fast and accurate evaluation of double surface integrals in time domain integral equation formulations a novel integration approach is developed for efficiently evaluating double surface integrals in time domain integral equation formulations the approach mainly consists of an angular integration scheme for inner 2 d integrals and a modified outer integration scheme the approach proposed can handle the singularity and near hypersingularity of the 4 d integrals and is sufficiently general for arbitrary types of basis functions over planar domains as several numerical results will demonstrate the proposed approach has high accuracy and rapid convergence rate for a variety of integral kernels

application of analytical retarded time potential expressions to the solution of time domain integral equations recently exact closed form expressions of the electric and magnetic fields and potentials due to impulsively excited rao wilton glisson basis functions have been presented in this work the application of these expressions in the solution of the combined field integral equation cfie is presented solutions via analytical expressions of the electric and magnetic fields are verified and compared with the conventional marching on in time mot algorithm solutions that employ numerical basis integrations it is shown that the accuracy and stability of the solutions obtained with the proposed analytical approach are better when compared to those obtained with the conventional numerical method in addition a discussion section about the effect of the proposed approach in solving the electric field integral equation efie is added in this section it is demonstrated that the dependency of the solution via analytical expressions of the fields are less sensitive to the time step size in comparison to the conventional solution and that the increase in accuracy is a necessary but not sufficient condition for stability

practical output regulation for bounded linear infinite dimensional state space systems we develop the mathematical foundations of practical state space output regulation for bounded infinite dimensional linear systems by practical output regulation we mean asymptotic tracking of references and rejection of disturbances with a given accuracy our main results are general upper bounds for the norms perturbations to the parameters of the exosystem the plant and a controller which achieves exact output regulation these bounds depend explicitly on the desired tracking accuracy e 0 in this paper all perturbations are assumed to be bounded additive and linear our results apply for both feedforward and error feedback controllers and for arbitrary bounded uniformly continuous reference disturbance signals

a novel scheme for the solution of the time domain integral equations of electromagnetics a new method to numerically solve time domain integral equations pertinent to electromagnetic surface scattering phenomena is presented the method uses approximate prolate spheroidal wave functions and standard rao wilton glisson basis functions to effect the temporal and spatial discretization of the integral equations respectively because the temporal basis functions are noncausal an extrapolation scheme is used to construct a system of equations that can be solved by marching on in time numerical results show that the proposed method is stable and that its solutions converge exponentially fast with the time bandwidth product of the approximate prolate spheroidal wave functions to results from a frequency domain method of moments solver that uses spatial basis functions and integration rules identical to those in the time domain solver

fast and accurate computation of hypersingular integrals in galerkin surface integral equation formulations via the direct evaluation method hypersingular 4 d integrals arising in the galerkin discretization of surface integral equation formulations are computed by means of the direct evaluation method the proposed scheme extends the basic idea of the singularity cancellation methods usually employed for the regularization of the singular integral kernel by utilizing a series of coordinate transformations combined with a reordering of the integrations the overall algebraic manipulation results in smooth 2 d integrals that can be easily evaluated via standard quadrature rules finally the reduction of the dimensionality of the original integrals together with the smooth behavior of the associated integrands lead up to unmatched accuracy and efficiency

a hierarchical fft algorithm hil fft for the fast analysis of transient electromagnetic scattering phenomena a fast algorithm for accelerating the time marching solution of time domain integral equations pertinent to the analysis of free space electromagnetic scattering from perfectly conducting platelike and uniformly meshed structures is presented the matrix vector multiplications required by the time marching scheme are accelerated by use of the fast fourier transform fft this acceleration is achieved in a multilevel fashion by hierarchically grouping sparse interactions to extract denser pieces that are efficiently evaluated by the fft the total computational cost and storage requirements of this algorithm scale as o n sub t n sub s log sup 2 n sub s and o n sup 1 5 respectively as opposed to o n sub t n sub s sup 2 and o n sub s sup 2 for classical time marching methods n sub s and n sub t denote the total number of spatial unknowns and time steps respectively simulation results demonstrate the accuracy and efficiency of the algorithm

polar integration for exact space time quadrature in time domain integral equations a space time polar quadrature technique for numerical integration of green s function interactions in time domain integral equations is presented the method transforms 2 d surface space time integrals associated with vector and scalar potentials to a 1 d integral that is performed using gauss legendre integration the advantage of the presented technique compared to standard 2 d gaussian quadrature is that time delays between each section of the source basis function and the observation point are accounted for exactly in an analytic manner this ensures highly accurate temporal behavior of the green s function interactions thereby contributing to the stability of the overall time domain integral equations

a time domain volume integral equation and its marching on in degree solution for analysis of dispersive dielectric objects a marching on in degree mod based scheme for analyzing transient electromagnetic scattering from three dimensional dispersive dielectric objects is proposed a time domain volume integral equation tdvie for the electric flux density throughout the object is first formulated and then solved using the mod scheme with the use of weighted laguerre polynomials as entire domain temporal basis functions the convolution of the electric flux density and the medium susceptibility and its derivatives can be handled analytically by employing the galerkin temporal testing procedure the time variable is eliminated in the resultant recursive matrix equation so that the proposed algorithm overcomes the late time instability problem that may occur in the conventional marching on in time mot approach some complex dispersive media such as the debye lorentz and drude media are simulated to illustrate the validity of the tdvie mod algorithm

an accurate scheme for the solution of the time domain integral equations of electromagnetics using higher order vector bases and bandlimited extrapolation despite the numerous advances made in increasing the computational efficiency of time domain integral equation tdie based solvers the stability and accuracy of tdie solvers remain problematic this paper introduces a new numerical method for the accurate solution of tdies for scattering from arbitrary perfectly conducting surfaces the work described in this paper uses the higher order divergence conforming basis functions of graglia et al for spatial discretization and bandlimited interpolation functions for the temporal discretization of the relevant integral equations since the basis functions used for the temporal representation are noncausal an extrapolation scheme is employed to recover the ability to solve the problem by marching on in time numerical results demonstrate that the proposed method is stable and that it exhibits superlinear convergence with regard to the spatial discretization and exponential convergence with respect to the temporal discretization

directed structure at infinity for infinite dimensional systems in this article the structure at infinity of infinite dimensional linear time invariant systems with finite dimensional input and output spaces is discussed it is shown that a diagonal form describing behaviour near infinity can be found this diagonal form is a generalisation of the smith mcmillan form at infinity for rational matrices it is then used to simplify certain solvability conditions of a regulation problem examples on time delay and distributed parameter systems are given

what periodic signals can an exponentially stabilizable linear feedforward control system asymptotically track we study asymptotic tracking and rejection of continuous periodic signals in the context of exponentially stabilizable linear infinite dimensional systems our reference signals are in sobolev type spaces h omega n f n and they as well as the disturbance signals are generated by an infinite dimensional exogenous system we show that there exists a feedforward controller which achieves output regulation if and only if the so called regulator equations are satisfied and a decomposability condition holds for siso systems this result allows us to completely answer the question posed in the title we show that if the stabilized plant does not have transmission zeros at the frequencies i omega n of the reference signals then all reference signals in h omega n f n can be asymptotically tracked in the presence of disturbances if and only if bigl h k i omega n 1 1 h d n f n 1 bigr n in i in ell 2 here h k i omega n n in i is the transfer function of the stabilized plant evaluated at i omega n and h d n n in i is a sequence of disturbance coefficients for the stabilized plant moreover the sequence f n n in i consists of weights for the fourier coefficients of the reference signals we give four examples to illustrate the theory

a finite difference delay modeling approach to the discretization of the time domain integral equations of electromagnetics a new method for solving the time domain integral equations of electromagnetic scattering from conductors is introduced this method called finite difference delay modeling appears to be completely stable and accurate when applied to arbitrary structures the temporal discretization used is based on finite differences specifically based on a mapping from the laplace domain to the z transform domain first and second order unconditionally stable methods are derived spatial convergence is achieved using the higher order divergence conforming vector bases of graglia et al low frequency instability problems are avoided with the loop tree decomposition approach numerical results will illustrate the accuracy and stability of the technique

two dimensional transverse magnetic time domain scattering using the nystro spl uml m method and bandlimited extrapolation a method is presented for the solution of the integral equations that describe the electromagnetic scattering from an infinitely long conducting cylinder in the time domain the method discretizes the integral equations spatially using a high order locally corrected nystro spl uml m method and temporally using a filtered kernel the filtering of the kernel both controls aliasing and reduces the order of its singularity on the other hand filtering also gives rise to a noncausal kernel so the time marching is accomplished with a bandlimited extrapolation scheme numerical results demonstrate the stability and accuracy of the proposed method

ray shooting and parametric search efficient algorithms for the ray shooting problem are presented given a collection gamma of objects in mathbb r d build a data structure so that for a query ray the first object of gamma hit by the ray can be quickly determined using the parametric search technique this problem is reduced to the segment emptiness problem for various ray shooting problems space query time trade offs of the following type are achieved for some integer b and a parameter m n leqslant m leqslant n b the queries are answered in time o n m 1 b log o 1 n with o m 1 varepsilon space and preprocessing time varepsilon 0 is arbitrarily small but fixed constant b lfloor d 2 rfloor is obtained for ray shooting in a convex d polytope defined as an intersection of n half spaces b d for an arrangement of n hyperplanes in mathbb r d and b 3 for an arrangement of n half planes in mathbb r 3 this approach also yields fast procedures for fin

stable electric field tdie solvers via quasi exact evaluation of mot matrix elements prior theoretical studies and experience confirm that the stability of marching on in time mot solvers pertinent to the analysis of scattering from free standing three dimensional perfect electrically conducting surfaces hinges on the accurate evaluation of mot matrix elements resulting from a galerkin discretization of the underlying time domain integral equation tdie unfortunately the accurate evaluation of the four dimensional spatial integrals involved in the expressions for these matrix elements is prohibitively expensive when performed by computational means here a method that permits the quasi exact evaluation of mot matrix elements is presented specifically the proposed method permits the analytical evaluation of three out of the four spatial integrations leaving only one integral to be evaluated numerically since the latter has finite range and a piecewise smooth integrand it can be evaluated to very high accuracy using standard quadrature rules as a result the proposed method permits the fast evaluation of mot matrix elements with arbitrary user specified accuracy extensive numerical experiments show that an mot solver for the electric field tdie that uses the proposed quasi exact method is stable for a very wide range of time step sizes and yields solutions that decay exponentially after the excitation vanishes

fast analysis of transient electromagnetic scattering phenomena using the multilevel plane wave time domain algorithm the computational complexity of classical marching on in time mot methods for solving time domain integral equations tdies pertinent to the analysis of transient scattering phenomena involving perfectly conducting targets grows as o n sub t n sub s sup 2 n sub t and n sub s denote the number of temporal and spatial degrees of freedom dof of the electric current on the target this scaling law impedes the application of these schemes to the analysis of large scale scattering phenomena the recently developed plane wave time domain pwtd algorithm permits the rapid evaluation of transient wave fields generated by temporally bandlimited sources and hence the acceleration of marching on in time based tdie solvers previously we described a two level pwtd enhanced tdie solver for analyzing electromagnetic scattering from perfectly conducting targets the computational complexity of this algorithm scales as o n sub t n sub s sup 1 5 logn sub s here a multilevel pwtd scheme for rapidly evaluating electric fields due to temporally bandlimited electric current sources is described in addition a multilevel pwtd enhanced tdie solver for analyzing electromagnetic scattering from perfectly conducting scatterers using o n sub t n sub s log sup 2 n sub s cpu resources is outlined last the accuracy and cpu memory efficiency of this solver are demonstrated by analyzing transient scattering from electrically large bodies

a fast higher order time domain finite element boundary integral method for 3 d electromagnetic scattering analysis a novel hybrid time domain finite element boundary integral method for analyzing three dimensional 3 d electromagnetic scattering phenomena is presented the method couples finite element and boundary integral field representations in a way that results in a sparse system matrix and solutions that are devoid of spurious modes to accurately represent the unknown fields the scheme employs higher order vector basis functions defined on curvilinear tetrahedral elements to handle problems involving electrically large objects the multilevel plane wave time domain algorithm is used to accelerate the evaluation of the boundary integrals numerical results demonstrate the accuracy and versatility of the proposed scheme

time domain adaptive integral method for surface integral equations an efficient marching on in time mot scheme is presented for solving electric magnetic and combined field integral equations pertinent to the analysis of transient electromagnetic scattering from perfectly conducting surfaces residing in an unbounded homogenous medium the proposed scheme is the extension of the frequency domain adaptive integral pre corrected fast fourier transform fft method to the time domain fields on the scatterer that are produced by space time sources residing on its surface are computed 1 by locally projecting for each time step all sources onto a uniform auxiliary grid that encases the scatterer 2 by computing everywhere on this grid the transient fields produced by the resulting auxiliary sources via global multilevel blocked space time ffts 3 by locally interpolating these fields back onto the scatterer surface as this procedure is inaccurate when source and observer points reside close to each other and 4 near fields are computed classically albeit pre corrected for errors introduced through the use of global ffts the proposed scheme has a computational complexity and memory requirement of o n sub t n sub s log sup 2 n sub s and o n sub s sup 3 2 when applied to quasiplanar structures and of o n sub t n sub s sup 3 2 log sup 2 n sub s and o n sub s sup 2 when used to analyze scattering from general surfaces here n sub s and n sub t denote the number of spatial and temporal degrees of freedom of the surface current density these computational cost and memory requirements are contrasted to those of classical mot solvers which scale as o n sub t n sub s sup 2 and o n sub s sup 2 respectively a parallel implementation of the scheme on a distributed memory computer cluster that uses the message passing interface is described simulation results demonstrate the accuracy efficiency and the parallel performance of the implementation

a hybrid method combining the multitemporal resolution time domain method of moments with the time domain geometrical theory of diffraction for thin wire antenna problems in this paper a hybrid method combining a multitemporal resolution mtr enhanced time domain method of moments td mom with the td geometrical theory of diffraction gtd is presented which allows to efficiently calculate the transient fields radiated by antennas in presence of large objects the mtr scheme tailors the time step size and thus implicitly the duration of the temporal basis function on the basis of the distance between source and test element additionally the voltage induced by source elements far away from the test element is interpolated in time the hybrid method is applied to calculate the radiation properties of thin wire antennas in presence of perfectly conducting flat scatterers to demonstrate its basic features and advantages

parallel pwtd accelerated explicit solution of the time domain electric field volume integral equation a parallel plane wave time domain pwtd accelerated explicit marching on in time mot scheme for solving the time domain electric field volume integral equation td efvie is presented the proposed scheme leverages pulse functions and lagrange polynomials to spatially and temporally discretize the electric flux density induced throughout the scatterers and a finite difference scheme to compute the electric fields from the hertz electric vector potentials radiated by the flux density the flux density is explicitly updated during time marching by a predictor corrector pc scheme and the vector potentials are efficiently computed by a scalar pwtd scheme the memory requirement and computational complexity of the resulting explicit pwtd pc efvie solver scale as o n s log n s and o n s n t respectively here n s is the number of spatial basis functions and n t is the number of time steps a scalable parallelization of the proposed mot scheme on distributed memory cpu clusters is described the efficiency accuracy and applicability of the resulting parallelized pwtd pc efvie solver are demonstrated via its application to the analysis of transient electromagnetic wave interactions on canonical and real life scatterers represented with up to 25 million spatial discretization elements

a fast time domain integral equation based scheme for analyzing scattering from dispersive objects a fast integral equation based scheme for analyzing transient scattering from inhomogeneous dispersive bodies is presented a time domain integral equation in terms of the electric flux inside the body is constructed by invoking the volume equivalence principle i e by equating the sum of the incident electric field and that radiated by equivalent volume polarization currents to the total electric field the proposed algorithm for solving this time domain integral equation incorporates a recursive convolution scheme that updates the polarization current from knowledge of the electric flux to reduce the computational cost and memory requirement of the resulting marching on in time scheme it is augmented with the plane wave time domain algorithm numerical results that validate the proposed approach and demonstrate its accuracy are presented

analysis of transient electromagnetic scattering phenomena using a two level plane wave time domain algorithm a fast algorithm is presented for solving electric magnetic and combined field time domain integral equations pertinent to the analysis of surface scattering phenomena the proposed two level plane wave time domain pwtd algorithm permits a numerically rigorous reconstruction of transient near fields from their far field expansion and augments classical marching on in time mot based solvers the computational cost of analyzing surface scattering phenomena using pwtd enhanced mot schemes scales as o n sub i n sub s sup 2 3 log n sub s as opposed to spl oscr n sub t n sub s sup 2 for classical mot methods where n sub t and n sub s are the numbers of temporal and spatial basis functions discretizing the scatterer current numerical results that demonstrate the efficacy of the proposed solver in analyzing transient scattering from electrically large structures and that confirm the above complexity estimate are presented

evaluation of green s function integrals in conducting media this work presents an accurate integration method for computing green s function operators related to lossy conducting media the presented approach is ultrawideband i e the integration schemes cover the entire range of frequency behavior from high frequencies where skin current is prevalent to low frequencies where volume current flow dominates the scheme is a step toward permitting exact ultrawide band frequency domain surface only based integral equation simulation of arbitrarily shaped three dimensional conductors and toward obviating the need for volume based explicit frequency dependent skin effect modeling this work deals specifically with the computation of green s functions and not with the unrelated but important low frequency conditioning issue associated with the standard electric field integral equation

solution of time domain electric field integral equation using the laguerre polynomials in this paper we propose a numerical method to obtain a solution for the time domain electric field integral equation td efie for arbitrary shaped conducting structures this method does not utilize the customary marching on in time mot solution method often used to solve a hyperbolic partial differential equation instead we solve the wave equation by expressing the transient behaviors in terms of laguerre polynomials by using these causal orthonormal basis functions for the temporal variation the time derivatives can be handled analytically in order to solve the wave equation we introduce two separate testing procedures a spatial and temporal testing by introducing first the galerkin temporal testing procedure the mot procedure is replaced by a recursive relation between the different orders of the weighted laguerre polynomials the other novelty of this approach is that through the use of the entire domain laguerre polynomials for the expansion of the temporal variation of the current the spatial and the temporal variables can be separated and the temporal variables can be integrated out for convenience we use the hertz vector as the unknown variable instead of the electric current density to verify our method we compare the results of a td efie and inverse fourier transform of a frequency domain efie

a hybrid time domain technique that combines the finite element finite difference and method of moment techniques to solve complex electromagnetic problems this paper describes a hybrid technique directly operating in time domain that combines the finite element time domain fetd the finite difference time domain fdtd and the integral equation based method of moments in the time domain momtd techniques to analyze complex electromagnetic problems involving thin wire antennas radiating in the presence of inhomogeneous dielectric bodies whose shape can be arbitrary the method brings together the ability of the fdtd scheme to deal with arbitrary material properties the versatility of the fetd to accurately model curved geometries and that of the mom to analyze thin wire structures working in the time domain provides wide band information from a single execution of the marching on in time procedure and simplifies the interfacing of the fe and mom methods with the fdtd an approach specifically designed for time domain analysis numerical results that validate the hybrid method and show its capabilities are presented in the paper

approximate polytope membership queries in the polytope membership problem a convex polytope k in mathbb r d is given and the objective is to preprocess k into a data structure so that given any query point q in mathbb r d it is possible to determine efficiently whether q in k we consider this problem in an approximate setting given an approximation parameter varepsilon the query can be answered either way if the distance from q to k s boundary is at most varepsilon times k s diameter we assume that the dimension d is fixed and k is presented as the intersection of n halfspaces previous solutions to approximate polytope membership were based on straightforward applications of classic polytope approximation techniques by dudley approx theory 10 1974 pp 227 236 and bentley faust and preparata commun acm 25 1982 pp 64 68 the former is optimal in the worst case with respect to space and the latter is optimal with respect to query time we present four main results first we show how

exact evaluation of retarded time potential integrals for the rwg bases a new analytical approach for obtaining the time samples of the retarded time scalar and vector potentials due to an impulsively excited rao wilton glisson rwg basis function is presented the approach is formulated directly in the time domain without any assumptions regarding the temporal behavior of the currents represented by the rwg bases to the best knowledge of the authors analytical evaluation of the potential integrals due to the rwg bases have not been formulated prior to the present work either in the time domain or the frequency domain it is shown that the aforementioned potentials are related to the arc segments formed by the intersection of the triangular supports of the rwg basis and the sphere that is centered at the observation point and that has a radius r ct where c is the speed of light in particular the scalar potential is directly proportional to the total arc length and the vector potential is a function of the bisectors of these arc segments a simple algorithm to evaluate these quantities is also presented the validity of the obtained time domain formulae is demonstrated through comparison of results to those obtained in the frequency domain by using numerical quadrature and transformed into time domain

numerical solution of time domain volume integral equations for transient electromagnetic scattering by dielectric objects electromagnetic em interaction with penetrable objects can be described by volume integral equations vies in integral equation approach and time domain vies tdvies are required for formulating transient em problems with such objects the tdvies are usually solved by combining the method of moments mom with well designed basis function in space domain and a march on in time mot scheme in time domain the space domain mom requires conforming meshes in geometric discretization and twofold numerical integrations in matrix generation while the mot in time domain suffers from a late time instability problem in this communication we propose an alternative approach that uses the nystrom method to discretize the vies in space domain while employing the mom with laguerre basis and testing functions to discretize the equations in time domain the proposed approach can simplify the numerical implementation and produce a march on in degree procedure similar to that in frequency domain approaches numerical examples are presented to illustrate the approach and good results have been observed

function generators the operator equation πs aπ bq and inherited dynamics in inhomogenous cauchy problems abstract this article concerns the interrelation between the existence of a bounded solution to the operator equation s a bq in d s and the asymptotic behaviour of the mild solutions z t of the abstract cauchy problem z t az t bu t t 0 in a banach space z here b and q are bounded whereas a and s generate c 0 semigroups t a t and t s t on z and w w is a banach space respectively banach space valued inputs u t u are generated by linear dynamical systems we define asymptotically inherited dynamics of z t and show that for strongly stable semigroups t a t z t asymptotically inherits the dynamics of the inputs if there exists l w z such that s a bq in d s if t a t and t s t are bounded then z t is bounded and uniformly continuous provided that s a bq in d s for the converse we show that if z t asymptotically inherits the dynamics of the inputs and if t s t is a suitable c 0 group then t a t is strongly stable and there exists l w z such that s a bq in a subspace of d s we also discuss why inputs u t frequently completely determine the asymptotic properties of z t if t a t is exponentially stable as an application we consider almost periodic inputs u t in sobolev spaces h u f n n

spatially large domain and temporally entire domain electric field integral equation method of moments for 3 d scattering analysis in time domain a novel spatially large domain and temporally entire domain method of moments mom is proposed for surface integral equation sie modeling of 3 d conducting scatterers in the time domain td the method uses higher order curved lagrange interpolation generalized quadrilateral geometrical elements higher order spatial current expansions based on hierarchical divergence conforming polynomial vector basis functions and temporal current modeling by means of orthogonal weighted associated laguerre basis functions it implements full temporal and spatial galerkin testing and marching on in degree mod scheme for an iterative solution of the final system of spatially and temporally discretized mom td equations numerical examples demonstrate excellent accuracy efficiency convergence and versatility of the new mom mod method the results also demonstrate very effective large domain mom td sie models of scatterers using flat and curved patches of electrical sizes of up to about 1 7 wavelengths at the maximum frequency in the frequency spectrum of the pulse excitation higher order current expansions of spatial orders from 2 to 8 in conjunction with entire domain laguerre temporal bases and minimal numbers of unknowns

internal model theory for distributed parameter systems in this paper we consider robust output regulation of distributed parameter systems and the internal model principle the main purpose is to generalize the internal model principle by francis and wonham for infinite dimensional systems and clarify the relationships between different generalizations of the internal model we also construct a signal generator capable of generating infinite dimensional polynomially increasing signals

fast detection of polyhedral intersection abstract methods are given for unifying and extending previous work on detecting intersections of suitably preprocessed polyhedra new upper bounds of o log n and o log2 n are given on plane polyhedron and polyhedron polyhedron intersection problems

a stabilized marching on in degree scheme for the transient solution of the electric field integral equation time domain electric integral equation methods td efie suffer from the numerical stability problem numerous schemes have been proposed over the years for the purpose of taking care of this instability among them the marching on in degree mod method is one of the newly proposed algorithms for calculating the various transient responses the mod solver employs a set of associated laguerre functions and incorporates exact temporal galerkin testing although the mod scheme is assumed to be more stable when compared with marching on in time mot there are few numerical or theoretical investigations on the stability of the various numerical recursive operations for the mod methodology it has been shown that the time domain magnetic field integral equation td mfie using the mod method can be stabilized by using a filon type quadrature formula to accurately integrate the highly oscillatory laguerre functions which has caused instability for the mod solvers using a higher degree of approximation on the other hand the analytical expression of temporal derivatives used in the mod scheme is strongly affected by an unbounded initial value of the transient current in this paper a novel filon type radial integration method and a sequential constraint term for td efie mod are proposed which make the stabilized mod solver accurate and stable for the arbitrary degree of the laguerre polynomials some numerical results are presented to illustrate the validity of the stabilized mod solution of td efie for transient scattering problems

explicit time marching schemes for solving the magnetic field volume integral equation a method for constructing explicit marching on in time mot schemes to solve the time domain magnetic field volume integral equation td mfvie on inhomogeneous dielectric scatterers is proposed the td mfvie is cast in the form of an ordinary differential equation ode and the unknown magnetic field is expanded using curl conforming spatial basis functions inserting this expansion into the td mfvie and spatially testing the resulting equation yield an ode system with a gram matrix this system is integrated in time for the unknown time dependent expansion coefficients using a linear multistep method the gram matrix is sparse and well conditioned for galerkin testing and consists of only four diagonal blocks for point testing the resulting explicit mot schemes which call for the solution of this matrix system at every time step are more efficient than their implicit counterparts which call for inversion of a fuller matrix system at lower frequencies numerical results compare the efficiency accuracy and stability of the explicit mot schemes and their implicit counterparts for low frequency excitations the results show that the explicit mot scheme with point testing is significantly faster than the other three solvers without sacrificing from accuracy

approximating extent measures of points we present a general technique for approximating various descriptors of the extent of a set p of n points in rd when the dimension d is an arbitrary fixed constant for a given extent measure and a parameter e 0 it computes in time o n 1 eo 1 a subset q p of size 1 eo 1 with the property that 1 e p q p the specific applications of our technique include e approximation algorithms for i computing diameter width and smallest bounding box ball and cylinder of p ii maintaining all the previous measures for a set of moving points and iii fitting spheres and cylinders through a point set p our algorithms are considerably simpler and faster in many cases than previously known algorithms

quadrature over a pyramid or cube of integrands with a singularity at a vertex a simple transformation is introduced which facilitates the evaluation of integrals over certain square based pyramids or cubes in cases where the integrand has a singularity at a vertex

implicit runge kutta methods for the discretization of time domain integral equations implicit runge kutta based schemes are proposed for solving the time domain integral equations of electromagnetic theory the proposed technique maps a laplace domain equation to a domain equation using the butcher tableau of the implicit runge kutta scheme a discrete time domain system is recovered by computing the inverse transform numerically the resulting technique is capable of third or fifth order accuracy in time and is stable independent of time step numerical results illustrate the accuracy and stability of the technique

solving time domain electric field integral equation without the time variable an improved testing procedure using the marching on in order method to solve the time domain electric field integral equation td efie for conducting objects using the laguerre polynomials is presented exact temporal testing is performed before the spatial testing therefore the retarded terms composed of the spatial and the temporal variables can be analytically separated the uniqueness of this testing procedure is that the time variable can be analytically integrated out and the accuracy can be improved this paper is then an improvement over the earlier marching on in order method in addition this methodology is quite different from the conventional marching on in time algorithm as the present method leads to a set of final equations which need to be numerically solved containing only the spatial variables therefore there is no requirement to have a courant stability condition in this procedure how the singular integrals are treated is also discussed several examples are simulated both for radiation and scattering problem the results are compared with the inverse discrete fourier transform of the frequency domain data and they agree well

efficient evaluation of double surface integrals in time domain integral equation formulations a new integration approach is presented for accurately calculating time domain efie mfie and cfie matrix elements over triangular domains it mainly consists of a radial integration scheme for handling weakly singular and near hypersingular inner integrals and some new smoothing techniques for treating outer two dimensional 2 d integrals the proposed approach has sufficient generality and efficiency for solving time domain integral equations tdie with arbitrary types of temporal basis functions and temporal discretization schemes such as marching on in time mot marching on in degree mod and finite difference delay modeling convolution quadrature fddm cq etc the numerical results for calculating some typical integrals are given to demonstrate its capability with high accuracy and rapid convergence rate achieved

a space time discretization criterion for a stable time marching solution of the electric field integral equation numerical techniques based on a time domain recursive solution of the electric field integral equation efie may exhibit instability phenomena induced by the joint space time discretization the above problem is addressed with specific reference to the evaluation of electromagnetic scattering from perfectly conducting bodies of arbitrary shape we analyze a particular formulation of the method of moments which relies on a triangular patch geometrical model of the exterior surface of the scattering body and operates according to a marching on in time scheme whereby the surface current distribution at a given time step is recursively evaluated as a function of the current distribution at previous steps a heuristic stability condition is devised which allows us to define a proper time step as well as a geometrical discretization criterion ensuring convergence of the numerical procedure and therefore eliminating insurgence of late time oscillations the stability condition is discussed and validated by means of a few working examples

design of temporal basis functions for time domain integral equation methods with predefined accuracy and smoothness a key parameter in the design of integral equation methods for transient electromagnetic scattering is the definition of temporal basis functions the choice of temporal basis functions has a profound impact on the efficiency and accuracy of the numerical scheme this paper presents a framework for the design of temporal basis functions with predefined accuracy and varying smoothness properties the well known shifted lagrange basis functions naturally fit in this framework new spline basis functions will be derived that have the same interpolation accuracy as shifted lagrange basis functions and with the added advantage of being smooth numerical experiments show the positive influence of smoothness on the quadrature error in the numerical integration procedure the global accuracy in time of the numerical scheme based on shifted lagrange and spline basis functions has been experimentally analyzed for a given interpolation error the experiments confirm the expected accuracy for the shifted lagrange basis functions but remarkably show a higher order of accuracy for the spline basis functions

space time tradeoffs for approximate nearest neighbor searching nearest neighbor searching is the problem of preprocessing a set of n point points in d dimensional space so that given any query point q it is possible to report the closest point to q rapidly in approximate nearest neighbor searching a parameter e 0 is given and a multiplicative error of 1 e is allowed we assume that the dimension d is a constant and treat n and e as asymptotic quantities numerous solutions have been proposed ranging from low space solutions having space o n and query time o log n 1 ed 1 to high space solutions having space roughly o n log n ed and query time o log n e we show that there is a single approach to this fundamental problem which both improves upon existing results and spans the spectrum of space time tradeoffs given a tradeoff parameter where 2 1 e we show that there exists a data structure of space o n d 1 log 1 e that can answer queries in time o log n 1 e d 1 2 when e 2 this yields a data structure of space o n log 1 e that can answer queries in time o log n 1 e d 1 2 when e 1 e it provides a data structure of space o n ed 1 log 1 e that can answer queries in time o log n e our results are based on a data structure called a t e avd which is a hierarchical quadtree based subdivision of space into cells each cell stores up to t representative points of the set such that for any query point q in the cell at least one of these points is an approximate nearest neighbor of q we provide new algorithms for constructing avds and tools for analyzing their total space requirements we also establish lower bounds on the space complexity of avds and show that up to a factor of o log 1 e our space bounds are asymptotically tight in the two extremes e 2 and e 1 e

stabilization of time domain acoustic boundary element method for the interior problem with impedance boundary conditions the time domain boundary element method bem is associated with numerical instability that typically stems from the time marching scheme in this work a formulation of time domain bem is derived to deal with all types of boundary conditions adopting a multi input multi output infinite impulse response structure the fitted frequency domain impedance data are converted into a time domain expression as a form of an infinite impulse response filter which can also invoke a modeling error in the calculation the response at each time step is projected onto the wave vector space of natural radiation modes which can be obtained from the eigensolutions of the single iterative matrix to stabilize the computation unstable oscillatory modes are nullified and the same decay rate is used for two nonoscillatory modes as a test example a transient sound field within a partially lined parallelepiped box is used within which a point source is excited by an octave band impulse in comparison with the results

analysis of transient scattering from composite arbitrarily shaped complex structures a time domain surface integral equation approach based on the electric field formulation is utilized to calculate the transient scattering from both conducting and dielectric bodies consisting of arbitrarily shaped complex structures the solution method is based on the method of moments mom and involves the modeling of an arbitrarily shaped structure in conjunction with the triangular patch basis functions an implicit method is described to solve the coupled integral equations derived utilizing the equivalence principle directly in the time domain the usual late time instabilities associated with the time domain integral equations are avoided by using an implicit scheme detailed mathematical steps are included along with representative numerical results

time domain integral equation analysis of scattering from composite bodies via exact evaluation of radiation fields a novel marching on in time and poggio miller chang harrington wu tsai pmchwt based time domain integral equation solver for analyzing transient scattering from composite multiregion structures comprising homogeneous penetrable volumes and perfectly conducting surfaces is presented to render the marching on in time procedure stable observer and source integrals are approximated via multipoint collocation and evaluated in closed form the proposed scheme avoids the costly evaluation of five dimensional integrals required in full space time galerkin schemes and proves to be stable for all targets investigated including coated perfect electrically conducting surfaces and multiregion penetrable volumes

on the stability of time marching schemes for the general surface electric field integral equation we demonstrate that time marching algorithms which use the electric field integral equation to compute the current induced on a perfect conductor by a transient electric field may have unstable modes that are due to the particular basis functions used to represent the current on the conductor these modes are not removed by averaging the solution in time but they can be eliminated by averaging in space appropriately

numerical evaluation of singular and near singular potential integrals a simple and efficient numerical procedure using a singularity cancellation scheme is presented for evaluating singular and near singular potential integrals with 1 r singularities the procedure not only has several advantages over singularity subtraction methods but also improves on some aspects of other singularity cancellation methods such as polar and duffy transformations a theoretical analysis is presented for triangles quadrilaterals tetrahedrons bricks and prisms and numerical results are presented for triangles and prisms

reduction of singular surface integrals to nonsingular line integrals in integral equations for planar geometries a novel procedure is presented for the evaluation of matrix elements of the tensor green function with rao wilton glisson basis functions appearing in surface integral equations in electromagnetics the procedure at this point applicable to planar geometries or geometries composed of parallel planar sheets reduces 4 d surface integrals with singular integrands to line integrals over triangle edges with regular integrands the main advantage of the derived expressions is that they offer simplicity and easily controllable accuracy achieved at a computational cost significantly lower than for previously considered techniques in particular the conventional singularity subtraction method

calculation of mom interaction integrals in highly conductive media the construction of the impedance matrix in the method of moments requires the calculation of interaction integrals between the expansion functions through the green s function and its derivatives the singular behavior of the green s function poses considerable problems for an accurate numerical evaluation of these integrals requiring techniques such as singularity extraction or cancellation in this contribution we will show why these methods fail when the medium is highly conductive a novel technique is proposed to handle these highly challenging integrals the complexity of the new method is independent of the conductivity

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

towards a stable two dimensional time domain source model solution by use of a combined source formulation the application of the source model technique to the solution of two dimensional 2 d transient scattering problems directly in the time domain is described special attention is given to the accuracy and the stability of the numerical solution scheme a detailed comparison is made between the more often used single type source solution scheme and a newly proposed combined source solution scheme it is found that the combined source scheme can offer a significant advantage in terms of stability without any appreciable loss in accuracy over the single type source scheme

robust solution of time domain integral equations using loop tree decomposition and bandlimited extrapolation a stabilization method that eradicates low frequency instabilities in the solution of the time domain integral equations of electromagnetic scattering is presented the method uses the loop tree decomposition originally suggested for the solution of low frequency scattering problems via the method of moments specifically a temporally differentiated form of the pertinent integral equation is tested using tree basis functions and the undifferentiated form is tested using solenoidal basis functions the underlying solution method uses bandlimited interpolation functions blifs and the higher order divergence conforming vector bases of graglia et al for the temporal and spatial discretization of the integral equations respectively an extrapolation technique has been implemented to overcome the noncausality introduced into the system by the blifs numerical results will demonstrate the stability and accuracy of the proposed technique

time domain bie analysis of large three dimensional electromagnetic scattering problems a time domain boundary integral equation bie solution of the magnetic field integral equation mfie for large electromagnetic scattering problems is presented it employs isoparametric curvilinear quadratic elements to model fields geometry and time dependence eliminating staircasing problems the approach is implicit which seems to provide both stability and permits arbitrary local mesh refinement to model geometrically difficult regions without the significant cost penalty explicit methods suffer error dependence on discretization is investigated accurate results are obtained with as few as five nodes per wavelength the performance both on large scatterers and on low radar cross section rcs scatterers is demonstrated including the six wavelength nasa almond two spheres a thirteen wavelength missile and a high q cavity

numerical solution of time domain integral equations for arbitrarily shaped conductor dielectric composite bodies in this work we present a numerical solution of the coupled time domain integral equations to obtain induced currents and scattered far fields on a three dimensional arbitrary shaped conducting dielectric composite body illuminated by a gaussian electromagnetic plane wave pulse the coupled integral equations are derived utilizing the equivalence principle the solution method is based on the method of moments and involves the triangular patch modeling of the composite body in conjunction with the patch basis functions detailed mathematical steps along with several numerical results are presented to illustrate the efficacy of this approach

intersection of convex objects in two and three dimensions one of the basic geometric operations involves determining whether a pair of convex objects intersect this problem is well understood in a model of computation in which the objects are given as input and their intersection is returned as output for many applications however it may be assumed that the objects already exist within the computer and that the only output desired is a single piece of data giving a common point if the objects intersect or reporting no intersection if they are disjoint for this problem none of the previous lower bounds are valid and algorithms are proposed requiring sublinear time for their solution in two and three dimensions

the influence of the exact evaluation of radiation fields in finite precision arithmetic on the stability of the time domain integral equation method transient electromagnetic scattering phenomena can effectively be simulated with time domain integral equation methods the stability and accuracy of the marching on in time scheme is usually established with exact evaluation of the radiation fields due to singularities in their analytical expressions straightforward evaluation in finite precision arithmetic can jeopardize the accuracy of the radiation fields computational experiments confirm this and show that it can even lead to late time instability of the numerical model hence a reformulation is necessary to remove the singular behavior and obtain the robustness required for industrial application to this end highly accurate and well behaved expressions for the quasi exact integration method in finite precision arithmetic will be derived in this paper numerical experiments confirm the robustness and stability of the improved marching on in time scheme

analytical evaluation of transient magnetic fields due to rwg current bases a new analytical approach for obtaining the time samples of the magnetic field intensity due to an impulsively excited rao wilton glisson rwg basis function is presented the approach is formulated directly in the time domain it is shown that the magnetic field is related to the arc segments formed by the intersection of the triangular patch of the rwg basis with the sphere that is centered at the observation point and that has a radius of where is the speed of light in particular the magnetic field can be expressed as the variations of two quantities with respect to the first quantity is the arc segment length and the second quantity is the bisecting vector of the arc segment analytical representations of these quantities are presented contrary to previous studies these representations do not require the calculation of the intersection points of the sphere with the boundaries of the bases the validity of the obtained time domain formulae is demonstrated through comparison of the results with those obtained in the frequency domain by using numerical quadrature finally it is demonstrated that the derived formulae yield closed form expressions when convolved with piecewise polynomial temporal basis functions

numerical evaluation of the two dimensional generalized exponential integral an exact technique for the evaluation of the two dimensional generalized exponential integral as required in structures involving rectangular planar radiators and transmission lines is presented it is shown that the singularity is integrable if integration is performed in polar coordinates the integral can be calculated exactly and with minimal computational effort even if integration over the origin of the coordinate system is required regardless of whether the origin is an internal or boundary point of the integration region comparison with a standard technique proves the presented approach superior stability of the algorithm and convergence is discussed performance is demonstrated for the example of an asymmetrically edge fed patch antenna

on the numerical integration of the linear shape functions times the 3 d green s function or its gradient on a plane triangle formulas for the static and dynamic potentials due to linearly varying source distributions defined on a planar triangle are presented the general linear variation of the source is represented in terms of three linear basis functions each one associated with a different vertex of the triangular domain the singular kernels considered are given by the 3 d green s function and its gradient both for the static and dynamic case in the static case the evaluation of potentials is performed analytically and compact form results are given in the dynamic case the results are given in a form suited for numerical integration

fast transient analysis of acoustic wave scattering from rigid bodies using a two level plane wave time domain algorithm it is well known that the computational cost associated with the application of classical time domain integral equation methods to the analysis of scattering from acoustical targets scales unfavorably with problem size indeed performing a three dimensional scattering analysis using these methods requires o ntns2 operations where ns denotes the number of basis functions that model the spatial field distribution over the surface of the scatterer and nt is the number of time steps in the analysis recently novel plane wave time domain algorithms that augment these classical methods and thereby reduce their high computational cost have been introduced this paper describes such a plane wave time domain algorithm within the context of the analysis of acoustic scattering from rigid bodies and outlines its incorporation into a time domain integral equation solver in a two level setting it is shown that the resulting scheme has a computational complexity of o ntns1 5 log ns examples comparing the accuracy

a simple robust controller for the approximate regulation of almost periodic signals for linear systems by using a delay line as a signal generator we design a simple robust controller for the approximate regulation i e approximate asymptotic tracking and rejection of almost periodic signals for linear systems as opposed to the related existing results our controller design does not require online parameter tuning besides the usual assumptions about stabilizability detectability and nonexistence of transmission zeros for the plant the controller design algorithm of this paper only requires knowledge of the desired tracking accuracy based on this information alone we can only design a robust controller achieving in the presence of unknown trigonometric polynomial disturbances and additive perturbations to the plant and the controller here is the output of the plant and is an arbitrary almost periodic reference signal taken from an infinite dimensional generalized sobolev space of almost periodic functions in this paper we also study robust output regulation in the limiting case where it turns out that due to the general loss of exponential closed loop stability asymptotic tracking rejection can also be lost as unless the exogenous signals are smooth enough this last result extends some recent theorems on nonrobust open loop output regulation for infinite dimensional exosystems the results of this paper are new and potentially useful for finite dimensional plants but the main results are also true for infinite dimensional systems with bounded control and observation operators

treating the instabilities in marching on in time method from a different perspective electromagnetic scattering a general method is presented to treat the instabilities which are frequently observed in the electromagnetic transient solutions using the marching on in time method the basic idea is to apply an finite impulse response fir filter with a constant group delay during the course of marching in time an electric field integral equation efie formulation for perfectly conducting bodies is used as a vessel to demonstrate the method sample numerical results are presented and discussed the computed results while showing good agreement with the data obtained from other methods present great stability improvement

an accurate method for the calculation of singular integrals arising in time domain integral equation analysis of electromagnetic scattering an accurate method for the evaluation of the cauchy principal value integrals arising in time domain electromagnetic wave scattering is presented this is applied to a boundary integral equation bie method employing quadratic curvilinear surface elements where such singularities do not vanish as they generally do when simpler but less accurate discretizations are employed the technique involves weakening the singularity in the original kernel to a degree where conventional integration methods may be employed and transforming the strong singularity to a line integral in a form which allows cancellation of its singular components the effectiveness of the method is demonstrated by scattering calculations on a variety of targets and the computational cost of the approach is trivial