axisymmetric solutions for the multi layered transversely isotropic piezoelectric medium by introducing the precise integration algorithm pia and the technique of the mixed variable formalism accounting for any number of layers variations of components of the axisymmetric piezoelectric field including elastic displacement vertical normal stress electric potential and electric displacement along the axis of symmetry in the cylindrical coordinate system are explored the piezoelectric field is induced by the vertical loadings of mechanical or electric types uniformly distributed over a circular region with the aid of the mixed variable formulations along with the hankel integral transform and the corresponding matrix algebraic operations the governing partial differential equations of equilibrium expressed in terms of displacements and electric potential are reduced to the first order ordinary differential matrix equations as a highly accurate algorithm the pia is provided to evaluate the obtained ordinary differential matrix equations in the transformed domain both mechanical and electrical quantities in the physical domain can be acquired by taking the inversion of the hankel integral transform an example as benchmark is illustrated to examine the applicability and performance of the proposed technique compared with results in the literature numerical examples are used to demonstrate the influence of the degree of the material anisotropy and stratified parameters

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

hp discontinuous galerkin method based on local higher order reconstruction we present a new adaptive higher order finite element method hp fem for the solution of boundary value problems formulated in terms of partial differential equations pdes the method does not use any information about the problem to be solved which makes it robust and equation independent it employs a higher order reconstruction scheme over local element patches which makes it faster and easier to parallelize compared to hp adaptive methods that are based on the solution of a reference problem on a globally hp refined mesh the method can be used for the solution of linear as well as nonlinear problems discretized by conforming or non conforming finite element methods and it can be combined with arbitrary a posteriori error estimators the performance of the method is demonstrated by several examples carried out by the discontinuous galerkin method

advanced methods for calculating green s function and its derivatives for three dimensional anisotropic elastic solids abstract three advanced methods are presented for constructing and evaluating green s function and its derivatives for three dimensional anisotropic elastic solids the first one is obtained from a line integral followed by cauchy s residue theorem and expressed in terms of stroh s eigenvalues the second one is obtained by using the explicit solutions of stroh s eigenvector matrix available in two dimensional anisotropic elasticity whereas the last one is derived from the solution obtained from 2d radon transform and expressed in terms of the fundamental elasticity matrix in vertical planes which makes the derivatives simpler than those obtained from the line integral operated on an oblique plane the novelty of the first two methods lies in the construction and computation of the first and second derivatives of the green s function though the green s function itself in the first two methods is rather known in contrast the third method is quite new for both the green s function itself and its first and second derivatives the advantages and disadvantages of these three solution methods are investigated and discussed through their derivations and numerical implementations for isotropic transversely isotropic and fully anisotropic elastic solids good agreement between the results calculated by these three methods is shown in all numerical examples among these three methods the last one is proved to be the most efficient one

efficient computation of 1 d periodic layered mixed potentials for the analysis of leaky wave antennas with vertical elements an efficient mixed potential integral equation formulation is proposed for the analysis of one dimensional 1 d periodic leaky wave antennas lwas based on planar stratified configurations with inclusions of arbitrarily oriented metallic or dielectric perturbations both the transverse and vertical components of the mixed potential green s functions due to a 1 d phased array of dipoles in a layered medium are accelerated using suitable homogeneous medium asymptotic extractions from the standard spectral series of floquet harmonics a novel acceleration procedure is applied for the computation of the vertical potentials whose extracted terms can be expressed as potentials from a 1 d phased array of half line sources in a homogeneous medium their numerical calculation requires a suitable modification of the ewald method thus resulting in new modified spectral and spatial series having gaussian convergence even in the case of complex modes and improper harmonics numerical comparisons for the 1 d periodic potentials both in the case of bounded and unbounded e g leaky harmonics validate the efficiency and accuracy of the proposed acceleration technique the method is illustrated and verified by determining the dispersion behavior of both bound and leaky modes for several lwa test cases

three dimensional green s function and its derivative for materials with general anisotropic magneto electro elastic coupling explicit expressions of green s function and its derivative for three dimensional infinite solids are presented in this paper the medium is allowed to exhibit a fully magneto electro elastic mee coupling and general anisotropic behaviour in particular new explicit expressions for the first order derivative of green s function are proposed the derivation combines extended stroh formalism radon transform and cauchy s residue theory in order to cover mathematical degenerate and non degenerate materials in the stroh formalism context a multiple residue scheme is performed expressions are explicit in terms of stroh s eigenvalues this being a feature of special interest in numerical applications such as boundary element methods as a particular case simplifications for mee materials with transversely isotropic symmetry are derived details on the implementation and numerical stability of the proposed solutions for degenerate cases are studied

an all at once approach for the optimal control of the unsteady burgers equation we apply an all at once method for the optimal control of the unsteady burgers equation the nonlinear burgers equation is discretized in time using the semi implicit discretization and the resulting first order optimality conditions are solved iteratively by newton s method the discretize then optimize approach is used because it leads to a symmetric indefinite saddle point problem numerical results for the distributed unconstrained and control constrained problems illustrate the performance of the all at once approach with semi implicit time discretization

triangular prisms for edge based vector finite element analysis of conformal antennas this paper deals with the derivation of the edge based shape functions for the distorted triangular prism and their applications for the analysis of doubly curved conformal antennas in the context of the finite element method fem although the tetrahedron is often the element of choice for volume tessellation mesh generation using tetrahedra is cumbersome and the central processing unit cpu intensive on the other hand the distorted triangular prism allows for meshes which are unstructured in two dimensions and structured in the third dimension this leads to substantial simplifications in the meshing algorithm and many conformal printed antenna and microwave circuit geometries can be easily tessellated using such a mesh the new edge based shape functions are first validated by computing the eigenvalues of three different cavities rectangular cylindrical and pie shell we then proceed with their application to computing the input impedance of conformal patch antennas on planar spherical conical and other doubly curved ogival platforms where the fem mesh is terminated using an artificial absorber applied conformal to the platform use of artificial absorbers for mesh termination avoids introduction of green s functions and in contrast to absorbing boundary conditions a knowledge of the principal radii of curvature of the closure s boundary is not required

analysis of semi implicit dgfem for nonlinear convection diffusion problems on nonconforming meshes the paper deals with the numerical analysis of a scalar nonstationary nonlinear convection diffusion equation the space discretization is carried out by the discontinuous galerkin finite element method dgfem on general nonconforming meshes formed by possibly nonconvex elements with nonsymmetric treatment of stabilization terms and interior and boundary penalty the time discretization is carried out by a semi implicit euler scheme in which the diffusion and stabilization terms are treated implicitly whereas the nonlinear convective terms are treated explicitly we derive a priori asymptotic error estimates in the discrete l l2 l l2 norm l2 h1 l2 h1 seminorm and l h1 l h1 seminorm with respect to the mesh size h and time step numerical examples demonstrate the accuracy of the method and manifest the effect of nonconvexity of elements and nonconformity of the mesh

alternate bem formulations for 2 and 3 d anisotropic thermoelasticity abstract direct boundary element formulations are presented for the elastostatic analysis of two and three dimensional general anisotropic media subject to known temperature distributions the thermal effects are incorporated in the analysis through a volume integral or alternatively using particular integrals a multi region boundary element approach is adopted in which particular integrals are derived assuming a quadratic temperature distribution in each sub region a multiple regression scheme is used for the best fit quadratic temperature distribution in each sub region for temperature data given at discrete points the multi region analysis capability of the numerical implementation enhances its capacity to model discontinuous temperature fields as well as piecewise homogeneous media such as laminated composites the formulations presented are incorporated in a general purpose system and are illustrated with examples

high order derivatives of green s functions in magneto electro elastic materials abstract three dimensional green s functions and their arbitrary order derivatives in general anisotropic magneto electro elastic materials are derived by using fourier transform they are analytical solutions expressed in line integral forms and can be evaluated by a standard numerical integration method with this method we can obtain results with high accuracy besides a numerical finite difference method is also given to evaluate the second order derivatives quickly when setting the appropriate material coefficients to zero the piezoelectric piezomagnetic and purely anisotropic elastic green s functions and their derivatives can all be obtained from the current solutions

use of asymptotic waveform evaluation technique in the analysis of multilayer structures with doubly periodic dielectric gratings the reflection and dispersion characteristics of multilayer structures that involve periodically implanted material blocks are obtained by using the mom solution of the volume integral equation the asymptotic waveform evaluation awe technique is utilized to obtain a pade approximation of the solution in terms of a parameter such as frequency or incident angle the use of awe technique enables a fast sweep with respect to the approximation parameter moreover a robust method for extracting the dispersion characteristics of periodic structures via pade approximation is proposed the awe procedure requires the calculation of high order derivatives of the complicated kernel function that consists of green s functions for stratified medium these derivatives are calculated by employing the automatic differentiation theory the reflection coefficient propagation constant and band diagram of the structure are obtained both via point by point simulations and through the use of awe technique it is observed that awe technique increases the computational efficiency without losing accuracy

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

integral identities for a semi infinite interfacial crack in anisotropic elastic bimaterials the focus of the article is on the analysis of a semi infinite crack at the interface between two dissimilar anisotropic elastic materials loaded by a general asymmetrical system of forces acting on the crack faces recently derived symmetric and skew symmetric weight function matrices are introduced for both plane strain and antiplane shear cracks and used together with the fundamental reciprocal identity betti formula in order to formulate the elastic fracture problem in terms of singular integral equations relating the applied loading and the resulting crack opening the proposed compact formulation can be used to solve many problems in linear elastic fracture mechanics for example various classic crack problems in homogeneous and heterogeneous anisotropic media as piezoceramics or composite materials this formulation is also fundamental in many multifield theories where the elastic problem is coupled with other concurrent physical phenomena

an efficient numerical evaluation of the green s function for the helmholtz operator on periodic structures abstract numerical methods which are based on boundary integral formulations require the numerical evaluation of the green s function associated with the problem in the case of periodic structures the green s function is often an infinite series this infinite series may converge slowly making numerical evaluation expensive here we present a practical computer implementation of a technique which dramatically speeds up the convergence of the infinite series green s function associated with the helmholtz operator to show the consequences of using this technique we include some numerical examples

efficient computation of the 3d green s function for the helmholtz operator for a linear array of point sources using the ewald method the ewald method is applied to accelerate the evaluation of the green s function gf of an infinite equispaced linear array of point sources with linear phasing only a few terms are needed to evaluate ewald sums which are cast in terms of error functions and exponential integrals to high accuracy it is shown analytically that the choice of the standard optimal ewald splitting parameter e0 causes overflow errors at high frequencies period large compared to the wavelength and convergence rates are analyzed a recipe for selecting the ewald splitting parameter is provided

finite element time domain analysis of electrically and magnetically dispersive periodic structures a formulation is presented for the finite element time domain fetd analysis of periodic structures that contain electrically and or magnetically dispersive materials the formulation is based on the previously developed transformed field variable approach and the floquet absorbing boundary condition which are both applicable to arbitrary scan or incident angles the paper describes an implicit finite element time marching equation for the transformed electric field variable coupled with a finite difference type equation for the evaluation of the transformed magnetic field variable the technique is applicable to general dispersive materials although the required convolution calculations can be greatly accelerated when the electric and magnetic susceptibilities can be represented by a pole expansion numerical examples are presented to demonstrate the validity and capability of the proposed numerical approach which is effective for the efficient broadband analysis of complex periodic structures such as engineered materials and phased array antennas

the boundary due terms in the green operator of inclusion patterns from distant to contact and to connected situations using radon transforms illustration for spheroid alignments in isotropic media abstract we examine the boundary due components in the mean modified green operator integral green operator for short of an inclusion pattern in distant contact and contact connection transitions the direct rt and inverse irt radon transforms which allow specification of the different contributions to the mean green operator of the pattern in simple geometrical terms are used the already well documented case of axially symmetric alignments of equidistant identical oblate spheroids in an infinite matrix of isotropic elastic like or dielectric like properties is treated up to infinite alignments and for any aspect ratio from unity spheres to infinitesimal platelets simple closed forms for this mean green operator and for its different parts are newly obtained these closed forms allow an easy parametric study of the operator variations in terms of the alignment characteristics from distant to contact situations from contact to connection of the inclusions the changes in the green operator s contributions are pointed what provides relevant operator forms for the connected patterns these results are of interest in problems where phase percolation connectivity inversions or co continuity are implied

a hybrid finite boundary element method for periodic structures on non periodic meshes using an interior penalty formulation for maxwell s equations this paper presents a hybrid finite element boundary element febe method for periodic structures periodic structures have been efficiently analyzed by solving for a single unit cell utilizing floquet s theorem however most of the previous works require periodic meshes to properly impose the boundary conditions on the outer surfaces of the unit cell to alleviate this restriction the interior penalty method is adopted and implemented in this work also the proper treatment of the boundary element part is addressed to account for the non conformity of the boundary element mesh another ingredient of this work is the use of the efficient boundary element computation accelerated by the ewald transformation for the calculation of the periodic green s function finally the method is validated through examples which are discretized without the constraint of a periodic mesh

higher order interpolatory vector bases on pyramidal elements in the numerical solution of three dimensional 3 d electromagnetic field problems the regions of interest can be discretized by elements having tetrahedral brick or prismatic shape however such different shape elements cannot be linked to form a conformal mesh to this purpose pyramidal elements are required in this paper we define interpolatory higher order curl and divergence conforming vector basis functions on pyramidal elements with extension to curved pyramids and discuss their completeness properties a general procedure to obtain vector bases of arbitrary polynomial order is given and bases up to second order are explicitly reported these new elements ensure the continuity of the proper vector components across adjacent elements of equal order but different shape results to confirm the faster convergence of higher order functions on pyramids are presented

mindlin s problem for an anisotropic piezoelectric half space with general boundary conditions this paper considers mindlin s problem in an anisotropic and piezoelectric halfspace with general boundary conditions including 16 different sets of surface conditions the green s function due to

hybrid fem floquet modes po technique for multi incidence rcs prediction of array antennas an original method is proposed which associates rigorous 3d finite element methods fem with floquet modes through factopo multidomain formalism for computing the radar cross section rcs of large array antennas the most original aspect of the method is the fact that the source unit cell is characterized by a generalized scattering matrix gsm which does not depend on the plane wave incidence impinging the structure consequently the factorization step of the fem matrix which is the main computational effort is performed only once the assembling procedure consists then in expressing the fem gsm matrix in the floquet mode basis for each incidence and to solve a linear system giving the complex amplitude of the floquet modes on the array cell interface associated with this formalism lateral and back structure effects can be treated using physical optics po combined with the equivalent current method ecm to improve the accuracy for far broadside incidence

analysis of a bdf dgfe scheme for nonlinear convection diffusion problems we deal with the numerical solution of a scalar nonstationary nonlinear convection diffusion equation we employ a combination of the discontinuous galerkin finite element method for the space semi discretization and the k step backward difference formula for the time discretization the diffusive and stabilization terms are treated implicitly whereas the nonlinear convective term is treated by a higher order explicit extrapolation method which leads to the necessity to solve only a linear algebraic problem at each time step we analyse this scheme and derive a priori asymptotic error estimates in the discrete l l 2 norm and the l 2 h 1 seminorm with respect to the mesh size h and time step for k 2 3 numerical examples verifying the theoretical results are presented

a posteriori error estimation for discontinuous galerkin solutions of hyperbolic problems abstract we analyze the spatial discretization errors associated with solutions of one dimensional hyperbolic conservation laws by discontinuous galerkin methods dgms in space we show that the leading term of the spatial discretization error with piecewise polynomial approximations of degree p is proportional to a radau polynomial of degree p 1 on each element we also prove that the local and global discretization errors are o x2 p 1 and o x2p 1 at the downwind point of each element this strong superconvergence enables us to show that local and global discretization errors converge as o xp 2 at the remaining roots of radau polynomial of degree p 1 on each element convergence of local and global discretization errors to the radau polynomial of degree p 1 also holds for smooth solutions as p these results are used to construct asymptotically correct a posteriori estimates of spatial discretization errors that are effective for linear and nonlinear conservation laws in regions where solutions are smooth

a multiresolution method for simulating infinite periodic arrays hierarchical mixed order tangential vector finite elements tvfes for tetrahedra are attractive for accurate and efficient analysis of a wide class of electromagnetic radiation and scattering problems they provide versatile geometrical modeling and accurate field representation by allowing combination of lowest and higher order tvfes in this letter the finite element boundary integral fe bi method with hierarchical tvfes for tetrahedra is used for analysis of infinite doubly periodic antenna arrays it is shown that accurate prediction of array scanning properties can be obtained by using higher order tvfes in the regions where large fields and rapid field variations are expected and lowest order tvfes elsewhere this is demonstrated in the case of a microstrip patch array

three dimensional green s functions in anisotropic piezoelectric solids abstract explicit expressions for three dimensional extended green s displacements in general anisotropic piezoelectric solids are derived a very efficient procedure for the numerical evaluation of the derivatives of the extended green s displacements is also proposed numerical comparisons are carried out for a transversely isotropic piezoelectric solid for which exact closed form solutions are available it is found that the extended green s displacements and their derivatives obtained with the present explicit formulation are in perfect agreement with the exact closed form solutions these green s functions can be used in the boundary integral equations for piezoelectric solids of general anisotropy and for subsequent numerical solutions of these equations by means of the boundary element method

residual based error estimate and quasi interpolation on polygonal meshes for high order bem based fem abstract only a few numerical methods can treat boundary value problems on polygonal and polyhedral meshes the bem based finite element method is one of the new discretization strategies which make use of and benefits from the flexibility of these general meshes that incorporate hanging nodes naturally the article in hand addresses quasi interpolation operators for the approximation space over polygonal meshes to prove interpolation estimates the poincare constant is bounded uniformly for patches of star shaped elements these results give rise to the residual based error estimate for high order bem based fem and its reliability as well as its efficiency are proven such a posteriori error estimates can be used to gauge the approximation quality and to implement adaptive fem strategies numerical experiments show optimal rates of convergence for meshes with non convex elements on uniformly as well as on adaptively refined meshes

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

lattice sums for the helmholtz equation a survey of different representations for lattice sums for the helmholtz equation is made these sums arise naturally when dealing with wave scattering by periodic structures one of the main objectives is to show how the various forms depend on the dimension d of the underlying space and the lattice dimension d lambda lattice sums are related to and can be calculated from the quasi periodic green s function and this object serves as the starting point of the analysis

finite element analysis of periodic structures without constrained meshes a finite element analysis is detailed of periodic structures without constrained meshes the infinite periodic analysis domain is reduced to the unit cell analysis by means of the floquet bloch decomposition where an admittance type matrix approach is carried out special emphasis is placed on the admittance type matrix generation in such a way that the constrained meshing problem is no longer required as a result periodic ports are permitted in the unit cell and the floquet bloch periodic conditions are easily applied in the admittance type matrix by means of a connection like handling several infinite periodic antennas are shown to be analyzed appropriately

an hp local discontinuous galerkin method for some quasilinear elliptic boundary value problems of nonmonotone type in this paper an hp local discontinuous galerkin method is applied to a class of quasilinear elliptic boundary value problems which are of nonmonotone type on hp quasiuniform meshes using the brouwer fixed point theorem it is shown that the discrete problem has a solution and then using lipschitz continuity of the discrete solution map uniqueness is also proved a priori error estimates in broken h 1 norm and l 2 norm which are optimal in h suboptimal in p are derived these results are exactly the same as in the case of linear elliptic boundary value problems numerical experiments are provided to illustrate the theoretical results

higher order bem based fem on polygonal meshes the bem based finite element method is reviewed and extended with higher order basis functions on general polygonal meshes these functions are defined implicitly as local solutions of the underlying homogeneous problem with constant coefficients they are treated by means of boundary integral formulations and are approximated using the boundary element method in the numerics to obtain higher order convergence a new approximation of the material coefficient is proposed since previous strategies are not sufficient following recent ideas error estimates are proved which guarantee quadratic convergence in the h 1 norm and cubic convergence in the l 2 norm the numerical realization is discussed and several experiments confirm the theoretical results

integral equation modeling of multilayered doubly periodic lossy structures using periodic boundary condition and a connection scheme this paper presents a boundary integral formulation to analyze multilayered doubly periodic lossy structures with arbitrary geometry the formulation is based on the moment method using first order triangular patch basis functions each individual layer is analyzed separately using the simple free space green s function after discretization periodic boundary conditions are imposed on each region and a connection scheme is used to connect the regions metallic patches between layers or on the periodic boundary are also included in the model several examples are presented showing both the flexibility and the accuracy of the method

error estimates for a combined finite volume finite element method for nonlinear convection diffusion problems the subject of this paper is the analysis of error estimates of the combined finite volume finite element fv fe method for the numerical solution of a scalar nonlinear conservation law equation with a diffusion term nonlinear convective terms are approximated with the aid of a monotone finite volume scheme considered over the finite volume mesh dual to a triangular grid whereas the diffusion term is discretized by piecewise linear conforming triangular finite elements under the assumption that the exact solution possesses some regularity properties and the triangulations are of a weakly acute type with the aid of the discrete maximum principle and a priori estimates error estimates of the method are proved

hybrid fe bi modeling of 3 d doubly periodic structures utilizing triangular prismatic elements and an mpie formulation accelerated by the ewald transformation we present the formulation of a finite element boundary integral method for the analysis of three dimensional doubly periodic structures based on arbitrary nonorthogonal lattice configurations the method starts from a functional description of the field problem where only a single unit cell of the array is considered this unit cell is meshed with triangular prismatic volume elements and the electric field intensity is discretized with edge based expansion functions on the sidewalls of the unit cell phase boundary conditions are employed to relate the fields on opposing walls of the unit cell on the top and or bottom unit cell planar surfaces the mesh is terminated using a mixed potential integral equation the required space domain periodic green s function is calculated after applying the ewald 1921 transformation to convert the slowly converging series representation into two rapidly converging series the method is validated for simple slot and strip frequency selective surfaces as well as microstrip dipole arrays more complex geometries investigated are slot coupled microstrip patches photonic bandgap materials and the so called artificial puck plate frequency selective surface bandpass structure

a novel efficient technique for the calculation of the green s functions in rectangular waveguides based on accelerated series decomposition a new efficient technique for computing the green s functions inside rectangular waveguides is presented after a summary of the classical approaches and their difficulties a new strategy is proposed based on the decomposition of the main spectral series into simpler terms although the resulting series present better convergence rate several acceleration techniques are combined to further improve the efficiency several results are presented to demonstrate the improvements in convergence rates obtained using the new decomposition

integral equation analysis of scattering from doubly periodic array of 3 d conducting objects the integral equation ie method formulated in the spatial domain is employed to calculate the scattering from the doubly periodic array of three dimensional 3 d perfect electric conductor pec objects the special testing and basis functions are proposed to handle the problem with non zero normal components of currents at the boundary of one period moreover a relationship between the scattering from the pec screen and its complementary structure is established in order to efficiently compute the matrix elements from the ie approach an acceleration technique with the exponential convergence rate is applied to evaluate the doubly periodic green s function the formulations in this technique are appropriately modified so that the new form facilitates numerical calculation for the general cases

array decomposition method for the accurate analysis of finite arrays presented in this paper is a fast method to accurately model finite arrays of arbitrary three dimensional elements the proposed technique referred to as the array decomposition method adm exploits the repeating features of finite arrays and the free space green s function to assemble a nonsymmetric block toeplitz matrix system the toeplitz property is used to significantly reduce storage requirements and allows the fast fourier transform fft to be applied in accelerating the matrix vector product operations of the iterative solution process each element of the array is modeled using the finite element boundary integral fe bi technique for rigorous analysis consequently we demonstrate that the complete lu decomposition of the matrix system from a single array element can be used as a highly effective block diagonal preconditioner on the larger array matrix system this rigorous method is compared to the standard fe bi technique for several tapered slot antenna tsa arrays and is demonstrated to generate the same accuracy with a fraction of the storage and solution time

three dimensional green s functions for infinite anisotropic piezoelectric media abstract a direct effective and concise method is adopted in this paper to find out the green s functions for infinite anisotropic piezoelectric media the partial differential equations satisfied by the green s functions turn into a set of inhomogeneous algebraic equations after by using fourier transform then inverse transform the solutions of the algebraic equations the green s functions can be expressed by contour integral finally the explicit expression can be obtained for the green s functions by using residual theory the method demonstrated in this paper is easier to follow by people without knowledge of radon transform which has been used to obtain the green s functions by others

quasi 3 d mixed potential integral equation formulation for periodic structures this paper introduces the use of the quasi 3 d mixed potential integral equation formulation for structures with a periodicity in two dimensions the quasi 3 d formulation allows to use both horizontal and vertical conductors and dielectric inclusions the key innovation is the use of an effective algorithm to calculate periodic green s functions pgfs for vertical currents in the planar multilayered background medium this algorithm retains the same scheme as for a single source green s function gf in both cases the gfs are calculated via an inverse fourier transform of the gfs in the spectral domain which are known in closed form in order to remedy the poor convergence for small source observation distances an asymptotic extraction is used yielding a very compact algorithm and acceleration techniques are applied simple guidelines are proposed to construct asymptotes having the required leading terms and a good convergence it is shown that many acceleration algorithms widely used in literature are actually able to perform well only in specific circumstances as far as the authors can see there is still no general and robust technique yielding highly accurate results under all circumstances several examples illustrate the efficiency of the technique

on the stability of the symmetric interior penalty method for the spalart allmaras turbulence model the stability and convergence of the interior penalty ip discontinuous galerkin method are closely related to the penalty coefficient s f using sharp trace inequalities adapted to the functional space shahbazi 2005 7 has derived optimal values of s f for constant diffusivity problems on triangular meshes we propose a generalisation of his analysis to account for mesh anisotropy and different element types on the one hand and strong variations of the diffusivity on the other which characterise the spalart allmaras rans turbulence model the adequacy of this new definition is illustrated by applications to benchmark 2d computations finally a comparison with two state of the art finite volume solvers is presented for a 3d high lift cascade flow

analysis of the discontinuous galerkin method for nonlinear convection diffusion problems abstract the subject matter is the analysis of the discontinuous galerkin finite element method applied to a nonlinear convection diffusion problem in the contrary to the standard fem the requirement of the conforming properties is omitted this allows us to consider general polyhedral elements with mutually disjoint interiors we do not require their convexity but assume only that they are star shaped we present an error analysis for the case of a nonsymmetric discretization of diffusion terms theoretical results are accompanied by numerical experiments

efficient interpolation algorithm of electro elastic green s function for boundary integral equation method and eshelby inclusion problem abstract this study proposes an efficient interpolation algorithm for electro elastic green s functions and its derivatives the extended concept of the interior and exterior point eshelby tensor and its application are also presented the computation efficiency of green s functions in the boundary integral equation method and eshelby inhomogeneity problem are greatly improved by the efficient interpolation of green s functions where the relevant tables of green s functions are preliminarily computed using spherical coordinates the validity of the interpolated electro elastic green s functions is tested by comparing the results to those of the effective electro elastic moduli deduced from the mori tanaka theory the boundary integral equation method and the extended concept of interior and exterior eshelby tensor

the general solution of three dimensional problems in piezoelectric media abstract the governing equations of three dimensional problems in transversely isotropic piezo electric material are composed of four second order partial differential equations in which the displacement components and electric potential functions are the essential unknowns in this paper the so called general solutions of these equations are obtained with the aid of a set of new potential functions which are used to express the components of displacements and the electric potential functions as an application of the general solution the problem of a half space piezoelectrics acted by a concentrated lateral shear force is solved

a new acceleration technique with exponential convergence rate to evaluate periodic green functions we propose a new approach to compute the dynamic potential green function from two and three dimensional periodic arrays of point sources in a three dimensional space the method has at least exponential convergence rate in some cases it has gaussian convergence rate the convergence rate is independent of the position of the observation point in the unit cell the proposed approach can also be used to calculate the derivatives of the green function very efficiently

a three dimensional time domain finite element formulation for periodic structures a formulation is presented for a three dimensional time domain finite element method that can be used to analyze the scattering of a plane wave obliquely incident on a doubly infinite periodic structure using one unit cell a broadband frequency response can be obtained in a single execution the specifics of the method are shown for scattering problems but it should be straightforward to extend it to radiation problems the method solves for a transformed field variable instead of solving directly for the electric field in order to easily enable periodic boundary conditions in the time domain the accuracy and stability of the method is demonstrated by a series of examples where the new formulation is compared with reference solutions accurate results are obtained when the excitation frequency range and the geometry are such that no higher order propagating floquet modes are present the accuracy is degraded in the presence of higher order propagating modes due to the rather simple absorbing boundary condition that is used with the present formulation the method is found to be stable even for angles of incidence close to grazing

analysis and application of the iipg method to quasilinear nonstationary convection diffusion problems we develop a numerical method for the solution of convection diffusion problems with a nonlinear convection and a quasilinear diffusion we employ the so called incomplete interior penalty galerkin iipg method which is suitable for a discretization of quasilinear diffusive terms we analyse a use of the iipg technique for a model scalar time dependent convection diffusion equation and derive hp a priori error estimates in the l 2 norm and the h 1 seminorm moreover a set of numerical examples verifying the theoretical results is performed finally we present a preliminary application of the iipg method to the system of the compressible navier stokes equations

analysis of space time discontinuous galerkin method for nonlinear convection diffusion problems the paper presents the theory of the discontinuous galerkin finite element method for the space time discretization of a nonstationary convection diffusion initial boundary value problem with nonlinear convection and linear diffusion the problem is not singularly perturbed with dominating convection the discontinuous galerkin method is applied separately in space and time using in general different space grids on different time levels and different polynomial degrees p and q in space and time dicretization in the space discretization the nonsymmetric symmetric and incomplete interior and boundary penalty nipg sipg iipg approximation of diffusion terms is used the paper is concerned with the proof of error estimates in l 2 l 2 and dg norm formed by the l 2 h 1 seminorm and penalty terms a special technique based on the use of the gauss radau interpolation and numerical integration has been used for the derivation of an abstract error estimate in the dg norm the error estimates are optimal with respect to the size of the space grid they are optimal with respect to the time step if the dirichlet boundary condition has behaviour in time as a polynomial of degree q

application of hypersingular integral equation method to three dimensional crack in electromagnetothermoelastic multiphase composites a three dimensional crack problem in electromagnetothermoelastic multiphase composites emte mcs under extended loads is investigated in this paper using green s functions the extended general displacement solutions are obtained by the boundary element method this crack problem is reduced to solving a set of hypersingular integral equations coupled with boundary integral equations in which the unknown functions are the extended displacement discontinuities then the behavior of the extended displacement discontinuities around the crack front terminating at the interface is analyzed by the main part analysis method of hypersingular integral equations analytical solutions for the extended singular stresses the extended stress intensity factors sifs and the extended energy release rate near the crack front in emte mcs are provided also a numerical method of the hypersingular integral equations for a rectangular crack subjected to extended loads is put forward with the extended displacement discontinuities approximated by the product of basic density functions and polynomials in addition distributions of extended sifs varying with the shape of the crack are presented the results show that the present method accurately yields smooth variations of extended sifs along the crack front

a hybrid ewald spectral cavity green s function boundary element method with spectral domain acceleration for modeling of over moded cavities a hybrid ewald spectral cavity green s function cgf boundary element method bem with spectral domain acceleration is presented in contrast to all previous work on the cgf bem the presented method relieves the two major drawbacks of the cgf approach 1 the high frequency complexity is decreased using a hybrid ewald spectral representation of the cgf and 2 the costly evaluation of the interaction integrals is accelerated with a fast group spectral domain approach results demonstrate that cavities containing small medium sized and large objects are efficiently modeled over a wide frequency range

integral equation analysis of scattering from multilayered periodic array using equivalence principle and connection scheme an integral equation approach is presented to analyze the two dimensional 2 d scattering from multilayered periodic array the proposed approach is capable of handling scattering from the array filled with different media in different layers combining the equivalence principle algorithm epa and connection scheme epacs it can be avoided to find and evaluate the multilayered periodic green s functions for 2n identical layers the elimination of the unknowns between top and bottom surfaces can be accelerated using the logarithm algorithm more importantly based on epacs an approach is proposed to effectively handle the semi infinitely layered case in which a unit consisting of several layers is repeated infinitely in one direction

boundary element free method for fracture analysis of 2 d anisotropic piezoelectric solids this paper considers a 2 d fracture analysis of anisotropic piezoelectric solids by a boundary element free method a traction boundary integral equation bie that only involves the singular terms of order 1 r is first derived using integration by parts new variables namely the tangential derivative of the extended displacement the extended displacement density for the general boundary and the tangential derivative of the extended crack opening displacement the extended displacement dislocation density are introduced to the equation so that solution to curved crack problems is possible this resulted equation can be directly applied to general boundary and crack surface and no separate treatments are necessary for the upper and lower surfaces of the crack the extended displacement dislocation densities on the crack surface are expressed as the product of the characteristic terms and unknown weight functions and the unknown weight functions are modelled using the moving least squares mls approximation the numerical scheme of the boundary element free method is established and an effective numerical procedure is adopted to evaluate the singular integrals the extended stress intensity factors sifs are computed for some selected example problems that contain straight or curved cracks and good numerical results are obtained copyright 2006 john wiley sons ltd

trefftz indirect methods for plane piezoelectricity in this paper a unified theory for the general solutions of three dimensional elasticity is employed to transform the governing equations of plane piezoelectricity into three generalized laplace equations the latter equations are uncoupled and can be pursued separately by introducing three generalized complex variables the complete solution sets for plane piezoelectricity are constructed by adopting the constituents in the solution sets as the trial functions the trefftz collocation and the trefftz galerkin methods are formulated both methods fall into the category of trefftz indirect methods as the coefficients of their trial functions are non physical numerical examples are presented to illustrate the efficacy of the formulations copyright 2005 john wiley sons ltd

three dimensional time harmonic elastodynamic green s functions for anisotropic solids a method based on the radon transform is presented to determine the displacement field in a general anisotropic solid due to the application of a time harmonic point force the radon transform reduces the system of coupled partial differential equations for the displacement components to a system of coupled ordinary differential equations this system is reduced to an uncoupled form by the use of properties of eigenvectors and eigenvalues the resulting simplified system can be solved easily a back transformation to the original coordinate system and a subsequent application of the inverse radon transform yields the displacements as a summation of a regular elastodynamic term and a singular static term both terms are integrals over a unit sphere for the regular dynamic term the surface integration can be evaluated numerically without difficulty for the singular static term the surface integral has been reduced to a line integral over half a unit circle reductions to the cases of isotropy and transverse isotropy have been worked out in detail examples illustrate applications of the method

phased array antenna analysis with the hybrid finite element method a new analysis technique for infinite phased array antennas was developed and demonstrated it consists of the finite element method fem in combination with integral equation radiation conditions and a novel periodic boundary condition for 3 d fem grids accurate modeling of rectangular circular and circular coaxial feeds is accomplished by enforcing continuity between the fem solution and several waveguide modes across an aperture in the array s ground plane the radiation condition above the array is enforced by a periodic integral equation in the form of a floquet mode summation thus reducing the solution to that of a single array unit cell the periodic boundary condition at unit cell side walls is enforced through a matrix transformation that mathematically folds opposing side walls onto each other with a phase shift appropriate to the array lattice and scan angle the unit cell electric field is expanded in vector finite elements galerkin s method is used to cast the problem as a matrix equation which is solved by the conjugate gradient method a general purpose computer code was developed and validated for cases of open ended waveguides microstrip patches clad monopoles and printed flared notches showing that the analysis method is accurate and versatile

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

a multisolver scheme based on robin transmission conditions for electromagnetic modeling of highly complex objects a multisolver scheme based on robin transmission conditions rtcs is proposed for electromagnetic modeling of highly complex objects different from the traditional finite element boundary integral fe bi method that applies bi equations to truncate the fe domain the proposed multisolver scheme employs both fe and bi equations to model an object along with its background to be specific the entire computational domain consisting of the object and its background is first decomposed into multiple nonoverlapping subdomains with each modeled by either an fe or bi equation the equations in the subdomains are then coupled into a multisolver system by enforcing the rtc at the subdomain interfaces finally the combined system is solved iteratively with the application of an extended preconditioner based on an absorbing boundary condition and the multilevel fast multipole algorithm to obtain an accurate solution both the rao wilton glisson and the buffa christiansen functions are employed as the testing functions to discretize the bi equations this scheme is applied to a variety of benchmark problems and the scattering from an aircraft with a launched missile to demonstrate its accuracy versatility and capability the proposed scheme is compared with the multisolver scheme based on combined field integral equations to illustrate the differences between the two schemes

accelerated computation of the free space green s function gradient of infinite phased arrays of dipoles in this communication we provide an efficient algorithm for the evaluation of the semi infinite array green s function sagf for a semi infinite planar periodic phased array of dipoles in free space for observation points not too far from the array plane the algorithm uses a hybrid spectral spatial representation of the green s function accelerated with the levin t method that we show to be faster than the shanks method for observation points sufficiently far away from the array plane we show that the sagf is efficiently evaluated by using asymptotic field expressions asymptotics is also used to explain the loss of accuracy of the levin t accelerator in certain regions and a correction procedure is proposed to overcome this problem

residual error estimate for bem based fem on polygonal meshes a conforming finite element method on polygonal meshes is reviewed which handles hanging nodes naturally trial functions are defined to fulfil the homogeneous pde locally and they are treated by means of local boundary integral equations using a quasi interpolation operator of clement type a residual based error estimate is obtained this a posteriori estimator can be used to rate the accuracy of the approximation over polygonal elements or it can be applied to an adaptive bem based fem the numerical experiments confirm our results and show optimal convergence for the adaptive strategy on general meshes

a nonstandard schwarz domain decomposition method for finite element mesh truncation of infinite arrays a nonstandard schwarz domain decomposition method is proposed as finite element mesh truncation for the analysis of infinite arrays the proposed methodology provides an asymptotic numerically exact radiation condition regardless of the distance to the sources of the problem and without disturbing the original sparsity of the finite element matrices furthermore it works as a multi floquet mode propagating and evanescent absorbing boundary condition numerical results illustrating main features of the proposed methodology are shown

general solutions for coupled equations for piezoelectric media abstract three general solutions are obtained for the coupled dynamic equations for a transversely isotropic piezoelectric medium these solutions are expressed in terms of the two functions and f where satisfies a second degree partial differential equation and f a sixth degree partial differential equation respectively if the terms concerning the derivatives of time are removed the results become three general solutions for the corresponding equilibrium equations in which the function f can be represented by functions fi i 1 2 3 each of which satisfies a second degree partial differential equation by utilizing a generalized almansi theorem and the solution wang and zheng int j solids structures32 105 115 1995 obtained is proved to be consistent with one case of one of the three general solutions when the constants e15 e31 e33 0 the piezo electric coupling is absent then two of the solutions reduce to the elasticity general solutions for a transversely isotropie medium one of which is the result hu acta scientia sin 2 2 145 151 1953 obtained the other one has not been published last the solution in the limiting explicit form for the problem for a half space with concentrated loads at the boundary is obtained by utilizing the general solutions

efficient calculation of the dispersion diagram of planar electromagnetic band gap structures by the mom bi rme method the characterization of planar electromagnetic band gap structures requires the calculation of the dispersion diagram of the modes supported by the periodic structure and the phase of the reflection coefficient under plane wave illumination we present a novel method for the calculation of the dispersion diagram the electromagnetic analysis is based on the method of moments boundary integral resonant mode expansion mom bi rme method and leads to the formulation of a homogeneous matrix problem the solution of this problem is performed by an iterative procedure for a given value of the propagation phase constant the frequency range is scanned to find the frequencies where the field equation has a nontrivial solution the search of these frequencies is based on the tracking of the eigenvalues in the complex plane and proved more efficient than other classical methods direct search of the determinant zeros singular value decomposition the reflection coefficient can be readily determined by using the mom bi rme method already developed for the analysis of the scattering from frequency selective surfaces the method is applied to the characterization of the classical uniplanar compact photonic bandgap structure and analysis results show the accuracy of the method its efficiency and its convergence properties

a discontinuous galerkin method for viscous compressible multifluids abstract we present a generalized discontinuous galerkin method for a multicomponent compressible barotropic navier stokes system of equations the system presented has a functional viscosity which depends on the pressure p p i of the flow with the density and the local concentration i high order runge kutta time discretization techniques are employed and different methods of dealing with arbitrary coupled boundary conditions are discussed analysis of the energy consistency of the scheme is performed in addition to inspection of the relative error of the solution compared to exact analytic test cases finally several examples comparisons generalizations and physical applications are presented

discontinuous hp finite element methods for advection diffusion reaction problems we consider the hp version of the discontinuous galerkin finite element method dgfem for second order partial differential equations with nonnegative characteristic form this class of equations includes second order elliptic and parabolic equations advection reaction equations as well as problems of mixed hyperbolic elliptic parabolic type our main concern is the error analysis of the method in the absence of streamline diffusion stabilization in the hyperbolic case an hp optimal error bound is derived here we consider only advection reaction problems which satisfy a certain standard positivity condition in the self adjoint elliptic case an error bound that is h optimal and p suboptimal by frac 1 2 a power of p is obtained these estimates are then combined to deduce an error bound in the general case for elementwise analytic solutions the method exhibits exponential rates of convergence under p refinement the theoretical results are illustrated by numerical experiments

improved model based parameter estimation approach for accelerated periodic method of moments solutions with application to the analysis of convoluted frequency selected surfaces and metamaterials an improved smart interpolation approach known as model based parameter estimation mbpe is applied to the wide band interpolation of periodic method of moments pmm impedance matrices for normal and oblique incidence cases prior to interpolation easy to calculate but hard to interpolate phase terms are removed from the impedance matrices an efficient spectral domain pmm formulation is introduced for the accelerated analysis of frequency selective surface fss problems with a large number of unknowns employing a one dimensional o n log n fft based method to speed up the computation of matrix vector products within the bi conjugate gradient bcg iterative solver which is made possible by the asymmetric multilevel block toeplitz structure of the impedance matrix the mbpe interpolation algorithm provides a faster matrix fill time than the brute force method and is comparable or even faster than the 2 d fft based method for a large number of unknowns it also has the advantage that it can be applied to non uniform gridding cases the accuracy and efficiency of the proposed techniques for large fss problems are demonstrated by several design examples for both the normal and oblique incidence cases we also apply this efficient analysis tool to the design of multiband single layer fss filters and artificial magnetic conductors amc comprised of a 2 d periodic arrangement of convoluted metallic strips in the shape of a hilbert curve the multiband properties of the hilbert curve fss filters are studied for different iteration orders i e different degrees of space filling