particle swarm optimization in electromagnetics the particle swarm optimization pso new to the electromagnetics community is a robust stochastic evolutionary computation technique based on the movement and intelligence of swarms this paper introduces a conceptual overview and detailed explanation of the pso algorithm as well as how it can be used for electromagnetic optimizations this paper also presents several results illustrating the swarm behavior in a pso algorithm developed by the authors at ucla specifically for engineering optimizations ucla pso also discussed is recent progress in the development of the pso and the special considerations needed for engineering implementation including suggestions for the selection of parameter values additionally a study of boundary conditions is presented indicating the invisible wall technique outperforms absorbing and reflecting wall techniques these concepts are then integrated into a representative example of optimization of a profiled corrugated horn antenna

on the derivation of the numerical permittivity and stability of the cds fdtd implementation of high order constitutive relations recently the derivation of the numerical permittivity and stability of the finite difference time domain fdtd implementation of a 4 pole complex rational function by using the central difference scheme cds have been studied in this communication the accuracy and the stability limitation of this scheme are investigated in addition alternative fdtd implementation based on the mobius transformation mt is presented it is observed that the cds implementation is less accurate and more stability restrictive than the mt counterpart

fdtd dispersive modeling of human tissues based on quadratic complex rational function we propose a dispersive finite difference time domain fdtd suitable for the electromagnetic analysis of human tissues the dispersion relation of biological tissues is characterized by a quadratic complex rational function qcrf that leads to an accurate fdtd algorithm in 400 mhz 3 ghz qcrf coefficients are extracted by applying the complex curve fitting technique without initial guess numerical examples are used to illustrate the computational accuracy and stability of qcrf based fdtd

z transform theory and the fdtd method in implementing the finite difference time domain fdtd method on materials which are dispersive or nonlinear the relationship between the flux density and the electric field can be the most complicated part of the problem because the fdtd method is a sampled time domain method this relationship can be can be looked upon as a digital filtering problem the z transform is typically used in digital filtering and signal processing problems the paper illustrates the use of the z transform in implementing the fdtd method where complicated dispersive or nonlinear materials are involved

time domain finite difference and finite element methods for maxwell equations in complex media extensions of finite difference time domain fdtd and finite element time domain fetd algorithms are reviewed for solving transient maxwell equations in complex media also provided are a few representative examples to illustrate the modeling capabilities of fdtd and fetd for complex media the term complex media refers here to media with dispersive bi anisotropic inhomogeneous and or nonlinear properties present in the constitutive tensors

invariant properties of the stress in plane elasticity and equivalence classes of composites attention is drawn to the invariance of the stress field in a two dimensional body loaded at the boundary by fixed forces when the compliance tensor scr g chi is shifted uniformly by ell text i lambda lambda where lambda is an arbitrary constant and scr g text i kappa mu is the compliance tensor of a isotropic material with two dimensional bulk and shear moduli kappa and mu this invariance is explained from two simple observations first that in two dimensions the tensor scr g text i frac 1 2 frac 1 2 acts to locally rotate the stress by 90 degrees and the second that this rotated field is the symmetrized gradient of a vector field and therefore can be treated as a strain for composite materials the invariance of the stress field implies that the effective compliance tensor ell ast also gets shifted by scr g text i lambda lambda when the constituent moduli are each shifted by ell text i lambda lambda this imposes constraints on the functional dependence of ell ast on the material moduli of the components applied to an isotropic composite of two isotropic components it implies that when the inverse bulk modulus is shifted by the constant 1 lambda and the inverse shear modulus is shifted by 1 lambda then the inverse effective bulk and shear moduli undergo precisely the same shifts in particular it explains why the effective young s modulus of a two dimensional media with holes does not depend on the poisson s ratio of the matrix material

some remarks on the stability of time domain electromagnetic simulations aspects of the stability of time domain update schemes for electromagnetic problems are examined based on the consideration of system amplification matrices arising from the discretization of maxwell s equations in the sequence space we discuss time domain stability for a given discretization scale and under three different assumptions of decreasing generality general updates general leapfrog updates and reciprocal leapfrog updates

optimal bounds on the effective bulk modulus of polycrystals the classical problem of bounding the effective bulk modulus of isotropic polycrystalline aggregates built from a single anisotropic phase is studied for three dimensional composites we find that the voigt and reuss bounds are each attained by multi layered laminate geometries and hence are optimal for two dimensional composites the reuss lower bound is proved to be optimal while a new optimal upper bound is derived

perfectly matched layer for the time domain finite element method a new perfectly matched layer pml formulation for the time domain finite element method is described and tested for maxwell s equations in particular we focus on the time integration scheme which is based on galerkin s method with a temporally piecewise linear expansion of the electric field the time stepping scheme is constructed by forming a linear combination of exact and trapezoidal integration applied to the temporal weak form which reduces to the well known newmark scheme in the case without pml extensive numerical tests on scattering from infinitely long metal cylinders in two dimensions show good accuracy and no signs of instabilities for a circular cylinder the proposed scheme indicates the expected second order convergence toward the analytic solution and gives less than 2 root mean square error in the bistatic radar cross section rcs for resolutions with more than 10 points per wavelength an ogival cylinder which has sharp corners supporting field singularities shows similar accuracy in the monostatic rcs

exact relations for effective tensors of polycrystals ii applications to elasticity and piezoelectricity an important necessary condition for an exact relation for effective moduli of polycrystals to hold is stability of that relation under lamination this requirement is so restrictive that it is possible if not always feasible to find all such relations explicitly in order to do this one needs to combine the results developed in part i of this paper and the representation theory of the rotation groups so 2 and so 3 more precisely one needs to know all rotationally invariant subspaces of the space of material moduli this paper presents an algorithm for finding all such subspaces we illustrate the workings of the algorithm on the examples of 3 dimensional elasticity where we get all the exact relations and the examples of 2 dimensional and 3 dimensional piezoelectricity where we get some possibly all of them

differential forms galerkin duality and sparse inverse approximations in finite element solutions of maxwell equations we identify primal and dual formulations in the finite element method fem solution of the vector wave equation using a geometric discretization based on differential forms these two formulations entail a mathematical duality denoted as galerkin duality galerkin dual fem formulations yield identical nonzero dynamical eigenvalues up to machine precision but have static zero eigenvalue solution spaces of different dimensions algebraic relationships among the degrees of freedom of primal and dual formulations are explained using a deep rooted connection between the hodge helmholtz decomposition of differential forms and descartes euler polyhedral formula and verified numerically in order to tackle the fullness of dual formulation algebraic and topological thresholdings are proposed to approximate inverse mass matrices by sparse matrices

piecewise linear recursive convolution for dispersive media using fdtd electromagnetic propagation through linear dispersive media can be analyzed using the finite difference time domain fdtd method by employing the recursive convolution rc approach to evaluate the discrete time convolution of the electric field and the dielectric susceptibility function the rc approach results in a fast and computationally efficient algorithm however the accuracy achieved is not generally as good as that obtained with other methods a new piecewise linear recursive convolution plrc method is described here that has greatly improved accuracy over the original rc approach but retains its speed and efficiency advantages

a high order mixed vector finite element method for solving the time dependent maxwell equations on unstructured grids we present a mixed vector finite element method for solving the time dependent coupled ampere and faraday laws of maxwell s equations on unstructured hexahedral grids that employs high order discretization in both space and time the method is of arbitrary order accuracy in space and up to 4th order accurate in time making it well suited for electrically large problems where grid anisotropy and numerical dispersion have plagued other methods in addition the method correctly models both the jump discontinuities and the divergence free properties of the electric and magnetic fields is charge and energy conserving conditionally stable and free of spurious modes several computational experiments are performed to demonstrate the accuracy efficiency and benefits of the method

on the effective viscoelastic moduli of two phase media i rigorous bounds on the complex bulk modulus the dynamic response of isotropic composites of two viscoelastic isotropic phases mixed in fixed proportions is considered in the frequency range where the acoustic wavelength is much larger than the inhomogeneities the effective bulk modulus bounds of hashin shtrikman walpole are extended to viscoelasticity in this quasi static regime where the properties of the isotropic composite can be described by complex bulk and shear moduli the effective bulk modulus is shown to be constrained to a lens shaped region of the complex plane bounded by the outermost pair of four circular arcs three circular arcs in the case of two dimensional elasticity this is proved using a new variational principle for viscoelasticity together with two established techniques for deriving bounds on effective moduli namely the translation method and the hashin shtrikman method in this application the hashin shtrikman method needs to be generalized to allow the reference tensor to have an associated quasiconvex energy microstructures are identified which have bulk moduli that correspond to various points on each of the circular arcs thus these microstructures have extremal viscoelastic behaviour when the associated arc forms one of the outermost pair the bounds and the extremal microstructures are similar to those obtained for the complex dielectric constant but the methods used here are entirely different

bi fdtd a novel finite difference time domain formulation for modeling wave propagation in bi isotropic media this paper presents a newly developed finite difference time domain fdtd technique referred to as bi fdtd for modeling electromagnetic wave interactions with bi isotropic bi media the theoretical foundation for the bi fdtd method will be developed based on a wavefield decomposition the main advantage of this approach is that the two sets of wavefields are uncoupled and can be viewed as propagating in an equivalent isotropic medium which makes it possible to readily apply conventional fdtd analysis techniques the bi fdtd scheme will also be extended to include the dispersive nature of chiral media an important subclass of bi isotropic media this extension represents the first of its kind in the fdtd community validations of this new model are demonstrated for a chiral half space and a chiral slab

rank one plus a null lagrangian is an inherited property of two dimensional compliance tensors under homogenisation assume that the local compliance tensor of an elastic composite in two space dimensions is equal to a rank one tensor plus a null lagrangian there is only one symmetric one in 2d the purpose of this paper is to prove that the effective compliance tensor has the same representation rank one plus the null lagrangian this statement generalizes the well known result of hill 14 15 that a composite of isotropic phases with a common shear modulus is necessarily elastically isotropic and shares the same shear modulus it also generalizes the surprising discovery in 1 that under a certain condition on the pure crystal moduli the shear modulus of an isotropic polycrystal is uniquely determined the present paper sheds light on this effect by placing it in a more general framework and using some elliptic pde theory rather than the translation method our results allow us to calculate the polycrystalline g closures of the special class of crystals under consideration our analysis is contrasted with a two dimensional model problem for shape memory polycrystals we show that the two problems can be thought of as elastic percolation problems one elliptic one hyperbolic

fdtd dispersive modeling with high order rational constitutive parameters in this work we present a dispersive finite difference time domain fdtd algorithm using a four pole complex rational function crf for the sake of a better curve fitting of the four pole crf dispersion model we use a particle swarm optimization technique we also discuss an efficient memory storage strategy using a state space approach the numerical aspects of four pole crf fdtd the numerical accuracy and the numerical stability are investigated in detail numerical examples are used to validate four pole crf fdtd and numerical stability issues are discussed in detail we also discuss the computational accuracy and the computational efficiency of an arbitrary n pole crf fdtd

a modification of the dewilde van der veen method for inversion of finite structured matrices abstract we study a class of block structured matrices r r ij i j 1 n with a property that the solution of the corresponding system rx y of linear algebraic equations may be performed for o n arithmetic operations in this paper for finite invertible matrices we analyze in detail factorization and inversion algorithms these algorithms are related to those suggested by p m dewilde and a j van der veen time varying systems and computations kluwer academic publishers new york 1998 for a class of finite and infinite matrices with a small hankel rank the algorithms presented here are more transparent and are a modification of the algorithms from the above reference the approach and the proofs are essentially different from those in the above mentioned reference the paper contains also analysis of complexity and results of numerical experiments

finite difference and pseudospectral time domain methods applied to backward wave metamaterials backward wave bw materials that have simultaneously negative real parts of their electric permittivity and magnetic permeability can support waves where phase and power propagation occur in opposite directions these materials were predicted to have many unusual electromagnetic properties among them amplification of the near field of a point source which could lead to the perfect reconstruction of the source field in an image j pendry phys rev lett vol 85 pp 3966 2000 often systems containing bw materials are simulated using the finite difference time domain technique we show that this technique suffers from a numerical artifact due to its staggered grid that makes its use in simulations involving bw materials problematic the pseudospectral time domain technique on the other hand uses a collocated grid and is free of this artifact it is also shown that when modeling the dispersive bw material the linear frequency approximation method introduces error that affects the frequency of vanishing reflection while the auxiliary differential equation the z transform and the bilinear frequency approximation method produce vanishing reflection at the correct frequency the case of vanishing reflection is of particular interest for field reconstruction in imaging applications

finite difference time domain modeling of curved surfaces em scattering the finite difference time domain fdtd method is generalized to include the accurate modeling of curved surfaces this generalization the contour path cp method accurately models the illumination of bodies with curved surfaces yet retains the ability to model corners and edges cp modeling of two dimensional electromagnetic wave scattering from objects of various shapes and compositions is presented

optimal g closure bounds via stability under lamination optimal bounds for a two dimensional g closure problem are proved they are obtained by combining together bounds derived using fine properties of quasiconformal mappings and a stability property of the g closure which is known as stability under lamination

efficient solution of linear systems of equations with recursive structure abstract inversion algorithms of order n2 for n n matrices with recursive structure are derived in a unified way several known algorithms as well as some new ones for toeplitz type hilbert type and vandermonde type matrices are given

direct approach to the band completion problem we study the problem of completion of a matrix with a specified band in such a way that the inverse be a band matrix with the same width for the general block matrix case a new approach to solve this and related problems is proposed the relations with the class of quasiseparable matrices play an important role

asymptotic estimates on uncertainty of the elastic moduli of completely random trigonal polycrystals because of the uncertain irregular microgeometry a random polycrystalline aggregate the shape and crystalline orientations of the constituent anisotropic grains of which are uncorrelated may have elastic moduli scattered over some though small intervals while the conventional macroscopic homogeneity and isotropy hypotheses for it may be considered only as approximate with corresponding uncertainty our formal bounds are proposed to provide the estimates on those uncertainties in asymptotic sense explicit expressions for the aggregates of trigonal crystals classes 3m 32 3m are derived

multiple lu factorizations of a singular matrix a singular matrix a may have more than one lu factorizations in this work the set of all lu factorizations of a is explicitly described when the lower triangular matrix l is nonsingular to this purpose a canonical form of a under left multiplication by unit lower triangular matrices is introduced this canonical form allows us to characterize the matrices that have an lu factorization and to parametrize all possible lu factorizations formulae in terms of quotient of minors of a are presented for the entries of this canonical form

lu factorization for matrices in quasiseparable form via orthogonal transformations abstract the paper presents a new algorithm to compute the lu factorization of a matrix represented in a quasiseparable or semiseparable form i e using generators it obtains the quasiseparable representations of the factors l and u of an n n block matrix via o n arithmetic operations on the block entries the algorithm uses recursions based exclusively on unitary transformations which provide numerical stability even in singular cases the method of the paper is based on the theory developed in 1 and provides an alternative to the approach proposed in 7 for strongly regular matrices the algorithm presented here works also for some matrices with possibly singular principle submatrices the results of numerical tests show that also for strongly regular matrices the new algorithm is comparable with the previous methods

mur nedelec finite element schemes for maxwell s equations we study mapped mass lumped edge elements for approximating a three dimensional scattering problem the elements are mapped mur nedelec second kind elements and the scheme is designed to handle anisotropic inhomogeneous scatterers with moderately complicated geometry a novel aspect of the scheme is the use of an unusual choice of the magnetic field finite element that results in a very efficient discrete curl operator using a non standard dispersion analysis we show that the phase accuracy of the cubic edge element does not deteriorate disastrously when the mesh is deformed our numerical experiments in two dimensions confirm that the scheme performs well on a distorted mesh and that it is efficient compared to the standard yee scheme

an efficient vector finite element method for nonlinear electromagnetic modeling we have developed a mixed vector finite element method vfem for maxwell s equations with a nonlinear polarization term the method allows for discretization of complicated geometries with arbitrary order representations of the b and e fields in this paper we will describe the method and a series of optimizations that significantly reduce the computational cost additionally a series of test simulations will be presented to validate the method finally a nonlinear waveguide mode mixing example is presented and discussed

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

an efficient finite difference scheme for electromagnetic logging in 3d anisotropic inhomogeneous media we consider a problem of computing the electromagnetic field in 3d anisotropic media for electromagnetic logging the proposed finite difference scheme for maxwell equations has the following new features based on some recent and not so recent developments in numerical analysis coercivity i e the complete discrete analogy of all continuous equations in every grid cell even for nondiagonal conductivity tensors a special conductivity averaging that does not require the grid to be small compared to layering or fractures and a spectrally optimal grid refinement minimizing the error at the receiver locations and optimizing the approximation of the boundary conditions at infinity all of these features significantly reduce the grid size and accelerate the computation of electromagnetic logs in 3d geometries without sacrificing accuracy

null lagrangians weak continuity and variational problems of arbitrary order abstract we consider the problem of minimizing integral functionals of the form i u f x k u x dx where r p u r and k u denotes the set of all partial derivatives of u with orders k the method is based on a characterization of null lagrangians l ku depending only on derivatives of order k applications to elasticity and other theories of mechanics are given

on characterizing the set of possible effective tensors of composites the variational method and the translation method a general algebraic framework is developed for characterizing the set of possible effective tensors of composites a transformation to the polarization problem simplifies the derivation of the hashin shtrikman variational principles and simplifies the calculation of the effective tensors of laminate materials a general connection is established between two methods for bounding effective tensors of composites the first method is based on the variational principles of hashin and shtrikman the second method due to tartar murat lurie and cherkaev uses translation operators or equivalently quadratic quasiconvex functions a correspondence is established between these translation operators and bounding operators on the relevant non local projection operator t1 an important class of bounds namely trace bounds on the effective tensors of two component media are given a geometrical interpretation after a suitable fractional linear transformation of the tensor space each bound corresponds to a tangent plane to the set of possible tensors a wide class of translation operators that generate these bounds is found the extremal translation operators in this class incorporate projections onto spaces of antisymmetric tensors these extremal translations generate attainable trace bounds even when the tensors of the two components are not well ordered in particular they generate the bounds of walpole on the effective bulk modulus the variational principles of gibiansky and cherkaev for bounding complex effective tensors are reviewed and used to derive some rigorous bounds that generalize the bounds conjectured by golden and papanicolaou an isomorphism is shown to underlie their variational principles this isomorphism is used to obtain dirichlet type variational principles and bounds for the effective tensors of general non selfadjoint problems it is anticipated that these variational principles which stem from the work of gibiansky and cherkaev will have applications in many fields of science

discontinuous galerkin methods for dispersive and lossy maxwell s equations and pml boundary conditions in this paper we will present a unified formulation of discontinuous galerkin method dgm for maxwell s equations in linear dispersive and lossy materials of debye type and in the artificial perfectly matched layer pml regions an auxiliary differential equation ade method is used to handle the frequency dependent constitutive relations with the help of auxiliary polarization currents in the computational and pml regions the numerical flux for the dispersive lossy maxwell s equations with the auxiliary polarization current variables is derived various numerical results are provided to validate the proposed formulation

homogenization and optimal bounds in linear elasticity in their celebrated paper of 1963 hashin shtrikman 1 addressed the problem of determining optimal bounds for the bulk and shear moduli of a statistically isotropic elastic composite material with arbitrary isotropic phase geometry they derived a set of bounds for these moduli in the physically meaningful case of three dimensional elasticity in the case of a two phase composite let k 1 1 and k 2 2 respectively denote the bulk and shear moduli for the first and the second phase let k denote their analogues for the composite and let 0 stand for the volume fraction of the first phase in the composite under the ordering restriction that both

an integral representation and bounds on the effective diffusivity in passive advection by laminar and turbulent flows precise necessary and sufficient conditions on the velocity statistics for mean field behavior in advection diffusion by a steady incompressible velocity field are developed here under these conditions a rigorous stieltjes integral representation for effective diffusivity in turbulent transport is derived this representation is valid for all peclet numbers and provides a rigorous resummation of the divergent perturbation expansion in powers of the peclet number one consequence of this representation is that convergent upper and lower bounds on effective diffusivity for all peclet numbers can be obtained utilizing a prescribed finite number of terms in the perturbation series explicit rigorous examples of steady incompressible velocity fields are constructed which have effective diffusivities realizing the simplest upper or lower bounds for all peclet numbers a nonlocal variational principle for effective diffusivity is developed along with applications to advection diffusion by random arrays of vortices a new class of rigorous examples is introduced these examples have an explicit stieltjes measure for the effective diffusivity furthermore the effective diffusivity behaves likek0 pe 1 2 in the limit of large peclet numbers wherek0 is the molecular diffusivity formal analogies with the theory of composite materials are exploited systematically

fdtd for nth order dispersive media previously a method for applying the finite difference time domain fdtd method to dispersive media with complex permittivity described by a function with a single first order pole was presented this method involved the recursive evaluation of a discrete convolution and was therefore relatively efficient in this work the recursive convolution approach is extended to media with dispersions described by multiple second order poles the significant change from the first order implementation is that the single backstore variable for each second order pole is complex the approach is demonstrated for a pulsed plane wave incident on a medium with a complex permittivity described by two second order poles and excellent agreement is obtained with the exact solution

on numerical artifacts of the complex envelope adi fdtd method we examine two spurious numerical artifacts of the complex envelope ce alternating direction implicit finite difference time domain adi fdtd method viz spurious charges and anomalous wave propagation modes with positive phase velocity and negative group velocity these artifacts are also present in the conventional adi fdtd however the spurious charges in ce adi fdtd have a fundamental distinction from those of adi fdtd they are static in adi fdtd and implicitly time harmonic in ce adi fdtd spurious charges are particularly detrimental to ce adi fdtd simulations because they produce secondary radiation we also show that spurious charges can be reduced by a fixed point iterative correction in ce adi fdtd