blind shape reconstruction from experimental data a method for reconstructing the shape of a bounded impenetrable object from measured scattered field data is presented the reconstruction algorithm is in principle the same as that used before for reconstructing the conductivity of a penetrable object and uses the fact that for high conductivity the skin depth of the scatterer is small in which case the only meaningful information produced by the algorithm is the boundary of the scatterer a striking increase in efficiency is achieved by incorporating into the algorithm the fact that for large conductivity the contrast is dominated by a large positive imaginary part this fact together with the knowledge that the scatterer is constrained in some test domain constitute the only a priori information about the scatterer that is used there are no other implicit assumptions about the location connectivity convexity or boundary conditions the method is shown to successfully reconstruct the shape of an object from experimental scattered field data in a blind test

adi scheme of a nonstandard fdtd method and its numerical properties an alternating direction implicit adi scheme for a nonstandard ns finite difference time domain fdtd method is proposed the ns fdtd method is derived by analyzing the dispersion relation two different groups of update coefficients are used to update the electric field and magnetic field respectively the dispersion property of the ns method is similar with that of the standard higher order method though it is only second order accurate in the space domain the total number of nonzero update coefficients for this method is fewer than that of the latter this small stencil property can be used to reduce computational burden in implicit formulation of this method the one step leapfrog adi scheme is adopted to examine this idea the detailed update equations of this adi scheme are derived the dispersion and stability properties are also analyzed and compared with the corresponding standard one the results show that the computational efficiency of the proposed method is higher than that of the standard one

fdfd a 3d finite difference frequency domain code for electromagnetic induction tomography abstract a new 3d code for electromagnetic induction tomography with intended applications to environmental imaging problems has been developed the approach consists of calculating the fields within a volume using an implicit finite difference frequency domain formulation the volume is terminated by an anisotropic perfectly matched layer region that simulates an infinite domain by absorbing outgoing waves extensive validation of this code has been done using analytical and semianalytical results from other codes and some of those results are presented in this paper the new code is written in fortran 90 and is designed to be easily parallelized finally an adjoint field method of data inversion developed in parallel for solving the fully nonlinear inverse problem for electrical conductivity imaging e g for mapping underground conducting plumes uses this code to provide solvers for both forward and adjoint fields results obtained from this inversion method for high contrast media are encouraging and provide a significant improvement over those obtained from linearized inversion methods

numerical vector green s function for s parameter measurement with waveport excitation we present a numerical vector green s function that directly links the object material property within the electric field volume integral equation vie to the scattered s parameters this green s function is particularly useful for microwave inverse scattering applications in which s parameter measurements are used to reconstruct the dielectric properties of unknown objects in an inhomogeneous background where the green s function does not have an analytic form unlike the dyadic green s function in a standard vie which relates the fields in the object domain vector to the scattered fields vector this vector green s function kernel relates the object domain fields vector to the measured s parameters scalar also this new vector green s function uses a waveport source method which accurately accounts for the measured scattered s parameters between antenna feeds of arbitrary impedance and modes a detailed derivation is presented and simulated and experimental examples are provided to validate this vector green s function for the prediction of scattered s parameters

fractional differential equations and lyapunov functionals abstract we consider a scalar fractional differential equation write it as an integral equation and construct several lyapunov functionals yielding qualitative results about the solution it turns out that the kernel is convex with a singularity and it is also completely monotone as is the resolvent kernel while the kernel is not integrable the resolvent kernel is positive and integrable with an integral value of one these kernels give rise to essentially different types of lyapunov functionals it is to be stressed that the lyapunov functionals are explicitly given in terms of known functions and they are differentiated using leibniz s rule the results are readily accessible to anyone with a background of elementary calculus

singular integral equations liapunov functionals and resolvents abstract this paper together with a recent paper by the second author on convex singular kernels establishes a base for further investigation of mildly singular equations with liapunov theory we study the two nonlinear scalar integral equations x t a t 0 t d t s x s g s x s d s and z t a t 0 t d t s g s z s d s where d has a singularity at t s the first equation is decomposed into three other simpler equations we then construct a liapunov functional for each of the equations which will yield l p properties of the solutions

resolvents and solutions of singular volterra integral equations with separable kernels the volterra integral equation 1 x t a t 0 tb t s x s dswith a kernel of the form b t s p t q s is investigated where a p and q are functions that are defined a e on an interval 0 t and are measurable the main result of this paper states that if qa is lebesgue integrable on 0 t the sign of b t s does not change for almost all t s and if there is a function f that is continuous on 0 t except possibly at countably many points with b t t f t a e on 0 t then the function x defined by 2 x t a t 0 tr t s a s ds where 3 r t s b t s e s t b u u d u solves 1 a e on 0 t three diverse examples illustrate the efficacy of using 2 and 3 to calculate solutions of 1 two of the examples involve singular kernels the solution of one of them is nowhere continuous on 0 t

lp solutions of singular integro differential equations abstract we study a variety of scalar integro differential equations with singular kernels including linear nonlinear and resolvent equations the first result involves a type of existence theorem which uses a fixed point mapping defined by the integro differential equation itself and produces a unique solution with a continuous derivative in a very simple way we then construct a liapunov functional yielding qualitative properties of solutions the work answers questions raised by volterra in 1928 by levin in 1963 and by grimmer and seifert in 1975 previous results had produced bounded solutions from bounded perturbations our results mainly concern integrable solutions from integrable perturbations

a 3 d enlarged cell technique ect for the conformal fdtd method in this paper we present an enlarged cell technique ect to avoid the time step reduction encountered in the conformal finite difference time domain cfdtd method due to small irregular cells truncated by metallic boundaries we focus our efforts on the discussion of the accuracy and stability of the ect and its comparison with other conformal methods especially the one called the uniformly stable conformal usc method we also provide a simplified ect which is much easier to implement in the ect a stability criterion is first constructed to identify instable irregular cells i e those having so small an area to cause instability those instable cells are then enlarged into their adjacent cells to obtain a large stable area careful treatment is performed on the communication between the intruding and intruded cells in terms of electromotive force by keeping the total electromotive force conservative this technique is verified by several 3 d numerical experiments results show that the ect is second order accurate and numerically stable at the regular courant time step limit

on the use of the geometric mean in fdtd near to far field transformations near to far field transformations require the tangential electric and magnetic fields over a surface which we call the integration boundary however the staggered nature of the finite difference time domain grid is problematic in that the electric and magnetic fields are not collocated in either space or time for harmonic transformations i e ones which rely upon a fourier transform of the time domain near fields one can account for the temporal offset with a simple phase correction in the frequency domain to account for spatial offsets previously an arithmetic mean of the time domain fields to either side of the integration boundary has been used here we show that superior results are obtained by instead using a geometric mean of the harmonic fields to either side of the integration boundary

flux limiting embedded boundary technique for electromagnetic fdtd a general approach for incorporating embedded boundaries into an electromagnetic finite difference time domain fdtd code is presented this algorithm is shown to satisfy gauss s law and enforces no magnetic monopoles while maintaining a globally second order result first order at physical boundaries with no added time step restriction theoretically predicted superior results are shown with an 11 time step reduction from the courant stability limit this is achieved through a physics based flux limiting scheme near physical boundaries stability local truncation error and energy conservation analysis are also provided

a new 3 d conformal pec fdtd scheme with user defined geometric precision and derived stability criterion a new conformal finite difference time domain cfdtd updating scheme for metallic surfaces nonaligned in the grid is presented in this paper in contrast to existing conformal models the new model can be formulated with the original yee fdtd update equation therefore the proposed scheme can be easily added in standard fdtd codes even if the codes are already parallelized or hardware accelerated in addition based on the commonly used conventional stability criterion a derivation of the stability is presented and based on the conformal geometric information a time step reduction formula is presented the time step reduction is used as a user defined parameter to tradeoff speed versus accuracy the achievable geometric precision is optimized to a given time step therefore even with the conventional time step no reduction the presented scheme profits from the conformal discretization to show the performance and the robustness of the proposed scheme canonical validations and two real world applications were investigated a broadband low profile circular antenna was successfully simulated showing the benefit of the conformal fdtd method compared to the conventional scheme furthermore a cad based mobile phone was conformally discretized and successfully simulated showing that the proposed scheme is highly suited for the simulation of advanced engineering problems

development of a novel fdtd 2 4 compatible conformal scheme for electromagnetic computations of complex curved pec objects we present a modified fourth order finite difference time domain fdtd 2 4 conformal scheme for accurately computing electromagnetic characteristics of some complex three dimensional 3d perfectly conducting pec objects it has higher accuracy and efficiency than those of conventional fdtd and fdtd 2 4 methods as coarse meshes are employed with staircase errors reduced effectively during its implementation two integration loops of the faraday s law are used for updating magnetic field components while the updating equations of electric field ones are the same as those in the normal fdtd method a rigorous analysis of its global stability based on the conventional high order fdtd stability criterion and the fourier method is also performed in order to obtain stable and accurate numerical results a user defined geometric precision technique which gives a criterion for determining the time step is employed for our computations it is numerically demonstrated that using our proposed fdtd 2 4 compatible conformal scheme high accuracy and low dispersion errors can be achieved for fast predicting radar cross sections as well as induced current distribution of some complex 3 d structures

a 3 d interface enriched generalized fem for electromagnetic problems with nonconformal discretizations an interface enriched generalized finite element method igfem is introduced for efficient 3 d electromagnetic analysis of heterogeneous materials without using meshes that conform to the material microstructures which greatly lessens the burden of mesh generation the method assigns generalized degrees of freedom dofs at material interfaces to capture the discontinuities of the field and its derivatives the generalized dofs are supported by enriched vector basis functions vbfs which are constructed through a linear combination of the vbfs from the subelements several verification examples are provided to show that the igfem is not sensitive to the quality of the subelements and maintains the same level of solution accuracy and computational complexity as the standard finite element method fem based on conformal meshes the potential of the proposed igfem is demonstrated by simulating some engineering problems with complex periodic internal structures including composite materials with randomly distributed spherical particles and ellipsoidal inclusions and microvascular channels

resolvents and solutions of weakly singular linear volterra integral equations abstract the structure of the resolvent r t s for a weakly singular matrix function b t s is determined where b t s is the kernel of the linear volterra vector integral equation e x t a t 0 t b t s x s d s and a t is a given continuous vector function using contraction mappings in a banach space of continuous vector functions with an exponentially weighted norm we show that when b t s satisfies certain integral conditions r t s has the form r t s b t s r 1 t s where r 1 t s is the unique continuous solution of the integral equation r 1 t s b 1 t s s t b t u r 1 u s d u and b 1 t s is defined by b 1 t s s t b t u b u s d u as examples the formulas of resolvents for a couple of weakly singular kernels of practical interest are derived we also obtain conditions under which a weakly singular integral equation e has a unique continuous solution x t and show that it can be expressed in terms of r t s by x t a t 0 t r t s a s d s finally we show that there are parallel results for an alternative resolvent r t s and examine when it and r t s are equivalent

a contraction mapping proof of the smooth dependence on parameters of solutions to volterra integral equations abstract we consider the linear volterra equation x t a t 0 t k t s x s d s and suppose that the kernel k and forcing function a depend on some parameters r d we prove that under suitable conditions the solutions depend on as smoothly the functions a and k the proof is based on the contraction mapping principle and the variational equation though our conditions are not the most generally possible they nonetheless include many important examples

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

a liapunov functional for a singular integral equation abstract we consider a scalar integral equation x t a t 0 t c t s g s x s d s where a l 2 0 while c t s has a significant singularity but is convex when t s 0 we construct a liapunov functional and show that g t x t a t l 2 0 and that x t a t 0 pointwise as t small perturbations are also added to the kernel in addition we consider both infinite and finite delay problems this paper offers a first step toward treating discontinuous kernels with liapunov functionals

deformation spaces of one dimensional formal modules and their cohomology abstract let m m be the formal scheme which represents the functor of deformations of a one dimensional formal module over f p equipped with a level m structure by work of boyer in equal characteristic and harris and taylor the l adic etale cohomology of the generic fibre m m of m m realizes simultaneously the local langlands and jacquet langlands correspondences the proofs given so far use drinfeld modular varieties or shimura varieties to derive this local result in this paper we show without the use of global moduli spaces that the jacquet langlands correspondence is realized by the euler poincare characteristic of the cohomology under a certain finiteness assumption on the cohomology groups it is shown that the correspondence is realized in only one degree one main ingredient of the proof consists in analyzing the boundary of the deformation spaces and in studying larger spaces which can be considered as compactifications of the spaces m m

a fourth order finite difference method for waveguides with curved perfectly conducting boundaries a novel high order finite difference method is introduced for optical waveguides with smoothly curved perfectly electric conducting pec boundaries the proposed method shares some similarities with our previous matched interface and boundary mib methods developed for treating dielectric interfaces of optical waveguides such as the use of a simple cartesian grid the standard finite difference schemes and fictitious values however the pec boundary conditions have a physical nature quite different from that of the jump conditions at the dielectric interfaces i e all six electric and magnetic field components are prescribed in the jump conditions while only three of them are known at the pec walls consequently the previously developed mib methods are not applicable to deal with the perfectly conducting boundaries to overcome this difficulty a novel ray casting fictitious domain method is constructed to enforce the pec conditions along the normal direction such a boundary implementation couples the transverse magnetic field components so that the resulting ray casting mib method is a full vectorial approach for the modal analysis of optical waveguides the new mib method is validated by considering both homogeneous and inhomogeneous waveguides numerical results confirm the designed fourth order of accuracy

an elliptical cylindrical fdtd algorithm for modeling conformal patch antenna an explicit finite difference time domain fdtd method is described using a uniform elliptical cylindrical spatial grid for time domain maxwell s equations to accurately and efficiently model conformal elliptical cylindrical line fed patch antennas and overcome stair casing errors such errors are encountered when a cartesian spatial grid is used for modeling curved surfaces in addition the method described in this paper obviates coding complexity encountered in modeling of curved surfaces which is manifest using cp fdtd or cfdtd techniques characterizing expressions representing the absorbing boundary condition and courant stability condition are presented and used to provide a highly effective algorithm to simulate conformal microstrip antennas the proposed fdtd algorithm is validated against hfss results showing excellent correlation

a novel fdtd time stepping scheme to calculate rcs of curved conducting objects using adaptively adjusted time steps the chief shortcoming of the conventional conformal finite difference time domain cfdtd method is a global time step reduction to ensure stability due to the small irregular cells truncated by the curved conducting geometry introducing the local time stepping into the cfdtd method is an efficient way and has been numerically proven in our previous work in this paper we further employ the concept of the equivalent material constants into the integral form of faraday s law to analyze the curved configuration with or without the coating hence we can theoretically derive the stability criterion of each irregular cell based on the same procedure for the courant friedrichs lewy cfl stability criterion therefore the local time step size of each small irregular cell can be chosen adaptively an adaptively adjusted time stepping procedure is presented and is theoretically proven to ensure numerical stability the radar cross section rcs results of various curved conducting objects with the coating are computed comparisons of accuracy and efficiency of our method with other established methods are performed

conformal fdtd modeling of imperfect conductors at millimeter wave bands the dey mittra conformal finite difference time domain cfdtd algorithm for perfect electrical conductors is modified for the analysis of finite conductivity conductors at millimeter wave frequencies formulas are derived for cfdtd coefficients using voltage state variables and a constant surface impedance boundary condition sibc the approach permits a fast implementation suitable for cuda type gpu hardware accuracy and stability are investigated with respect to the stability constraints on intersection areas introduced by dey mittra and benkler as well as the distance stability constraints of zagorodnov that permits 100 courant temporal sampling a relaxation of the zagorodnov distance constraints permits increased accuracy with respect to all alternative area constraints analytic solutions are used to judge the performance of the proposed cfdtd modifications for millimeter wave band applications

a conformal fdtd method with accurate waveport excitation and s parameter extraction we demonstrate a conformal finite difference time domain cfdtd technique with accurate waveport excitation and s parameter extraction we discuss under the cfdtd framework object modeling with effective subcell material impedance calibration for the conformal modeled coaxial feed waveport mode calculation with a newly developed conformal 2 d finite difference frequency domain solver waveport excitation with a modified total field scattered field method and a modified s parameter extraction scheme that is compatible with the cfdtd method lastly we present two specific validation cases intended as relevant precursors to the inverse scattering application modeling of the reflection coefficient of a tapered patch antenna and modeling of the transmission coefficient in a probe fed rectangular waveguide

induced representations of locally profinite groups let g be a separable locally prolinite i e locally compact and totally disconnected group with centre z and l an open subgroup of g containing z and such that l z is compact this note contains a couple of results on the structure of smooth representations of g induced from irreducible therefore finite dimensional representations of l the first demonstrates the equivalence of various finiteness conditions on the induced representation while the second gives a finiteness property in the general case an immediate corollary of the second is the fact well known for p adic reductive groups that a given irreducible representation of l can occur in at most finitely many irreducible supercuspidal representations of g in the case for example where g is a general linear group over a nonarchimedean local field and l is a maximal compact mod centre subgroup it has long been appreciated that an irreducible representation of g induced from l is automatically supercuspidal indeed this observation is the starting point of the current theory of classification of supercuspidals see for example 6 our results answer the frequently encountered question as to what happens when the induced representation is not irreducible as the extreme generality of our hypotheses indicates the results here are straightforward even formal in nature it is this essential simplicity as much as the results themselves which prompts me to write this rather easy little note

fast solution methods in electromagnetics various methods for efficiently solving electromagnetic problems are presented electromagnetic scattering problems can be roughly classified into surface and volume problems while fast methods are either differential or integral equation based the resultant systems of linear equations are either solved directly or iteratively a review of various differential equation solvers their complexities and memory requirements is given the issues of grid dispersion and hybridization with integral equation solvers are discussed several fast integral equation solvers for surface and volume scatterers are presented these solvers have reduced computational complexities and memory requirements

a new method to avoid reduction of time step in the cp fdtd method a new cp wcs fdtd method is developed to avoid the time step reduction in the conformal path fdtd method the stability condition in this method is not related with the shape and size of the distorted cell and the time step size in this method is only determined by the space discretization perpendicular to the curved metal surface the cp wcs fdtd method has the same accuracy as that for the cp fdtd method and due to large time step size can be used the cp wcs fdtd has higher computation efficiency which is demonstrated by numerical examples

resolvents for weakly singular kernels and fractional differential equations the solution r t s of the resolvent equation 1 r t s b t s stb t u r u s du where b t s denotes a given weakly singular matrix is obtained by means of fixed point mappings the result is a series that begins with some singular terms after which the remainder of the terms defines a continuous function in particular the resolvent is calculated for the kernel b t s t s q 1 of the scalar abel integral equation of the second kind 2 x t a t 0t1 t s 1 qx s ds where 0 q 1 it is then used to derive closed form formulas for the resolvents corresponding to q 1 2 and 1 3 furthermore a closed form formula for the resolvent for b t s s t2 s2 q 1 is derived thereby demonstrating that the results of this paper apply not only to kernels of convolution type but also to those of non convolution type as well finally the resolvent for the kernel of 2 is used to find a general solution of a linear fractional differential equation of caputo type