to model quasi 3 d structures in multilayered media a new and efficient integral equation approach is presented to model heterogeneous dielectric volumes in a multilayered environment the dielectric volumes can be vertically large they can cross dielectric interfaces and they should be quasi 3 d which means that the contour faces should be placed either horizontally or vertically in the multilayered environment in this way a perpendicular prismatic mesh can be fitted on the volumes and the 3 d displacement currents can be expanded in generalized rooftop functions with separated horizontal x y and vertical z dependencies this makes it possible to evaluate all z z reaction integrals fully analytically in the spectral domain and ensures an efficient implementation the formulation of the source field relations is adapted to the quasi 3 d geometries as a hybrid dyadic mixed potential form additionally the electromagnetic coupling between dielectric volumes and metal sheets is included using a coupled volume surface formulation this turns the implementation into a complete full wave solver for planar antennas containing both finite and infinite dielectric regions in order to illustrate and validate the presented approach two patch antennas with a local volumetric inhomogeneity under the patch are numerically analyzed in a multilayered environment eventually a matrix fill time comparison is used to demonstrate the improvement in computation efficiency

an efficient solution of the volume surface integral equation for electromagnetic scattering and radiation of the composite dielectric conductor objects with reduced number of unknowns an efficient method of moments mom solution of the volume surface integral equation vsie is presented for the analysis of electromagnetic em scattering and radiation of composite objects comprising arbitrarily contacted dielectrics and conductors in contrast to the conventional schaubert wilton glisson swg and rao wilton glisson rwg basis functions which were widely used in the mom solutions of the vsie a new hybrid pulse rooftop basis function is proposed to explicitly enforce the boundary condition of vanishing tangential electric field at the dielectric conductor interface as a consequence the displacement currents in the dielectrics can be efficiently modeled by a reduced number of volume bases on the same set of meshes particularly when thin dielectric slabs are involved in the composite structures the numerical results of em scattering and radiation of several composite objects are shown to illustrate the accuracy and efficiency of the proposed scheme since the new hybrid basis function can be easily implemented into the existing fast algorithms the vsie solution presented in this paper is promising for em problems of composite targets with large size

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

on the dual basis for solving electromagnetic surface integral equations a powerful technique for solving electromagnetic em surface integral equations sies for inhomogenous objects by the method of moments mom involves the well known rao wilton glisson rwg basis function to represent the electric current and for field orthogonality and numerical stability reasons a variation of the rwg basis known as the ntilde x rwg basis where ntilde is a unit normal vector at the object surface to represent the magnetic current though this combination provides a numerically efficient and effective solution that has been demonstrated on a variety of structures one cannot feel entirely comfortable because of the presence of fictitious magnetic current associated with the modified basis chen and wilton proposed a different smoother basis in 1990 that avoids the fictitious line charges but because of computational cost issues it has not been used beyond chen s dissertation recently this basis was rediscovered and has received considerable attention our work reexamines the dual basis exploring issues not addressed by chen and wilton and showing accurate solutions for a variety of em scattering structures

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

oscillation and global attractivity in a nonlinear delay periodic model of respiratory dynamics abstract in this paper we shall consider the nonlinear delay differential equation where m and n are positive integers and v t and t are positive periodic functions of period in the nondelay case we shall show that has a unique positive periodic solution x t and provides sufficient conditions for the global attractivity of x t in the delay case we shall present sufficient conditions for the oscillation of all positive solutions of about x t and establish sufficient conditions for the global attractivity of x t

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

volume integral equation with higher order hierarchical basis functions for analysis of dielectric electromagnetic scattering an efficient method of moments mom solution of volume electric field integral equation v efie with a kind of higher order basis functions is presented to model scattering from a dielectric object with arbitrary shapes and inhomogenuity this method is based on both higher order geometrical modeling and higher order current modeling which is realized using a family of higher order hierarchical vector hhov basis functions to expand the equivalent volume electric currents within curvilinear volume elements this higher order scheme of mom results in a significant reduction in meshing density and number of unknowns leading to a remarkable reduction of memory and cpu time in comparison with conventional low order mom while the accuracy of the solution remains at a comparable level numerical results agree with analytical solutions or with simulation results obtained by commercial software demonstrating the accuracy convergence efficiency flexibility and adaptability of the new approach

complex time representation of the sommerfeld type integrals and its application to 1 d periodic structures the concept of complex time is employed to derive the time domain representation of the green s function of a periodic structure for the first time the spatial domain green s function of the periodic structure in the frequency domain is separated into singular and nonsingular terms the nonsingular terms are approximated by using exponential functions resulting in the well known complex time representation of the time domain green s function in order to find a closed form expression for the singular terms a novel time domain representation of the sommerfeld type integrals is derived the proposed procedure is applied to the computation of the time domain green s function of a one dimensional periodic structure numerical experiments demonstrate the high accuracy of this method

evaluation of the green s function for the mixed potential integral equation mpie method in the time domain for layered media in the use of the time domain integral equation tdie method for the analysis of layered media it is important to have the time domain layered medium green s function computed for many source to field distances spl rho and time instants t in this paper a numerical method is used that computes the mixed potential green s functions g sub v spl rho t and g sub a spl rho t for a multilayered medium for many spl rho s and t s simultaneously the method is applicable to multilayered media and for lossless or lossy dispersive media salient features of the method are 1 the use of complex spl omega so that the surface wave poles are lifted off the real k sub spl rho axis such that pole extractions are not required 2 the use of half space extraction so that the integrand for the sommerfeld integral decays exponentially along the k sub spl rho axis to obtain fast convergence of the integral and 3 the use of the fast hankel transform so that the green s function is calculated for many values of spl rho simultaneously for a four layer medium we illustrate the numerical results by a three dimensional plot of spl rho g sub v spl rho t versus spl rho and t and demonstrate the space time evolution of these green s functions for a maximum frequency range of 8 ghz the method requires only a few cpu minutes to compute a table of 100 points in spl rho spl times 168 points in t uniformly spaced values of g sub v spl rho t on an 867 mhz pentium pc

beauville structures in finite p groups abstract we study the existence of unmixed beauville structures in finite p groups where p is a prime first of all we extend catanese s characterisation of abelian beauville groups to finite p groups satisfying certain conditions which are much weaker than commutativity this result applies to all known families of p groups with a good behaviour with respect to powers regular p groups powerful p groups and more generally potent p groups and generalised p central p groups in particular our characterisation holds for all p groups of order at most p p which allows us to determine the exact number of beauville groups of order p 5 for p 5 and of order p 6 for p 7 on the other hand we determine which quotients of the nottingham group over f p are beauville groups for an odd prime p as a consequence we give the first explicit infinite family of beauville 3 groups and we show that there are beauville 3 groups of order 3 n for every n 5

a potential integral equations method for electromagnetic scattering by penetrable bodies a method for computing the electromagnetic scattering by general inhomogeneous penetrable bodies is presented the method is based on the volume equivalence principle and it uses the electromagnetic potentials as unknowns the resulting coupled integral equations system is solved by the method of moments in combination with cubical and curvilinear meshes in the special case of purely dielectric scatterers to show the accuracy of the method numerical results of the transmitted and of the scattered fields are compared with existing analytical and experimental results

mlace mlfma combined with reduced basis method for efficient wideband electromagnetic scattering from metallic targets in this paper a fast interpolation algorithm multilevel accelerated cartesian expansion mlace multilevel fast multipole algorithm mlfma reduced basis method rbm is proposed for the first time by leveraging the benefits of the mlace the classical mlfma and the rbm furthermore a novel nonblind sampling method nbsm is proposed to approximate an orthogonal subspace for the mlace mlfma rbm by integrating the empirical interpolation method eim and the error based compensation method ebcm into the nbsm we first efficiently establish a robust and precision controllable orthogonal subspace next with the accurate orthogonal subspace the mlace mlfma rbm can simplify the iterative solution process of the mlace mlfma or the mlfma into n text g matrix vector multiplications mvms and the solution of a reduced n text g dimensional linear equation n text g is the number of orthonormal vectors note that only the mvms between the far region impedance matrix and the orthogonal vector bases are calculated in comparison with the classical mlace mlfma and the mlace mlfma rbm based on different sampling methods for wideband electromagnetic em responses our proposed algorithms require less memory and cpu time and integrate higher flexibility the numerical results are provided to demonstrate the accuracy efficiency and flexibility

extrapolation methods for sommerfeld integral tails a review is presented of the extrapolation methods for accelerating the convergence of sommerfeld type integrals i e semi infinite range integrals with bessel function kernels which arise in problems involving antennas or scatterers embedded in planar multilayered media attention is limited to partition extrapolation procedures in which the sommerfeld integral is evaluated as a sum of a series of partial integrals over finite subintervals and is accelerated by an extrapolation method applied over the real axis tail segment spl alpha spl infin of the integration path where spl alpha 0 is selected to ensure that the integrand is well behaved an analytical form of the asymptotic truncation error or the remainder which characterizes the convergence properties of the sequence of partial sums and serves as a basis for some of the most efficient extrapolation methods is derived several extrapolation algorithms deemed to be the most suitable for the sommerfeld integrals are described and their performance is compared it is demonstrated that the performance of these methods is strongly affected by the horizontal displacement of the source and field points spl rho and by the choice of the subinterval break points furthermore it is found that some well known extrapolation techniques may fail for a number of values of spl rho and ways to remedy this are suggested finally the most effective extrapolation methods for accelerating sommerfeld integral tails are recommended

a new representation for the green s function of multilayer media based on plane wave expansion in this paper a new representation for the space domain green s function of general multilayer media is presented this approach is based on an efficient plane wave expansion of the source incident field using the transmission line model for the multilayer medium the effect of the layered medium on the incident plane waves is determined by a transmission coefficient and the amplitude and phase of each plane wave at the field point are obtained the total field is evaluated by summing the resultant plane waves at the field point the main advantage of the proposed method is that the spatial domain green s function of multilayer media can be obtained easily as a summation of simple exponential functions without the need for sommerfeld integration or complex image approximation the plane wave approximation is independent of the parameters of the medium and is valid over a wide frequency range furthermore the exponential form of the plane wave solution makes it possible to compute the method of moments matrix elements analytically for most important types of basis functions in multilayer problems

a novel hybridization of higher order finite element and boundary integral methods for electromagnetic scattering and radiation problems a novel hybridization of the finite element fe and boundary integral methods is presented for an efficient and accurate numerical analysis of electromagnetic scattering and radiation problems the proposed method derives an adaptive numerical absorbing boundary condition abc for the finite element solution based on boundary integral equations unlike the standard finite element boundary integral approach the proposed method is free of interior resonance and produces a purely sparse system matrix which can be solved very efficiently unlike the traditional finite element absorbing boundary condition approach the proposed method uses an arbitrarily shaped truncation boundary placed very close to the scatterer radiator to minimize the computational domain and more importantly the method produces a solution that converges to the true solution of the problem to demonstrate its great potential the proposed method is implemented using higher order curvilinear vector elements a mixed functional is designed to yield both electric and magnetic fields on an integration surface without numerical differentiation to be used in the calculation of the adaptive abc the required evaluation of boundary integrals is carried out using the multilevel fast multipole algorithm which greatly reduces both the memory requirement and cpu time the finite element equations are solved efficiently using the multifrontal algorithm a mathematical analysis is conducted to study the convergence of the method finally a number of numerical examples are given to illustrate its accuracy and efficiency

periodic solutions of a single species discrete population model with periodic harvest stock abstract we discuss a discrete population model describing single species growth with periodic harvest stock the theory of coincidence degree is applied to show that the model equation admits two periodic solutions under minor technical assumptions we show that one of these two periodic solutions is positive and attracts almost all positive solutions

comparison of two sets of low order basis functions for tetrahedral vie modeling a convergence study is made for the two types of low order basis functions for the volume integral equation vie both functions impose the continuity of the normal component of the electric flux through the faces the one basis function is that of schaubert wilton and glisson 1984 and is face based another basis function was first introduced by de carvalho and de souza mendes 1999 and is edge based the exact number of unknowns for the edge based functions is determined in this study the study demonstrates a better performance of the edge based basis functions compared to the face based bases first the edge based basis functions have nearly the same or a faster convergence rate for equal tetrahedral meshes they also show a high numerical stability second for the same tetrahedral mesh the number of unknowns for the edge based functions is considerably smaller the ratio of unknowns edge based versus face based ranges from 0 6 for rough plate meshes to approximately 0 5 for large volumetric meshes third the edge based functions are piecewise constant and are easily implemented into the method of moments their disadvantage is a preliminary condition operation which implies the elimination of the nullspace of the basis set

alternative surface integral equation formulations for characteristic modes of dielectric and magnetic bodies in this paper the physical meanings and various computing methods of characteristic modes cms of dielectric and magnetic bodies are investigated two types of surface integral equation sie formulations based on the dependent relationships between the equivalent surface electric and magnetic currents are proposed following the two types of sie formulations two generalized eigenvalue equations are established to determine the cms of dielectric or magnetic bodies this is in contrast to the approach using induced volume currents it is found that the eigenvalues possess clear physical meanings similar to those of perfectly electric conducting bodies the cms can be used to describe the resonant features including resonant frequencies and resonant field distributions numerical results are presented to validate the proposed formulations

on the numerical integration of the linear shape functions times the 3 d green s function or its gradient on a plane triangle formulas for the static and dynamic potentials due to linearly varying source distributions defined on a planar triangle are presented the general linear variation of the source is represented in terms of three linear basis functions each one associated with a different vertex of the triangular domain the singular kernels considered are given by the 3 d green s function and its gradient both for the static and dynamic case in the static case the evaluation of potentials is performed analytically and compact form results are given in the dynamic case the results are given in a form suited for numerical integration

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

double higher order method of moments for surface integral equation modeling of metallic and dielectric antennas and scatterers a novel double higher order galerkin type method of moments based on higher order geometrical modeling and higher order current modeling is proposed for surface integral equation analysis of combined metallic and dielectric antennas and scatterers of arbitrary shapes the technique employs generalized curvilinear quadrilaterals of arbitrary geometrical orders for the approximation of geometry metallic and dielectric surfaces and hierarchical divergence conforming polynomial vector basis functions of arbitrary orders for the approximation of electric and magnetic surface currents within the elements the geometrical orders and current approximation orders of the elements are entirely independent from each other and can be combined independently for the best overall performance of the method in different applications the results obtained by the higher order technique are validated against the analytical solutions and the numerical results obtained by low order moment method techniques from literature the examples show excellent accuracy flexibility and efficiency of the new technique at modeling of both current variation and curvature and demonstrate advantages of large domain models using curved quadrilaterals of high geometrical orders with basis functions of high current approximation orders over commonly used small domain models and low order techniques the reduction in the number of unknowns is by an order of magnitude when compared to low order solutions