a 3 d hybrid finite element boundary element method for the unified radiation and scattering analysis of general infinite periodic arrays we present a rigorous frequency domain variational 3 d electromagnetic formulation for the general nonself adjoint infinite periodic array problem the hybrid method described combines the vector finite element and floquet boundary element techniques it is general in the sense that it is applicable to infinite periodic arrays of the open or aperture types it is thus effective for modeling both the scattering and radiation performance of diverse fss absorber and phased array structures the technique accurately handles arbitrarily complicated 3 d geometries lossy inhomogeneous media and internal as well as external excitations these analyses can be applied to general skewed grids under arbitrary scan and polarization conditions

on isospectral periodic potentials in rn ii on considere un reseau a n dimensions l dans r n et un potentiel q satisfaisant q x d q x pour d l on considere spec k q l ensemble des avec multiplicites telles que u qu u a une solution satisfaisant u x d u x exp 2i k d d l

a novel method for solving the inverse scattering problem for time harmonic acoustic waves in the resonance region ii in a previous paper siam j appl math 1985 pp 1039 1053 we presented a new method for determining the shape of an acoustically soft obstacle from a knowledge of the time harmonic incident wave and the far field pattern of the scattered wave the method given there was based on knowing the far field pattern for an interval of values of the square of the wave number k such that this interval contained the first eigenvalue lambda 1 of the interior dirichlet problem the purpose of this paper is to extend the methods of our earlier paper to treat the case when the far field pattern is only known for a single value of the wave number such that k 2 is not equal to lambda 1 in addition we show how to combine the results of this paper with the first to obtain a method that is valid for any fixed value of k independent of whether or not k 2 is an eigenvalue we also extend our analysis to include the case of the impedance boundary value problem numerical examples are given showing the pra

radiation of a coaxial line into a half space we present a new approach to the problem of radiation by a coaxial line into a half space we obtain boundary integral equations for the current densities over the walls of the coax and its opening to the half space using the modes of the coax for basis and testing functions we convert the integral equations to an infinite system of linear equations the unknowns being the coefficients of the current density expansions we demonstrate how by solving a small subsystem we can obtain the fields everywhere in space

a regularized sampling method for solving three dimensional inverse scattering problems the inverse scattering problem under consideration is to determine the shape of an obstacle in re 3 from a knowledge of the time harmonic incident acoustic wave and the far field pattern of the scattered wave with frequency in the resonance region a method for solving this nonlinear and improperly posed problem is presented which is based on solving a linear integral equation of the first kind and avoids the use of nonlinear optimization methods numerical examples are given showing the practicality of this new approach

generalized volume surface integral equation for modeling inhomogeneities within high contrast composite structures numerical solutions of volume integral equations with high contrast inhomogeneous materials require extremely fine discretization rates making their utility very limited given the application of such materials for antennas and metamaterials it is extremely important to explore computationally efficient modeling methods in this paper we propose a novel volume integral equation technique where the domain is divided into different material regions each represented by a corresponding uniform background medium coupled with a variation together representing the overall inhomogeneity this perturbational approach enables us to use different green s functions for each material region hence the resulting volume surface integral equation alleviates the necessity for higher discretizations within the higher contrast regions with the incorporation of a junction resolution algorithm for the surface integral equations defined on domain boundaries we show that the proposed volume surface integral equation formulation can be generalized to model arbitrary composite structures incorporating conducting bodies as well as highly inhomogeneous material regions

length dependence of solutions of fitzhugh nagumo equations a l aide de constructions et de methodes de semi groupe on obtient des resultats de decroissance sur les normes des differences entre la solution pour l infini et la solution l grand mais fini

scattering by cavity backed antennas on a circular cylinder conformal arrays are popular antennas for aircraft spacecraft and land vehicle platforms due to their inherent low weight drag and observables however to date there has been a dearth of rigorous analytical or numerical solutions to aid the designer in fact it has been common practice to use limited measurements and planar approximations in designing such nonplanar antennas we extend the finite element boundary integral method to scattering by cavity backed structures in an infinite metallic cylinder in particular we discuss the formulation specifics such as weight functions dyadic green s function implementation details and particular difficulties inherent to cylindrical structures special care is taken to ensure that the resulting computer program has low memory demand and minimal computational requirements scattering results are presented and validated as much as possible

a numerical study on the stability of a class of helmholtz problems this paper concerns the stability of a class of helmholtz problems in rectangular domains a well known application is the electromagnetic scattering from a rectangular cavity embedded in an infinite ground plane error analysis of numerical methods for cavity problems relies heavily on the stability estimates however it is extremely difficult to derive an optimal stability bound with the explicit dependency on wave numbers in this paper a high order finite element approximation is proposed for calculating the stability bound numerical experiments show that the stability depends strongly on wave numbers in extreme case and it is almost independent on the wave numbers in an average sense our numerical results also help to understand the stability of the multi frequency inverse problems

field singularities at metal dielectric wedges the wedges discussed are the dielectric wedge the metallic 90 deg corner on a dielectric plane and the adjacent 90 deg metallic and dielectric corners the field components perpendicular to the edge may become infinite according to a law 1 r n numerical data are given for n and plots of lines of force of bar e or bar h are shown

application of aim and mbpe techniques to accelerate modeling of 3 d doubly periodic structures with nonorthogonal lattices composed of bianisotropic media an efficient methodology is introduced for rapid analysis and design of three dimensional 3 d doubly periodic structures over a wide frequency range based on hybrid finite element boundary integral febi methods the 3 d doubly periodic structures can be represented as nonorthogonal lattices composed of general inhomogeneous bianisotropic media with arbitrarily shaped metallic patches based on floquet theory and periodic boundary conditions the original stated problem that involves infinite periodic structures can be converted into a single unit cell using the equivalence principle the derived bi equation formulation is applied to the top and bottom surfaces of the unit cell which results in a perfectly reflectionless boundary condition for the fe based approach then the unit cell was meshed using triangular prismatic volume elements which provide a great deal of flexibility in modeling complex planar geometries with arbitrary shapes in the transverse direction the adaptive integral method aim was employed to accelerate the calculation of the matrix vector product for the bi portion within the iterative solver furthermore a model based parameter estimation mbpe technique was proposed for the wide band interpolation of the required impedance matrix elements in the bi part for near field components that were used in the aim procedure the accuracy and efficiency of the proposed hybrid algorithms are demonstrated by the presented numerical results e g in comparison with analytical solutions several simulation results are presented to illustrate the flexibility of the proposed methods for analysis of frequency selective surfaces with arbitrarily shaped metallic patches bianisotropic materials and nonorthogonal lattice configurations

the three dimensional inverse scattering problem for acoustic waves abstract we consider the inverse scattering problem for an acoustically soft obstacle in r 3 by assuming a priori that the unknown scattering obstacle is starlike and has its boundary lying in a compact family of holder continuously differentiable surfaces it is shown that an optimal solution can be constructed which depends continuously on the measured far field data remarks are made on the numerical approximation of the optimal solution

on the numerical solution of the three dimensional inverse obstacle scattering problem abstract the inverse problem under consideration is to determine the shape of an impenetrable sound soft obstacle from the knowledge of a time harmonic incident plane acoustic wave and far field or near field measurements of the scattered wave we present a method for the approximate solution which avoids the solution of the corresponding direct problem and stabilizes the ill posed inverse problem by reformulating it as a nonlinear optimization problem the numerical implementation of the method is described and some three dimensional examples of reconstructions are given

a survey of finite element methods for time harmonic acoustics many of the current issues and methodologies related to finite element methods for time harmonic acoustics are reviewed the effective treatment of unbounded domains is a major challenge most prominent among the approaches that have been developed for this purpose are absorbing boundary conditions infinite elements and absorbing layers standard computational methods are unable to cope with wave phenomena at short wave lengths due to resolutions required to control dispersion and pollution errors leading to prohibitive computational demands since computation naturally separates the scales of a problem according to the mesh size multiscale considerations provide a useful framework for viewing these difficulties and developing methods to counter them other issues addressed are related to the efficient solution of systems of specialized algebraic equations and inverse problems of acoustics the tremendous progress that has been made in all of the above areas in recent years will surely continue leading to many more exciting developments

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

solution of radiation and scattering problems in complex environments using a hybrid finite integration technique uniform theory of diffraction approach the finite integration technique fit is combined with the uniform geometrical theory of diffraction utd for the solution of radiation and scattering problems in complex environments the presented hybrid formulation is capable of handling large objects allowing in the same time a precise modeling of important geometrical details and material inhomogeneities the part of the structure which contains the details of the geometrical model and the material inhomogeneities is discretized and solved using the fit discretization scheme whereas the influence of the large scatterers to the total solution is resolved by means of utd in contrast with other finite difference based hybridizations in the presented formulation the case of the strong coupling between the two subproblems without simplifications is considered this is accomplished by introducing an appropriate boundary operator derived by the equivalence principle the resulting equation system possesses a complex nearly dense system matrix which is difficult to handle even using iterative solvers to overcome this difficulty the system of equations is solved using a two step procedure i e the fit equation and the boundary condition are treated separately

a highly effective preconditioner for solving the finite element boundary integral matrix equation of 3 d scattering a highly effective preconditioner is presented for solving the system of equations obtained from the application of the hybrid finite element boundary integral fe bi method to three dimensional 3 d electromagnetic scattering problems different from widely used algebraic preconditioners the proposed one is based on a physical approximation and is constructed from the finite element method fem using an absorbing boundary condition abc on the truncation boundary it is shown that the large eigenvalues of the finite element fe abc system are similar to those of the fe bi system hence the preconditioned system has a spectrum distribution clustered around 1 in the complex plane consequently when a krylov subspace based method is employed to solve the preconditioned system the convergence can be greatly accelerated numerical results show that the proposed preconditioner can improve the convergence of an iterative solution by approximately two orders of magnitude for large problems

on the constructive determination of spectral invariants of the periodic schrodinger operator with smooth potentials in this paper we develop the asymptotic formulae obtained in my previous papers for the band functions and the bloch functions of the schrodinger operator with the smooth periodic potentials then using these formulae we determine constructively a family of spectral invariants of this operator from the given band functions some of these invariants generalize the well known invariants and others are entirely new the new invariants are explicitly expressed by fourier coefficients of the potential which present the possibility of determining the potential constructively by using the band functions as input data

a finite element boundary integral formulation for scattering by three dimensional cavity backed apertures a novel numerical technique is proposed for the electromagnetic characterization of the scattering by a three dimensional cavity backed aperture in an infinite ground plane the technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity specifically the finite element method is used to formulate the fields in the cavity region and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane unlike traditional approaches the proposed technique does not require a knowledge of the cavity s green s function and is therefore applicable to arbitrary shape depressions and material fillings furthermore the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms

theoretical modeling of cavity backed patch antennas using a hybrid technique a hybrid technique that combines the method of moments mom and the finite element method fem to analyze cavity backed patch antennas is presented this technique features the use of fem in solving the electromagnetic field distribution in the cavity and the use of mom in solving integral equations outside the cavity the results of mom and fem are combined through the continuity conditions on the boundary of the cavity due to the flexibility of fem complex cavities filled with inhomogeneous media can be analyzed by this technique the results obtained by this hybrid technique are compared to the finite difference time domain fdtd results and good agreement is found

a note on hybrid finite element method for solving scattering problems the hybrid finite element formulation hfem originated by p silvester and m s hsieh 1971 is modified in such a way that it results in a sparse or uniformly banded matrix rather than a partly full and partly sparse nonuniform matrix the modification is accomplished by changing the sequence of matrix substitutions and substantially improves the computational efficiency and enhances the capability of the method which is demonstrated by numerical examples a comparison with other numerical techniques is presented

a fast method for acoustic imaging of multiple three dimensional objects this paper is concerned with the inverse problem for imaging multiple three dimensional objects using the information of the far field pattern of the scattered wave a spatially dependent function which has noticeably different values inside and outside the obstacle is derived a numerical method based on the characterization is developed to obtain a visualization of the obstacle the most remarkable advantage of this method is that it does not need any prior knowledge about the geometry and physical properties of the scatterer and requires only the information of the far field measurements for a finite number of directions of incidence and observation distributed over a limited range furthermore the scheme is very simple and fast since it avoids the use of the iterative procedure and requires only the solution of a linear system some numerical examples with synthetic far field data are given showing the practicality and efficiency of this scheme

newton kantorovitch algorithm applied to an electromagnetic inverse problem an efficient algorithm is presented to compute the shape of perfectly conducting cylinders via knowledge of scattering cross sections this choice of scattering data avoids the difficulties linked with the phase measurements or reconstructions the mathematical analysis is performed in terms of operator and functions and the fundamental instability of the problem is demonstrated then the stability is restored by means of a tikhonov miller regularization the efficiency of the method is outlined by numerical examples references are given which show that the same algorithm applies to other electromagnetic inverse problems especially to gratings

electromagnetic scattering from three dimensional cavities via a connection scheme the electromagnetic scattering from arbitrary three dimensional cavities is presented to alleviate computational constraints for three dimensional problems a connection scheme is developed based on microwave network theory this scheme allows the cavity to be divided into sections and each section to be analyzed independently of the rest of the cavity each section of the cavity is represented by a generalized admittance matrix which if formulated via a boundary integral equation approach using the concept of input and load admittance the aperture admittance matrix of the cavity can be derived by cascading the admittance matrices of individual sections once the cavity aperture admittance matrix is obtained the aperture electric field and the backscattered field are found by the standard generalized network formulation numerical results are compared against modal solutions of regularly shaped cavities with good agreement this connection scheme leads to a reduction in computational resources especially for cavities with one dimension much larger than the other two

on the constructive determination of the periodic potentials from the bloch eigenvalues in this paper we consider the three dimensional schrodinger operator with a periodic relative to a lattice of potential q we construct a set d of trigonometric polynomials such that d is dense in where s 3 in the topology any element q of the set d can be determined constructively and uniquely modulo inversion and translation q x q x q x q x where from the given bloch eigenvalues of the schrodinger operator with the potential q

scattering from 3 d cavities with a plug and play numerical scheme combining ie pde and modal techniques in this paper we present a multidomain and multi method coupling scheme called factopo based on generalized scattering matrix computations on three dimensional 3 d subdomains the global target spl omega is split in n sub v subdomains v sub i i 1 n sub v separated by n sub i fictitious surfaces spl gamma sub j j 1 n sub i we use a modal representation of the tangent fields on the interfaces in each domain the generalized scattering matrix s sub i is computed with different methods such as the 3 d finite element method fem or the electric field integral equation efie this coupling scheme leads to an important reduction in computational resources especially for cavities with one dimension much larger than the other two the advantages of this formulation for parametric studies is illustrated by two cases computing the rcs of an air intake terminated with a flat pec or a fan channel and of an antenna structure coupled to an electronic feed with a varying parameter deneb numerical as well as experimental results are presented

a near resonance decoupling approach nrda for scattering solution of near resonant structures the generalized network formulation is applied in combination with the method of moments to calculate the electromagnetic scattering from conducting objects containing near resonant open ended cavities the presence of the cavity increases the iteration number in conjugate gradient iterations due to the near resonant modes and the multiple wave bounces inside the cavity the equivalence principle is used to separate the cavity region from the rest of the object allowing an independent solution of the cavity problem by a direct inversion algorithm using a connection scheme the solution of the cavity is then represented by a generalized admittance matrix numerical results for two dimensional 2 d composite targets show that the iteration number can be reduced significantly for objects containing long cavities this algorithm can also be applied to three dimensional problems

computation of the scattering from inhomogeneous objects with a discrete rotational symmetry and a nonsymmetric part using a specific solver for circulant matrices can reduce the cost of computing the scattering from a discrete rotational symmetric object by up to several orders of magnitude a solver is developed for symmetric objects with a nonsymmetrical part such as an antenna on a body of revolution this solver has been implemented in a finite element code based upon a hybrid formulation the hybrid formulation combines integral equations and partial differential equations it can handle inhomogeneous anisotropic objects of arbitrary shape results on inhomogeneous objects with defects are shown the solver can also be used to perform a parametric study of the defects

a hybrid sim sem method for 3 d electromagnetic scattering problems a new method combining the spectral integral method and spectral element method sim sem is proposed to simulate 3 d electromagnetic scattering from inhomogeneous objects in this hybrid technique a special case of the finite element boundary integral fem bi combination the sem with the mixed order curl conforming vector gauss lobatto legendre gll basis functions are used to represent the interior electric field with high accuracy while the sim on a cuboid surface is used as an exact radiation boundary condition the toeplitz property of the sim matrix is utilized to reduce the memory and cpu time costs in an iterative solver by using the fast fourier transform algorithm unlike the traditional fem bi combination where the bi portion usually dominates the computational complexity the computational costs are much lower in the sim sem method numerical results verify the accuracy and capability of this method confirming that the sim sem method is a good alternative for solving scattering problems from inhomogeneous objects

structural stability for the morris lecar neuron model this paper is concerned with the biological neuron model of morris lecar system of equations morris and lecar 1981 17 we prove the existence and uniqueness of strong solutions in addition we prove the continuous dependence of solutions to the leak conductance parameter

fem bem formulation for the analysis of cavity backed patch antennas on chiral substrates an extended variational formulation to study cavity backed microstrip patch antennas with chiral materials is presented a finite element boundary integral numerical approach is applied to satisfy the stationary condition associated with the variational formulation and some features of chiral media for patch antenna applications are investigated specifically an appreciable reduction of the antenna dimensions with respect to the isotropic case and an undesirable increase in the cross polarization levels are observed

parallel domain decomposition based algorithm of hybrid fe bi mlfma method for 3 d scattering by large inhomogeneous objects the hybrid method of the finite element boundary integral multilevel fast multipole algorithm fe bi mlfma has been recognized as one of the most powerful numerical methods for analyzing large inhomogeneous radiation scattering problems a domain decomposition algorithm dda of fe bi mlfma is presented in this paper by using the finite element tearing and interconnecting method feti the formulation of dda fe bi mlfma is presented and analyzed in detail the numerical performance of dda fe bi mlfma is investigated by numerical experiments from many aspects it includes the convergence speed versus types of domain decomposition number of subdomains types and inhomogeneity of dielectrics involving in solved problems and the scalability of dda fe bi mlfma the comparison of dda and previous algorithms of fe bi mlmfma is also carried out finally the capability of dda fe bi mlfma is shown for large inhomogeneous problems

an effective domain decomposition based preconditioner for the fe bi mlfma method for 3d scattering problems a domain decomposition based preconditioner ddp is presented for the hybrid finite element boundary integral multilevel fast multipole algorithm fe bi mlfma the formulation of fe bi is first approximated by the finite element method fem with absorbing boundary condition abc then this approximate fem abc formulation is solved by using the finite element tearing and interconnecting method feti finally an inner outer iterative algorithm with variable convergence threshold is designed for fe bi mlfma because of good numerical scalability of feti and good approximation of fem abc this ddp fe bi mlfma performs well even for large lossless objects

optimal shape design of a cavity for radar cross section reduction this paper focuses on the reduction of radar cross section rcs for a cavity embedded in an infinite ground plane by introducing a transparent boundary condition the unbounded scattering problem is reduced to a bounded domain problem rcs reduction for the cavity is formulated as a shape optimization problem involving the helmholtz equation the existence of the minimizer is proved under an appropriate constraint descent directions of the objective function with respect to the boundary may be found via the domain derivative it is used in a gradient based optimization scheme to find the optimal shape of the cavity numerical examples show that the rcs is effectively reduced at different incident frequencies

scattering from a large body with cracks and cavities by the fast and accurate finite element boundary integral method a large body with cracks and cavities is a typical structure widely existing in realistic targets in this paper a newly developed fast and accurate finite element boundary integral fa fe bi method is applied to compute scattering by this kind of scatterer a thorough analysis on this fa fe bi numerical technique is presented clearly demonstrating that this technique has computational complexity o n log n and memory requirement o n n is the total number of surface unknowns an inward looking approach is employed as a preconditioner to speed up the rate of convergence of iterative solvers for this structure under these techniques a powerful code is developed for this kind of scatterer whose accuracy efficiency and capability is well confirmed by various numerical results

an algorithm for finding the periodic potential of the three dimensional schrodinger operator from spectral invariants in this paper we investigate the three dimensional schr dinger operator with a periodic relative to a lattice of potential q a special class v of the periodic potentials is constructed which is easily and constructively determined from the spectral invariants first we give an algorithm for the unique determination of the potential q v of the three dimensional schr dinger operator from the spectral invariants that were determined constructively from the given bloch eigenvalues then we consider the stability of the algorithm with respect to the spectral invariants and bloch eigenvalues finally we prove that there are no other periodic potentials in the set of large class of functions whose bloch eigenvalues coincides with the bloch eigenvalues of q v

scattering and radiation analysis of three dimensional cavity arrays via a hybrid finite element method a hybrid numerical technique is presented for a characterization of the scattering and radiation properties of three dimensional cavity arrays recessed in a ground plane the technique combines the finite element and boundary integral methods and invokes floquet s representation to formulate a system of equations for the fields at the apertures and those inside the cavities the system is solved via the conjugate gradient method in conjunction with the fast fourier transform thus achieving an o n storage requirement by virtue of the finite element method the proposed technique is applicable to periodic arrays comprised of cavities having arbitrary shape and filled with inhomogeneous dielectrics several numerical results are presented along with new measured data which demonstrate the validity efficiency and capability of the technique

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