3d weakly conditionally stable fdtd method for analyzing periodic structures by dividing the 3d transformed maxwell s equations into two parts and applying the crank nicolson cn scheme to each part four substep implicit procedures are obtained after adjusting the order of four substeps a weakly conditionally stable finite difference time domain wcsfdtd method is derived for solving the 3d problems of oblique incident plane wave on periodic structures this method is very suitable for analyzing the problems which have fine structures in one or two directions and the courant friedrich levy cfl stability condition of it is more relaxed than that of the original held transformation methods numerical examples demonstrate that the presented technology is more efficient especially at the high incident angle

nonlocal theory solution of two collinear cracks in the functionally graded materials in this paper the interaction of two collinear cracks in functionally graded materials subjected to a uniform anti plane shear loading is investigated by means of nonlocal theory the traditional concepts of the nonlocal theory are extended to solve the fracture problem of functionally graded materials to make the analysis tractable it is assumed that the shear modulus varies exponentially with the coordinate vertical to the crack by use of the fourier transform the problem can be solved with the help of a pair of triple integral equations in which the unknown variable is the displacement on the crack surfaces to solve the triple integral equations the displacement on the crack surfaces is expanded in a series of jacobi polynomials unlike the classical elasticity solutions it is found that no stress singularity is present near the crack tips the nonlocal elastic solutions yield a finite hoop stress at the crack tip thus allowing us to use the maximum stress as a fracture criterion in functionally graded materials the magnitude of the finite stress field depends on the crack length the distance between two cracks the parameter describing the functionally graded materials and the lattice parameter of the materials

an efficient spectral wlp fdtd algorithm for periodic structures an efficient weighted laguerre polynomials based spectral finite difference time domain scheme for 2 d periodic structures is proposed in this communication by replacing the conventional single angle incident wave with a constant transverse wavenumber wave the periodic boundary condition can be directly implemented in the time domain for both oblique and normal incident waves the huge sparse matrix is transformed into one tridiagonal matrix and one untridiagonal matrix by adding a perturbation term then an iterative procedure is introduced to eliminate the error results from the numerical example and hfss have verified the accuracy and efficiency of the presented method

dependence of eigenvalues of sturm liouville problems with eigenparameter dependent boundary conditions abstract this paper is concerned with regular sturm liouville problems with eigenparameter dependent boundary conditions we obtain that the eigenvalues are not only continuously but also smoothly dependent on the parameters of the problem in particular eigenparameter dependent boundary condition matrix moreover the differential expression of the eigenvalues with respect to the data is given the dependence of the nth eigenvalue as a function of the parameters of the problem is also investigated by pr u fer transformation and the inequalities of eigenvalues

dependence of eigenvalues on the boundary conditions of sturm liouville problems with one singular endpoint abstract this paper is concerned with continuous and differentiable dependence of isolated eigenvalues on the boundary conditions of self adjoint sturm liouville problems with one singular endpoint locally continuous dependence of eigenvalues on the boundary conditions is proved especially in the limit point case the continuous dependence of isolated eigenvalues is shown by the relationships between weyl titchmarsh m function and the spectrum of the singular problems then continuous eigenvalue branches through each isolated eigenvalue over the space of boundary conditions are formed it is rigorously shown that the eigenfunctions for the eigenvalues along a continuous simple eigenvalue branch can be continuously chosen with uniform bound in l w 2 norm its proof is different from that in the regular sturm liouville problems the derivative formulas of the continuous simple eigenvalue branch with respect to all the parameters in the boundary conditions are given and thus its monotonicity with respect to some parameters is derived

axsiymmetric crack problem in bonded materials with a graded interfacial region the problem of a penny shaped crack in homogeneous dissimilar materials bonded through an interfacial region with graded mechanical properties is considered the applied loads are assumed to be axisymmetric but otherwise arbitrary the shear modulus of the interfacial region is assumed to be 2 z 1exp z and that of the adherents 1 and 3 1 1exp h h being the thickness of the region a crack of radius is located at the z 0 plane the axisymmetric mode iii torsion problem is separated and treated elsewhere because of material nonhomogeneity the deformation modes i and ii considered in this study are always coupled the related mixed boundary value problem is reduced to a system of singular integral equations the asymptotic behavior of the stress state near the crack tip is examined and the influence of the thickness ratio ha and the material nonhomogeneity parameter on the stress intensity factors and the strain energy release rate is investigated the results show that the stress state near the crack tip would always have standard square root singularity provided h 0 or the material properties are continuous but not necessarily differentiable functions of z

dependence of eigenvalues of sturm liouville problems with interface conditions this paper investigates sturm liouville problems with interface conditions we obtain that the eigen values depend not only continuously but also smoothly on the coefficient functions boundary conditions and interface conditions moreover the derivative of the eigenvalues with respect to each of these parameters is given

left definite sturm liouville problems abstract left definite regular self adjoint sturm liouville problems with either separated or coupled boundary conditions are studied we give an elementary proof of the existence of eigenvalues for these problems for any fixed equation we establish a sequence of inequalities among the eigenvalues for different boundary conditions and estimate the range of each eigenvalue as a function on the space of boundary conditions some of our results here yield an algorithm for numerically computing the eigenvalues of a left definite problem with an arbitrary coupled boundary condition our inequalities imply that the well known asymptotic formula for the eigenvalues in the separated case also holds in the coupled case moreover we study the continuous and differentiable dependence of the eigenvalues of the general left definite problem on all the parameters in its differential equation and boundary condition

reducing the phase error for finite difference methods without increasing the order the phase error in finite difference fd methods is related to the spatial resolution and thus limits the maximum grid size for a desired accuracy greater accuracy is typically achieved by defining finer resolutions or implementing higher order methods both these techniques require more memory and longer computation times in this paper new modified methods are presented which are optimized to problems of electromagnetics simple methods are presented that reduce numerical phase error without additional processing time or memory requirements furthermore these methods are applied to both the helmholtz equation in the frequency domain and the finite difference time domain fdtd method both analytical and numerical results are presented to demonstrate the accuracy of these new methods

evaluation of green s function derivatives for exponentially graded elasticity effective formulas for computing green s function of an exponentially graded three dimensional material have been derived in previous work the expansion approach for evaluating green s function has been extended to develop corresponding algorithms for its first and second order derivatives the resulting formulas are again obtained as a relatively simple analytic term plus a single double integral the integrand involving only elementary functions a primary benefit of the expansion procedure is the ability to compute the second order derivatives needed for fracture analysis moreover as all singular terms in this hypersingular kernel are contained in the analytic expression these expressions are readily implemented in a boundary integral equation calculation the computational formulas for the first derivative are tested by comparing with results of finite difference approximations involving green s function in turn the second derivatives are then validated by comparing with finite difference quotients using the first derivatives published in 2010 by john wiley sons ltd

dispersion relation preserving fdtd algorithms for large scale three dimensional problems we introduce dispersion relation preserving drp algorithms to minimize the numerical dispersion error in large scale three dimensional 3d finite difference time domain fdtd simulations the dispersion error is first expanded in spherical harmonics in terms of the propagation angle and the leading order terms of the series are made equal to zero frequency dependent fdtd coefficients are then obtained and subsequently expanded in a polynomial taylor series in the frequency variable an inverse fourier transformation is used to allow for the incorporation of the new coefficients into the fdtd updates butterworth or chebyshev filters are subsequently employed to fine tune the fdtd coefficients for a given narrowband or broadband range of frequencies of interest numerical results are used to compare the proposed 3d drp fdtd schemes against traditional high order fdtd schemes

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

an adi fdtd method for periodic structures in this communication the alternating direction implicit finite difference time domain adi fdtd method is extended to analyze periodic structures in the implicit updates of the adi fdtd method the periodic boundary condition leads to a cyclic matrix instead of inverting the cyclic matrix directly the problem is converted into two auxiliary linear systems that can be solved using the tridiagonal matrix solver consequently only 7n arithmetic operations are required for each implicit update and the efficiency of the adi fdtd method is retained numerical examples further demonstrate the effectiveness of this periodic adi fdtd method

equivalence of inverse sturm liouville problems with boundary conditions rationally dependent on the eigenparameter abstract three inverse problems for a sturm liouville boundary value problem y qy y y 0 cos y 0 sin and y 1 f y 1 are considered for rational f it is shown that the weyl m function uniquely determines f and q and is in turn uniquely determined by either two spectra from different values of or by the prufer angle for this it is necessary to produce direct results of independent interest on asymptotics and oscillation

dependence of the nth sturm liouville eigenvalue on the problem abstract we consider the nth eigenvalue as a function on the space of self adjoint regular sturm liouville problems with positive leading coefficient and weight functions the discontinuity of the nth eigenvalue is completely characterized

sturm liouville problems and discontinuous eigenvalues if a sturm liouville problem is given in an open interval of the real line then regular boundary value problems can be considered on compact sub intervals for these regular problems all with necessarily discrete spectra the eigenvalues depend on both the end points of the compact intervals and upon the choice of the real separated boundary conditions at these end points these eigenvalues are not in general continuous functionsof the end points and boundary conditions the paper shows the surprising form of these discontinuities the results have applications to the approximations of singular sturm liouville problems by regular problems and to the theoretical aspects of the sleign2 computer program

efficient implementation of 2 d split field fdtd method for analyzing periodic structures this communication presents an efficient implementation of the 2 d split field method for solving problems of the oblique incident plane wave on periodic structures first by only splitting one field quantity q x and adopting the locally one dimensional scheme the transformed maxwell s equations are reformulated into a concise form and then by some matrix operation the field updating of the proposed method is implemented in the explicit scheme compared with the traditional split field method the courant friedrich levy stability condition of the proposed method is weaker and the cpu time and memory are saved numerical results demonstrate that the proposed method is more efficient

eigenvalues of limit point sturm liouville problems abstract the dependence of the eigenvalues of self adjoint sturm liouville problems on the boundary conditions when each endpoint is regular or in the limit circle case is now due to some surprisingly recent results well understood here we study this dependence for singular problems with one endpoint in the limit point case

eigenvalues of regular sturm liouville problems abstract the eigenvalues of sturm liouville sl problems depend not only continuously but smoothly on the problem an expression for the derivative of an eigenvalue with respect to a given parameter an endpoint a boundary condition a coefficient or the weight function is found

an interaction integral method for 3d curved cracks in nonhomogeneous materials with complex interfaces this work derives an interaction integral for the computation of mixed mode stress intensity factors sifs in three dimensional 3d nonhomogeneous materials with continuous or discontinuous properties the present method is based on a two state integral by the superposition of actual and auxiliary fields in 3d domain formulation of the interaction integral derived here the integrand does not involve any derivatives of material properties furthermore the formulation can be proved to be still valid even when the integral domain contains material interfaces therefore it is not necessary to limit the material properties to be continuous for the present formulation on account of these advantages the application range of the interaction integral can be greatly enlarged this method in conjunction with the finite element method fem is employed to solve several representative fracture problems according to the comparison between the results and those from the published lectures good agreement demonstrates the validation of the interaction integral the results show that the present interaction integral is domain independent for nonhomogeneous materials with interfaces

group velocity in finite difference schemes the relevance of group velocity to the behavior of finite difference models of time dependent partial differential equations is surveyed and illustrated applications involve the propagation of wave packets in one and two dimensions numerical dispersion the behavior of parasitic waves and the stability analysis of initial boundary value problems

lattice electromagnetic theory from a topological viewpoint the language of differential forms and topological concepts are applied to study classical electromagnetic theory on a lattice it is shown that differential forms and their discrete counterparts cochains provide a natural bridge between the continuum and the lattice versions of the theory allowing for a natural factorization of the field equations into topological field equations i e invariant under homeomorphisms and metric field equations the various potential sources of inconsistency in the discretization process are identified distinguished and discussed a rationale for a consistent extension of the lattice theory to more general situations such as to irregular lattices is considered

implementation of the periodic boundary condition in the finite difference time domain algorithm for fss structures a method for implementing the general floquet boundary condition in the finite difference time domain algorithm fdtd is presented the floquet type of phase shift boundary condition is incorporated into the time domain analysis by illuminating the structure with a combination of sine and cosine excitations to generate a phasor representation of the solution at each time step with this approach the characteristics of periodic structures comprised of arbitrarily shaped inhomogeneous geometries can be computed for an arbitrary angle of incidence theoretical results are compared for various planar frequency selective surfaces fss and for one with a three dimensional element e g a thick double concentric square loop

cracks problem for non homogeneous composite material subjected to dynamic loading abstract in this paper we present a method to analyse the dynamic and steady response of non homogeneous composite materials differing from the existing works reported in literature the present method can be used for arbitrarily varying material properties through thickness direction and the crack number can be larger than one it is assumed that the composite material is orthotropic and all the material properties depend only on the coordinates y along the thickness direction the material non homogeneity is simulated by dividing the plate into a number of layers each layer is assigned slightly different material properties the method is based upon the fourier and laplace transforms to reduce the boundary value problem to a system of generalized singularity integral equations in the laplace transform domain the singular integral equations for the problem are derived and numerically solved by weighted residual value methods by utilized numerical laplace inversion the time dependent full field solutions are obtained as the numerical illustrates three different cracked specimens a functionally graded material a metal ceramic joint with functionally graded interlayer and a metal substrate functionally graded film structure are presented for various material non homogeneity parameters and or functionally graded layer thickness the results obtained demonstrate that the present model is an efficient tool in the fracture analysis of composite materials with properties varying in the thickness direction

the wlp fdtd method for periodic structures with oblique incident wave a new unconditionally stable finite difference time domain fdtd method for periodic structures is presented which is based on the field transformation method and the weighted laguerre polynomials fdtd wlp fdtd the proposed method uses a field transformation to remove the time gradient across the grid and then uses the concept of the wlp fdtd to get the implicit relationship between the transformed field variables it holds the advantages of the wlp fdtd can eliminate the restriction of the courant friedrich levy cfl stability condition compared with other field transform methods the new method needn t to do special treatment for the additional terms it appears to be much more efficient than the other field transformation fdtd method for solving periodic structures with fine structures and large incident angle to verify the accuracy and the efficiency of the proposed method we compare the results of the split field fdtd method with the proposed method

dynamic stress intensity factors for two parallel interface cracks between a nonhomogeneous bonding layer and two dissimilar elastic half planes subject to an impact load some composite materials are constructed of two dissimilar half planes bonded by a nonhomogeneous elastic layer in the present study a crack is situated at the interface between the upper half plane and the bonding layer of such a material and another crack is located at the interface between the lower half plane and the bonding layer the material properties of the bonding layer vary continuously from those of the lower half plane to those of the upper half plane incoming shock stress waves impinge upon the two interface cracks normal to their surfaces fourier transformations were used to reduce the boundary conditions for the cracks to two pairs of dual integral equations in the laplace domain to solve these equations the differences in the crack surface displacements were expanded in a series of functions that are zero valued outside the cracks the unknown coefficients in the series were solved using the schmidt method so as to satisfy the conditions inside the cracks the stress intensity factors were defined in the laplace domain and were inverted numerically to physical space dynamic stress intensity factors were calculated numerically for selected crack configurations

axisymmetric frictionless contact of a functionally graded piezoelectric layered half space under a conducting punch abstract this paper studies the axisymmetric frictionless contact of a functionally graded piezoelectric layered half space subjected to three typical rigid punches i e flat circular punch spherical punch and conical punch the punch is assumed as a perfect conductor with a constant electric potential the electro mechanical properties of the functionally graded piezoelectric materials fgpms vary exponentially along the thickness direction by employing the hankel integral transform technique the problem is reduced to a set of singular integral equations of the first kind these equations are then discretized and solved numerically to determine the unknown normal contact pressure and electric charge the effects of the gradient index and punch geometry on the surface electro mechanical contact behaviors are discussed in detail

a modified fdtd 2 4 scheme for modeling electrically large structures with high phase accuracy a new fourth order finite difference time domain fdtd scheme has been developed that exhibits extremely low phase errors at low grid resolutions compared to the conventional fdtd scheme moreover this new scheme is capable of combining with the standard yee 1966 scheme to produce a stable hybrid algorithm the problem of wave propagation through a building is simulated using this new hybrid algorithm to demonstrate the large savings in computing resources it could afford with this new development the fdtd method can now be used to successfully model structures that are thousands of wavelengths large using the present day computer technology

sturm liouville problems with boundary conditions rationally dependent on the eigenparameter ii necessary and sufficient conditions are given for two sequences n and n to be the eigenvalues and norming constants of a sturm liouville boundary value problem y qy y y 0 cos y 0 sin and y 1 f y 1 where f is a rational function of herglotz nevanlinna type it is also proved that q and f are uniquely determined by the sequences n and n