physical optics analysis of multiple interactions in large scatters using current modes an efficient scheme based on physical optics po to analyze the mutual interactions between the parts of large bodies is presented the po current is approximated by current modes defined as complex exponential functions both the body geometry and the current modes are represented by means of nonuniform rational bi spline surfaces functions the current modes are computed by extrapolation considering the current values in a set of sampling points a new interpolation scheme to obtain the phase of the current modes using samples of the spatial frequency is presented the field due to the current modes is calculated efficiently using analytical expressions some results are also presented that show the performances of the method

numerical method of estimating the blow up time and rate of the solution of ordinary differential equations an application to the blow up problems of partial differential equations a numerical method is proposed for estimating the blow up time and the blow up rate of the solution of ordinary differential equation ode when the solution diverges at a finite time that is the blow up time the main idea is to transform the ode into a tractable form by the arc length transformation technique s moriguti c okuno r suekane m iri k takeuchi ikiteiru suugaku suuri kougaku no hatten in japanese baifukan tokyo 1979 and to generate a linearly convergent sequence to the blow up time the sequence is then accelerated by the aitken 2 method the present method is applied to the blow up problems of partial differential equations pdes by discretising the equations in space and integrating the resulting odes by an ode solver that is the method of lines approach numerical experiments on the three pdes the semi linear reaction diffusion equation the heat equation with a nonlinear boundary condition and the semi linear reaction diffusion system show the validity of the present method

studies in numerical nonlinear instability ii a new look at u t uu x 0 abstract it is shown that in general leap frog schemes any particular unstable solution behaves as an attractor of other solutions for a leap frog discretization of u t uu x 0 a particular kind of unstable solution is constructed which generically attracts any other solution estimates of the overflow time are presented and related to the notions of stability threshold and restricted stability

an efficient hybrid mlfma fft solver for the volume integral equation in case of sparse 3d inhomogeneous dielectric scatterers electromagnetic scattering problems involving inhomogeneous objects can be numerically solved by applying a method of moments discretization to the volume integral equation for electrically large problems the iterative solution of the resulting linear system is expensive both computationally and in memory use in this paper a hybrid mlfma fft method is presented which combines the fast fourier transform fft method and the high frequency multilevel fast multipole algorithm mlfma in order to reduce the cost of the matrix vector multiplications needed in the iterative solver the method represents the scatterers within a set of possibly disjoint identical cubic subdomains which are meshed using a uniform cubic grid this specific mesh allows for the application of ffts to calculate the near interactions in the mlfma and reduces the memory cost considerably since the aggregation and disaggregation matrices of the mlfma can be reused additional improvements to the general mlfma framework such as an extention of the fft interpolation scheme of sarvas et al from the scalar to the vectorial case in combination with a more economical representation of the radiation patterns on the lowest level in vector spherical harmonics are proposed and the choice of the subdomain size is discussed the hybrid method performs better in terms of speed and memory use on large sparse configurations than both the fft method and the hf mlfma separately and it has lower memory requirements on general large problems this is illustrated on a number of representative numerical test cases

a method for the integration in time of certain partial differential equations abstract a method for the numerical solution of ordinary differential equations is analyzed that is explicit and yet can conserve the quadratic quantities conserved by the equations the method can be a useful alternative to the usual leapfrog technique in that it does not suffer from the occurrence of blowup phenomena numerical examples concerning the korteweg de vries equation and the nonlinear schrodinger equation are given

on the spatial bandwidth of scattered fields it is shown that the scattered fields are almost space bandlimited functions the effective bandwidth w is introduced and evaluated for a very general scattering system as well as the error made using functions bandlimited to w w for representing the scattered field the effective bandwidth is very simply related to the maximum dimension of the scattering system the error drops to negligible values for modest increases of w compared to w in the case of large scatterers important consequences of the above general results are finally stressed

an efficient perfectly matched layer based multilevel fast multipole algorithm for large planar microwave structures an efficient multilevel fast multipole algorithm mlfma formalism to model radiation and scattering by from large planar microwave structures is presented the technique relies on an electric field integral equation efie formulation and a series expansion for the green dyadic based on the use of perfectly matched layers pml in this way a new pml mlfma is developed to efficiently evaluate matrix vector multiplications arising in the iterative solution of the scattering problem the computational complexity of the new algorithm scales down to o n for electrically large structures the theory is validated by means of several illustrative numerical examples

fast integral equation solution by multilevel green s function interpolation combined with multilevel fast multipole method a fast wideband integral equation ie solver combining the multilevel interpolatory fast fourier transform accelerated approach mlipfft with the multilevel fast multipole method mlfmm is discussed on electrically fine levels within an oct tree multilevel structure coupling computations are performed by mlipfft this method is based on a 3d lagrange factorization of the pertinent green s functions with a smooth approximation error in space and it does not suffer a low frequency breakdown as known from mlfmm for high frequency integral equation problems mlipfft has decreased computational efficiency as the nyquist theorem requires increasing numbers of samples in 3 dimensions due to a transition from the interpolation point based mlipfft source receive formulation towards an appropriate k space representation at a certain level within the oct tree the high frequency efficient mlfmm can be employed for coarse levels the hybrid algorithm is hence well suited for fast wideband integral equation solutions both mixed potential and direct field formulations are considered furthermore a method for mlipfft extrapolation error reduction based on fine level interpolation domain spreading is introduced in several numerical examples the performance of the proposed algorithm is demonstrated

sphere plate casimir interaction in d 1 dimensional spacetime in this paper we derive the formula for the casimir interaction energy between a sphere and a plate in d 1 dimensional minkowski spacetime it is assumed that the scalar field satisfies the dirichlet or neumann boundary conditions on the sphere and the plate as in the d 3 case the formula is of tgtg type one of our main contributions is deriving the translation matrices which express the change of bases between plane waves and spherical waves for general d using orthogonality of gegenbauer polynomials it turns out that the final tgtg formula for the casimir interaction energy can be simplified to one that is similar to the d 3 case to illustrate the application of the formula both large separation and small separation asymptotic behaviors of the casimir interaction energy are computed the large separation leading term is proportional to l d 1 if the sphere is imposed with dirichlet boundary condition and to l d 1 if the sphere is imposed with neumann boundary condition where l is distan

a faster aggregation for 3d fast evanescent wave solvers using rotations a novel technique to accelerate the aggregation and disaggregation stages in evanescent plane wave methods is presented the new method calculates the six plane wave radiation patterns from a multipole expansion aggregation and calculates the multipole expansion of an incoming field from the six plane wave incoming field patterns it is faster than the direct approach for multipole orders larger than one and becomes six times faster for large multipole orders the method relies on a connection between the discretizations of the six integral representations and on the fact that the wigner d matrices become diagonal for rotations around the z axis the proposed technique can also be extended to the vectorial case in two different ways one of which is very similar to the scalar case the other method relies on a beltrami decomposition of the fields and is faster than the direct approach for any multipole order this decomposition is also not limited to evanescent wave solvers but can be used in any vectorial multilevel fast multipole algorithm

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

exact sampling approach for reflector antennas analysis a new method for computing the far field of a possibly shaped or deformed reflector antenna based on a sampling representation of the radiation integral is presented using a projection technique the required samples can be efficiently computed using a two dimensional fast fourier transform fft whereas the radiated field is reconstructed via standard sampling expansion numerical examples and computation time analysis are reported showing the effectiveness of the approach particularly for deformed reflectors and or plane cut field evaluation

a study of the recursion yn 1 yn tymn we provide a detailed study of the recursion y 0 1 y n 1 y n y m n n 0 1 m 1 which arises either as a model discretization of a nonlinear ode or in the use of the energy method sharp bounds and asymptotic estimates are given for the size of the iterates y n

spherical wave operators and the translation formulas translational formulas for both scalar and vector spherical wave solutions of the helmholtz equation are developed in a straightforward manner using differential operator representations for the modal functions and well known expressions for the scalar and dyadic free space green s functions the expansion coefficients are given in compact integral or differential operator forms useful for analytic investigation

the receiving antenna as a linear differential operator application to spherical near field scanning the general receiving antenna is represented as a linear differential operator converting the incident field and its spatial derivatives at a single point in space to an output voltage the differential operator is specified explicitly in terms of the multipole coefficients of the antenna s complex receiving pattern when the linear operator representation is applied to the special probes used in spherical near field measurements a probe corrected spherical transmission formula is revealed that retains the form applicability and simplicity of the nonprobe corrected equations the new spherical transmission formula is shown to be consistent with the previous transmission formula derived from the rotational and translational addition theorems for spherical waves

broadband multilevel fast multipole algorithm based on an approximate diagonalization of the green s function we present a broadband multilevel fast multipole algorithm mlfma for fast and efficient solutions of three dimensional multiscale problems involving large objects with dense discretizations the proposed solver is based on the approximate diagonalization of the green s function using scaled spherical and plane waves leading to stable interaction computations for arbitrarily short distances in terms of wavelength despite contradictory requirements on the scaling factor that limit the accuracy of the diagonalization the resulting low frequency scheme is extremely stable and easy to plug into conventional mlfma implementations by simply extending built in tree structures converting them into broadband solvers without needing dense programming efforts accuracy and efficiency of the broadband mlfma are demonstrated on canonical problems as well as on multiscale problems that cannot be solved efficiently via standard implementations of mlfma

a helmholtz stable fast solution of the electric field integral equation a new fast matrix vector multiplication scheme for the solution of the electric field integral equation is presented in this work similarly to other fast methods our approach reduces the matrix vector multiplication cost from o n2 to o n logn differently from other fast solvers however the effectiveness of efie preconditioning techniques such as quasi helmholtz decompositions or calderon approaches is maintained by our method even for very high matrix compression rates this is thanks to the fact that in the scheme we are proposing the contribution from the scalar potential when applied to or tested with solenoidal functions is always zero independent of the compression error in addition the new method will take advantage of the redundancies of the efie matrix in the low frequency dense discretization regime and it will further decrease both the memory storage and the multiplication cost with respect to currently available fast solvers numerical results will show the effectiveness of our approach and its impact on the solution of realistic problems

methods for the numerical solution of the nonlinear schroedinger equation optimal l2 rates of convergence are established for several fully discrete schemes for the numerical solution of the nonlinear schroedinger equation both finite differences and finite elements are considered for the discretization in space while the integration in time is treated either by the leap frog technique or by a modified crank nicolson procedure which generalizes the one suggested by delfour fortin and payne and possesses two useful conserved quantities

a nondirective plane wave mlfma stable at low frequencies a novel method called the nondirective stable plane wave multilevel fast multipole algorithm nspwmlfma is presented to evaluate the low frequency lf interactions that cannot be handled by the multilevel fast multipole algorithm mlfma it is well known that the mlfma cannot be used for lf interactions since it suffers from numerical instability contrary to current techniques the proposed technique is not based on the spectral representation of the green function instead the addition theorem of the mlfma is manipulated into a form that allows numerically stable translations along the z axis the translation operator for these translations is derived in closed form a qr based method is devised to allow stable translations in all the other directions interpolations and anterpolations are also provided allowing a full multilevel algorithm since the nspwmlfma is based on the same mathematical foundations as the mlfma it requires limited adaptations to existing mlfma codes the fact that a qr is needed limits this algorithm to lf interactions however a coupling with the mlfma is straightforward allowing the easy construction of a broadband algorithm the dc limit of the algorithm is also presented and it is shown that the algorithm remains valid for static problems finally it is shown that the error introduced in the different steps of the algorithm is controllable and a single level vectorial version of the algorithm is applied to a generic scattering application to demonstrate its validity

embedding calderon multiplicative preconditioners in multilevel fast multipole algorithms calderon preconditioners have recently been demonstrated to be very successful in stabilizing the electric field integral equation efie for perfect electric conductors at lower frequencies previous authors have shown that by using a dense matrix preconditioner based on the calderon identities the low frequency instability is removed while still maintaining the inherent accuracy of the efie it was also demonstrated that the spectral properties of the caldero n preconditioner are conserved during discretization if the efie operator is discretized with rao wilton glisson expansion functions and the preconditioner with buffa christiansen expansion functions in this article we will show how the calderon multiplicative preconditioner cmp can be combined with fast multipole methods to accelerate the numerical solution leading to an overall complexity of o n logn for the entire iterative solution at low frequencies where the cmp is most useful the traditional multilevel fast multipole algorithm mlfma is unstable and we apply the nondirectional stable plane wave mlfma nspwmlfma that resolves the low frequency breakdown of the mlfma the combined algorithm will be called the cmp nspwmlfma applying the cmp nspwmlfma at open surfaces or very low frequencies leads to certain problems which will be discussed in this article

singular perturbation analysis of the fokker planck equation kramers underdamped problem the one dimensional fokker planck equation for a bistable potential is considered in the underdamped limit using singular perturbation analysis an asymptotic series solution is constructed in the parameter associated with the small viscosity this series solution is not uniformly valid rather it consists of four different types of asymptotic series valid in different time intervals and or portions of phase space by matching these series representations across overlapping regions a reduced problem for the long term evolution of the distribution is extracted

efficient fast multipole method for low frequency scattering the solution of the helmholtz and maxwell equations using integral formulations requires to solve large complex linear systems a direct solution of those problems using a gauss elimination is practical only for very small systems with few unknowns the use of an iterative method such as gmres can reduce the computational expense most of the expense is then computing large complex matrix vector products the cost can be further reduced by using the fast multipole method which accelerates the matrix vector product for a linear system of size n the use of an iterative method combined with the fast multipole method reduces the total expense of the computation to n log n there exist two versions of the fast multipole method one which is based on a multipole expansion of the interaction kernel exp ikr r and which was first proposed by v rokhlin and another based on a plane wave expansion of the kernel first proposed by w c chew in this paper we propose a third approach the stable plane wave expansion spw fmm which has a lower computational expense than the multipole expansion and does not have the accuracy and stability problems of the plane wave expansion the computational complexity is n log n as with the other methods

wideband fast kernel independent modeling of large multiscale structures via nested equivalent source approximation we propose a wideband fast kernel independent modeling of large multiscale structures we employ a nested equivalent source approximation nesa to compress the dense system matrix the nesa was introduced by these authors for low and moderate frequency problems smaller than a few wavelengths here we introduce a high frequency nesa algorithm and propose a hybrid version with extreme wideband properties the equivalent sources of the wideband nesa wnesa are obtained by an inverse source process enforcing equivalence of radiated fields on suitably defined testing surfaces in the low frequency region the nesa is used unmodified with a complexity of mathcal o n in the high frequency region in order to obtain a fixed rank matrix compression we hierarchically divide the far coupling space into pyramids with angles related to the peer coupling group size and the nesa testing surfaces are defined as the boundaries of the pyramids this results in a directional nested low rank fixed rank approximation with mathcal o n log n computational complexity that is kernel independent overall the approach yields wideband fast solver for the modeling of large structures that inherits the efficiency and accuracy of low frequency nesa for multiscale problems numerical results and discussions demonstrate the validity of the proposed work

computation and storage of the bianisotropic scalar green s function and its derivatives a set of algorithms is proposed for the accurate and efficient computation and storage of the bianisotropic scalar green s function the computation is based on an expansion of the green s function into chebyshev polynomials the analytical properties of these polynomials are exploited to allow the accurate computation of the derivatives of the green s function as well as the green s function itself for lossy materials the proposed computation strategy is provably robust in addition a multilevel storage scheme with a favorable complexity based on the chebyshev polynomial expansion is proposed for the storage of the expansion coefficients numerical results showcase the accuracy and computational complexity of the proposed algorithms

multiple scattering by multiple spheres a new proof of the lloyd berry formula for the effective wavenumber we provide the first classical derivation of the lloyd berry formula for the effective wavenumber of an acoustic medium filled with a sparse random array of identical small scatterers our approach clarifies the assumptions under which the lloyd berry formula is valid more precisely we derive an expression for the effective wavenumber which assumes the validity of lax s quasi crystalline approximation but makes no further assumptions about scatterer size and then we show that the lloyd berry formula is obtained in the limit as the scatterer size tends to zero

efficient algorithms for computing a strong rank revealing qr factorization given anm n matrixm withm n it is shown that there exists a permutation fi and an integer k such that the qr factorization myi q ak ckbk reveals the numerical rank of m the k k upper triangular matrix ak is well conditioned ilckll2 is small and bk is linearly dependent on ak with coefficients bounded by a low degree polynomial in n existing rank revealing qr rrqr algorithms are related to such factorizations and two algorithms are presented for computing them the new algorithms are nearly as efficient as qr with column pivoting for most problems and take o ran2 floating point operations in the worst case

singular value decomposition of the radiation operator application to model order and far field reduction the time harmonic electromagnetic scattering or radiation problem is considered the singular value decomposition svd is applied to the radiation operator that maps the set of electric and magnetic currents defined on the surface of an inhomogeneous object onto the set of the far fields scattered or radiated from this object the svd yields orthonormal bases for both sets because the radiation operator is compact and regularizing it is demonstrated that the far field calculated from the series expansions of the currents on these bases converges exponentially fast to the exact one if a sufficient number of terms is considered in these series this number is closely related to the degrees of freedom that characterize the far field the latter can be computed from a reduced number of unknowns in the discretized integral equation that links electric and magnetic surface currents by writing it in the new currents bases also it allows the reduction of the far field in a given angular sector the numerical complexity of this technique is addressed and 2d numerical examples are presented that illustrate its potentialities

stability concepts and their applications the stability is one of the most basic requirement for the numerical model which is mostly elaborated for the linear problems in this paper we analyze the stability notions for the nonlinear problems we show that in case of consistency both the n stability and k stability notions guarantee the convergence moreover by using the n stability we prove the convergence of the centralized crank nicolson method for the periodic initial value transport equation the k stability is applied for the investigation of the forward euler method and the method for the cauchy problem with lipschitzian right side

a new method for avoiding the truncation error in near field antennas measurements a new method to avoid the truncation error in antenna near field measurements is presented the approach relies on the concept of information content of the field according to this point of view the truncation problem is solved by picking up the information that is lost due to the finite size of scanning area in points of the space reachable by the measurement system the method can be applied to any scanning geometry including the planar and cylindrical ones whenever the set up allows to vary the distance between the antenna under test and the probe during the scanning procedure application of the method to cylindrical near field scanning is numerically investigated assessing the effectiveness of the proposed technique

sums of spherical waves for lattices layers and lines we consider the connections between sums of spherical wave functions over lattices layers and lines the differences between sums over lattices and those over a doubly periodic constituent layer are expressed in terms of series with exponential convergence correspondingly sums over the layer can be regarded as composed of a sum over a central line and another sum over displaced lines exhibiting exponential convergence we exhibit formulas which can be used to calculate accurately and efficiently sums of spherical waves over lattices layers and lines which in turn may be used to construct quasiperiodic green s functions for the helmholtz equation of use in scattering problems for layers and lines of spheres and for finding the bloch modes of lattices of spheres we illustrate the numerical accuracy of our expressions

a brief survey on numerical methods for solving singularly perturbed problems in the present paper a brief survey on computational techniques for the different classes of singularly perturbed problems is given this survey is a continuation of work performed earlier by the first author and contains the literature of the work done by the researchers during the years 2000 2009 however some older important relevant papers are also included in this survey we also mentioned those papers which are not surveyed in the previous survey papers by the first author of this paper see appl math comput 30 1989 223 259 130 2002 457 510 134 2003 371 429 for details thus this survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems

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 low frequency efie mlfma solver based on approximate diagonalization of green s function the low frequency fast multipole algorithm lffma based on the approximate diagonalization of green s function for the electric field integral equation efie is proposed for open and complex structures with high accuracy moreover the multiresolution preconditioner is employed to the mixed potential form of efie with rwg basis functions for stability herein a triangle grouping scheme is adopted for the scalar potential so that the accuracy of the lffma can be guaranteed furthermore the computational resources can be reduced largely since part of the radiation pattern of vector potential can share one of the scalar potentials by taking advantage of some mathematical deductions

performing interpolation and anterpolation entirely by fast fourier transform in the 3 d multilevel fast multipole algorithm the fast multipole methods are used for solving a scalar acoustic or vector electromagnetic wave equation by integral equation methods with a large number of unknowns in this paper a new method is presented for performing interpolation and anterpolation in both spherical coordinates theta and phi by fft in the three dimensional 3 d multilevel fast multipole algorithm mlfma the key idea is to approximate functions on the unit sphere by truncated fourier series in two variables rather than by the usual spherical harmonics the proposed method is exact in interpolating and anterpolating and has the high numerical efficiency of fft the method is numerically compared to the method of performing interpolation and anterpolation using lagrangian interpolation which presently is probably the fastest method for those operations and the results suggest that the proposed new method is equally or more efficient depending on the desired accuracy

a mixed form fast multipole algorithm the fast multipole algorithm manifests in two very different forms at low frequencies and at mid frequencies each can operate in their respective regimes but are not tenable in the other regimes the paper reports on a way to factorize the green s function for fast algorithm using a mixed form the low frequency fast multipole algorithm lf fma will be used at low frequencies or the long wavelength regime and the multilevel fast multipole algorithm mlfma will be used for the mid frequencies or the shorter wavelength regime for object modeling where both long wavelength and wave physics are important we propose a mixed form fast multipole algorithm mf fma this algorithm has no low frequency break down and it can work seamlessly from static where circuit physics is important to dynamic where wave physics is important

note on interpolational basis functions in the method of moments em scattering efficient basis sets for the method of moments may be obtained using quasi localized bandlimited interpolational functions that broadly speaking are defined relative to a mean sampling rate that is adjusted to curvature and proximity to edges thus reflecting the local spatial frequency bandwidth computed scattering data in a number of structures including perfectly conducting circular and elliptical two dimensional cylinders as well as a flat infinite strip indicate that reasonable accuracy can be obtained with an average rate of between 2 5 and 3 basis functions per wavelength average sampling rates need not correspond strictly to the bandwidth of the basis functions and there is considerable latitude with respect to random variation of sampling intervals although each basis function typically extends over several sample points required integrals can be obtained speedily by the use of standard sampling theoretical methods

fast multilevel computation of low rank representation of mathcal h matrix blocks a physics based algorithm for accelerating the computation of method of moments matrix blocks low rank approximation is presented the algorithm relies on efficient sampling of phase and amplitude compensated interactions using nonuniform grids rank revealing analysis is applied in a multilevel fashion to matrices of reduced column and row dimensions that describe subdomains interactions with these coarse grids rather than to the original matrix blocks as a result significant savings are achieved especially for the inherently more compressible dynamic quasi planar and quasi static cases the algorithm s reduced storage and computation time requirements are estimated analytically and verified numerically for representative examples

on landau s eigenvalue theorem and information cut sets a variation of landau s eigenvalue theorem describing the phase transition of the eigenvalues of a time frequency limiting self adjoint operator is presented the total number of degrees of freedom of square integrable multidimensional bandlimited functions is defined in terms of kolmogorov s n width and computed in some limiting regimes where the original theorem cannot be directly applied results are used to characterize up to order the total amount of information that can be transported in time and space by multiple scattered electromagnetic waves rigorously addressing a question originally posed in the early works of toraldo di francia and gabor applications in the context of wireless communication and electromagnetic sensing are discussed

reflector antenna fields an exact aperture like approach a new computational approach is presented which allows fast analysis of radiation from large reflector antennas for an aperture a fourier transform ft relationship does exist between far field and aperture distribution accordingly the far field can be exactly reconstructed from the knowledge of approximately one sample per lobe shannon whittaker theorem applied at nyquist rate the finite reflector curvature introduces an extra factor in the radiation integral so that the radiation integral is no longer a ft in order to overcome this difficulty a new pseudosampling expansion which explicitly takes into account the extra factor is developed for parabolic reflector the sampling functions are related to the fresnel integrals and the far field can be exactly reconstructed in terms of aperture far field samples which can be computed using the fast fourier transform fft numerical computations and error analysis show the excellent performance of the method which can be generalized to deal with arbitrary reflector surfaces and near field evaluation

the numerical study of blowup with application to a nonlinear schrodinger equation abstract we discuss the use of numerical methods in the study of the solutions of evolution problems which exhibit finite time unbounded growth we first examine a naive approach in which the growth rate of the numerical solution is accepted as an approximation of the true growth rate as we shall demonstrate for a radial nonlinear schrodinger equation this approach is inadequate since different discretizations exhibit different growth rates the spurious behaviour of discretizations in the neighbourhood of the singularity is discussed a reliable procedure for the estimation of the blowup parameters is considered which eliminates the discrepancies between different numerical methods

a consistent method for the solution to reduced fpk equation in statistical mechanics abstract the solution of reduced fokker planck kolmogorov fpk equation resulted from the problems in statistical mechanics is formulated as an exponential function of polynomials in state variables special measure is taken to satisfy the fpk equation in the weak sense of integration with the assumed function examples are given to show the application of the method to the non linear systems with additive random excitations and those with both additive and multiplicative random excitations the pdf solutions obtained with the proposed method and conventional gaussian closure method are compared with the exact solutions in special cases numerical results showed that the solutions obtained with the proposed method are much close to the exact solutions even for highly non linear system and the system with both additive and multiplicative excitations the convergence of the approximate pdf solutions obtained with the method is also shown with numerical results

low frequency surface integral equation solution by multilevel green s function interpolation with fast fourier transform acceleration a fast low frequency solver for surface integral equations is presented multilevel lagrange interpolation of the pertinent homogenous space green s functions is employed for the factorization of the integral operators for high computational efficiency the resulting multilevel convolution translation operators are diagonalized by fast fourier transform a fast adaptive multilevel scheme of the interpolation procedure makes the approach also suitable for broadband applications the method is investigated for the solution of electric field and combined field integral equations for the electric field integral equation the dyadic and mixed potential integral equation formulations are considered and discussed furthermore the impact of extrapolation errors on the approximation accuracy of the respective green s functions is analyzed in several numerical examples excellent efficiency with respect to computation time and memory requirements as well as good accuracy of the obtained results is demonstrated

a low frequency stable plane wave addition theorem the multilevel fast multipole algorithm mlfma is a well known and very successful method for accelerating the matrix vector products required for the iterative solution of helmholtz problems the mlfma has an important drawback namely its inability to handle scattering problems with a lot of subwavelength detail due to the low frequency lf breakdown of the mlfma there is a need to extend the mlfma to lf since alternative methods are less efficient multipole methods or hard to implement spectral methods in this paper a new addition theorem will be developed that does not suffer from an lf breakdown instead it suffers from a high frequency hf breakdown the new method relies on a novel set of distributions the so called pseudospherical harmonics closely related to the spherical harmonics these allow the discretization points and translation operators to be calculated in closed form hence the method presented in this paper allows the easy implementation of a method that is stable at lf furthermore a combination of the traditional mlfma and the new method allows for the construction of a broadband mlfma

on the optimal synthesis of sum or difference patterns of centrosymmetric arrays under arbitrary sidelobe constraints this paper deals with the optimal synthesis of sum or difference patterns radiated by an array of fixed geometry the aim is to establish the most general class of arrays for which such synthesis can be reduced to a linear programming problem extending and completing previous results regarding uniformly spaced linear and planar arrays it is shown that such a class consists of the centrosymmetric arrays whose element patterns are either equal or hermitian symmetric with respect to the center of symmetry the optimal solutions are also hermitian symmetric and the corresponding patterns are real furthermore it is shown that the above class of arrays coincides with that of the arrays capable of radiating real patterns some numerical examples are provided to give an idea of the geometries and the synthesis problems to which the achieved result successfully applies and of the achievable computational advantage

on the simulation of nonlinear bidimensional spiking neuron models bidimensional spiking models are garnering a lot of attention for their simplicity and their ability to reproduce various spiking patterns of cortical neurons and are used particularly for large network simulations these models describe the dynamics of the membrane potential by a nonlinear differential equation that blows up in finite time coupled to a second equation for adaptation spikes are emitted when the membrane potential blows up or reaches a cutoff i the precise simulation of the spike times and of the adaptation variable is critical for it governs the spike pattern produced and is hard to compute accurately because of the exploding nature of the system at the spike times we thoroughly study the precision of fixed time step integration schemes for this type of model and demonstrate that these methods produce systematic errors that are unbounded as the cutoff value is increased in the evaluation of the two crucial quantities the spike time and the value of the adaptation variable at this time precise evaluation of these quantities therefore involves very small time steps and long simulation times in order to achieve a fixed absolute precision in a reasonable computational time we propose here a new algorithm to simulate these systems based on a variable integration step method that either integrates the original ordinary differential equation or the equation of the orbits in the phase plane and compare this algorithm with fixed time step euler scheme and other more accurate simulation algorithms