pairs of matrices satisfying certain polynomial identities abstract the main result describes the pairs a b of matrices which satisfy d axb d x where d is a schur function we also study the semigroup of matrices a satisfying d ax d xa

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

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

a novel td vie based on mot scheme for analysis of dispersive objects a novel time domain volume integral equation td vie is proposed to analyze the transient electromagnetic scattering from inhomogeneous dispersive objects in this td vie method the higher order nystrom method is applied in spatial domain namely the curvilinear tetrahedron elements are utilized to discretize dielectric objects and resulting unknowns are volume electric current density the lagrange interpolation polynomials are used to represent spatial basis functions in temporal domain the marching on in time mot scheme is applied and the shifted lagrange interpolation functions are used to represent temporal basis functions moreover the point matching method is applied both in spatial and temporal domain compared with the traditional spatial schaubert wilton glisson basis based on td vie this novel td vie method is more efficient several numerical examples have demonstrated that the proposed method is accurate stable and also more efficient than the traditional td vie

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

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

an improved marching on in degree method using a new temporal basis the marching on in degree mod method has been presented earlier for solving time domain electric field integral equations in a stable fashion this is accomplished by expanding the transient responses by a complete set of orthogonal entire domain associated laguerre functions which helps one to analytically integrate out the time variable from the final computations in a galerkin methodology so the final computations are carried out using only the spatial variables however the existing mod method suffers from low computational efficiency over a marching on in time mot method the two main causes of the computational inefficiency in the previous mod method are now addressed using a new form of the temporal basis functions and through a different computational arrangement for the green s function in this paper it is shown that incorporating these two new concepts can speed up the computational process and make it comparable to a mot algorithm sample numerical results are presented to illustrate the validity of these claims in solution of large problems using the mod method

λ g critical matrices the problem of finding the conditions for equality of nonzero decomposable symmetrized tensors has been considered several times i e given the vectors x1 xm y1 ym of v in what conditions one has x1 xm y1 ym 0 we present here a necessary condition for 1 introducing the concept of g critical matrix we present also some new results on the characterization of the set of the matrices a mm m c satisfying dg ax dg xa for all m by m matrices x over c

linear groups associated with elements of a group algebra let c be an arbitrary nonzero function from sm into a field k if a aij is an m square matrix over k define dc a smc i 1m ai i we are concerned with the characterization of the group of nonsingular matrices a satisfying dc ax dc x for all m square matrices x over k the author previously defined 13 a galois connection between the set of left ideals of the group algebra k sm ordered by inclusion and the set of subgroups of the full linear group also ordered by inclusion we characterize the closed elements of by the closure operation arising from this connection

pairs of matrices that preserve the value of a generalized matrix function on the set of the upper triangular matrices let h be a subgroup of the symmetric group of degree m and let be an irreducible character of h in this paper we give conditions that characterize the pairs of matrices that leave invariant the value of a generalized matrix function associated with h and on the set of the upper triangular matrices

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

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

a mass length scaling law for modeling muscle strength in the lower limb musculoskeletal computer models are often used to study muscle function in children with and without impaired mobility calculations of muscle forces depend in part on the assumed strength of each muscle represented by the peak isometric force parameter which is usually based on measurements obtained from cadavers of adult donors the aim of the present study was twofold first to develop a method for scaling lower limb peak isometric muscle forces in typically developing children and second to determine the effect of this scaling method on model calculations of muscle forces obtained for normal gait muscle volumes were determined from magnetic resonance mr images obtained from ten children aged from 7 to 13yr a new mass length scaling law was developed based on the assumption that muscle volume and body mass are linearly related which was confirmed by the obtained volume and body mass data two musculoskeletal models were developed for each subject one in which peak isometric muscle forces were estimated using the mass length scaling law and another in which these parameters were determined directly from the mr derived muscle volumes musculoskeletal modeling and quantitative gait analysis were then used to calculate lower limb muscle forces in normal walking the patterns of muscle forces predicted by the model with scaled peak isometric force values were similar to those predicted by the mr based model implying that assessments of muscle function obtained from these two methods are practically equivalent these results support the use of mass length scaling in the development of subject specific musculoskeletal models of children

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

on the stability of time domain magnetic field integral equation using laguerre functions the marching on in degree mod method has been proposed for solving time domain integral equations tdies and it uses the associated laguerre functions as temporal basis and testing functions although the mod scheme is assumed to be stable and accurate there exists little investigation into the accuracy of the integral operations involving the associated laguerre functions of high degree it is shown in this paper that the numerical quadrature for integrating the highly oscillatory laguerre functions may not be accurate and this may result in instability for the mod solvers in this paper the highly oscillatory nature of the high degree associated laguerre functions is investigated first based on that the numerical procedures are described which result in the inaccuracy of the numerical quadrature associated with the highly oscillatory nature for the higher order laguerre functions this can produce instability for the mod solvers when a solution requires a high degree of the laguerre functions hence a novel filon type quadrature method and a stabilized mod technique for time domain magnetic field integral equations td mfie smod are presented in this paper some numerical results are presented to illustrate the validity of the proposed filon type quadrature rule resulting in stable solution of the td mfie for transient scattering problems

equality of decomposable symmetrized tensors and matrix groups let g be a subgroup of the full symmetric group sn and a character of g a matrix can be defined as an n n matrix b which satisfies dgx bx dgx x for every n n matrix x they form a multiplicative group denoted s g x which plays a fundamental role in the study of equality of two decomposable symmetrized tensors the main result of this paper theorems 2 2 2 3 and 2 4 is a complete description of the matrices in s g x this description has many consequences that we present there are also results on related questions

choice of the scaling factor in a marching on in degree time domain technique based on the associated laguerre functions in marching on in degree time domain method of moment the transient responses are often expanded by a finite number of associated laguerre functions there is an error associated in truncating the associated laguerre function series beyond that what is necessary in the solution process this error is related to the scaling factor used in the argument of the associated laguerre functions that actually approximates the unknown temporal variations a least upper bound of this error is deduced based on this bound one can obtain an optimum scaling factor to minimize this error so that it is guaranteed to be below a certain bound

complex time representation of the sommerfeld type integrals and its application to 1 d periodic structures the concept of complex time is employed to derive the time domain representation of the green s function of a periodic structure for the first time the spatial domain green s function of the periodic structure in the frequency domain is separated into singular and nonsingular terms the nonsingular terms are approximated by using exponential functions resulting in the well known complex time representation of the time domain green s function in order to find a closed form expression for the singular terms a novel time domain representation of the sommerfeld type integrals is derived the proposed procedure is applied to the computation of the time domain green s function of a one dimensional periodic structure numerical experiments demonstrate the high accuracy of this method

marching on in degree method with delayed weighted laguerre polynomials for transient electromagnetic scattering analysis the large cost of computing resources has become a bottleneck of the marching on in degree mod solver of time domain integral equation tdie a set of delayed weighted laguerre polynomials is proposed to address this problem in this paper by incorporating the phase propagation information into itself the proposed temporal basis function can model the phase variation of the induced current at different places of the scatterer leading to a great reduction in the spatial unknowns moreover the curvilinear rao wilton glisson crwg basis functions are adopted for the spatial discretization to improve the modeling precision of curve surfaces numerical results show that the proposed method can greatly reduce the mesh density of the scatterer and save the computing resources it is both stable and efficient for the transient scattering analysis of perfect electrically conducting pec objects with large smooth surfaces

on pairs of matrices that satisfy certain polynomial identities abstract let f be an arbitrary field h be a subgroup of the symmetric group of degree m s m be an irreducible f valued character of h and d h be the generalized matrix function associated to h and in this note we present some properties of the pairs a b of m m matrices over f that satisfy d h axb d h x for all x we also describe the pairs a b satisfying d h ax d h xb for all x

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

a hybrid scheme with nystrom discretization for solving transient electromagnetic scattering by conducting objects the interaction of transient electromagnetic em waves with objects can be formulated by the integral equation approach in time domain for conducting objects or homogeneous penetrable objects the time domain surface integral equations tdsies can be applied traditionally the tdsies are solved by combining the method of moments mom in spatial domain and a march on in time mot scheme in temporal domain the mom usually requires conforming meshes with a well designed basis function and the mot may suffer from a stability problem in this work we propose a hybrid scheme in which the nystrom method is used in spatial domain while the mom with laguerre function as basis and testing functions is employed with a march on in degree mod manner in the temporal domain the nystrom method does not require any basis and testing functions and can use nonconforming meshes in spatial domain whereas the mom with laguerre function as basis and testing functions can fully eliminate the stability problem in temporal domain numerical examples for em scattering by typical conducting objects are presented to demonstrate the scheme and its merits have been verified

a higher order nystrom scheme for a marching on in time solution of time domain integral equation a marching on in time mot solution of the time domain integral equation tdie using the higher order nystrom scheme is developed to analyze the transient electromagnetic scattering from arbitrarily shaped perfect electrically conducting pec objects in this scheme the curvilinear triangular patches are utilized to discretize the pec objects for their great ability to model geometric configuration moreover we use the lagrange interpolation polynomials to stand for the spatial basis functions and the triangle functions to represent the temporal basis functions furthermore the spatial and temporal point matching is applied numerical examples demonstrate that the proposed scheme is stable accurate and efficient