multiple correction and continued fraction approximation abstract the main aim of this paper is to further develop a multiple correction method formulated in a previous work 6 as applications we find a kind of hybrid type finite continued fraction approximations in two cases of landau constants and lebesgue constants in addition we refine the previous results of lu 29 and xu and you 48 for the euler mascheroni constant

unified treatment of several asymptotic expansions concerning some mathematical constants recently various approximation formulas for some mathematical constants have been investigated and presented by many authors in this paper we first find that the relationship between the coefficients pj and qj is such that xj 0qjxj ln xj 0pjxj x where is the logarithmic derivative of the gamma function often referred to as psi function and p0 q0 1 next by using this result we give a unified treatment of several asymptotic expansions concerning the eulermascheroni constant landau and lebesgue constants glaisherkinkelin constant and choisrivastava constants

a fast analysis of scattering from large scale finite periodic microstrip patch arrays arranged on a non orthogonal lattice using sub entire domain basis functions a sub entire domain sed basis function method which was first introduced for modeling large scale finite periodic pec structures in free space has been extended for fast characterization of electromagnetic scattering from an electrically large planar finite periodic microstrip patch array the microstrip array may have a nonrectangular layout and non orthogonal lattice configurations e g hexagons or quadrangles based on the mixed potential integral equation and utilizing the proposed sed basis function algorithm the original large scale finite periodic array of microstrip patches can be efficiently simulated by decomposing it into two problems with matrix equations of small dimensions the first is to construct the sed basis functions for the corresponding microstrip arrays with orthogonal non orthogonal lattices three kinds of the sed basis functions are constructed including those related to the edge patch elements the interior patch elements and the corner patch elements the second is to solve the system equation with significantly reduced problem dimension as compared to the original larger problem based on the obtained sed basis functions the reduced matrix equation of small size can be generated by the galerkin procedure and solved by use of the lu lower upper decomposition based direct solver which results in a fast solution the accuracy and efficiency of the developed algorithms are demonstrated by numerical tests that include the scattering from several large scale finite periodic arrays of microstrip patches with rectangular non orthogonal lattices

on inequalities and asymptotic expansions for the landau constants we demonstrate how arbitrarily sharp asymptotic expansions for the landau constants can be derived and we prove some related inequalities the main tool used is brouncker s continued fraction formula we also show that the implied series expansion of the landau constants is in fact divergent

adaptive multiscale moment method ammm for analysis of scattering from perfectly conducting plates adaptive multiscale moment method ammm is presented for the analysis of scattering from a thin perfectly conducting plate this algorithm employs the conventional moment method and a special matrix transformation which is derived from the tensor products of the two one dimensional 1 d multiscale triangular basis functions that are used for expansion and testing functions in the conventional moment method the special feature of these new basis functions introduced through this transformation is that they are orthogonal at the same scale except at the initial scale and not between scales from one scale to another scale the initial estimate for the solution can be predicted using this multiscale technique hence the compression is applied directly to the solution and the size of the linear equations to be solved is reduced thereby improving the efficiency of the conventional moment method the basic difference between this methodology and the other techniques that have been presented so far is that we apply the compression not to the impedance matrix but to the solution itself directly using an iterative solution methodology the extrapolated results at the higher scale thus provide a good initial guess for the iterative method typically when the number of unknowns exceeds a few thousand unknowns the matrix solution time exceeds generally the matrix fill time hence the goal of this method is directed in solving electrically larger problems where the matrix solution time is of concern two numerical results are presented which demonstrate that the ammm is a useful method to analyze scattering from perfectly conducting plates

an efficient numerical method for studying interfacial motion in two dimensional creeping flows we present new methods for computing the motion of two dimensional closed interfaces in a slow viscous flow the interfacial velocity is found through the solution to an integral equation whose analytic formulation is based on complex variable theory for the biharmonic equation the numerical methods for solving the integral equations are spectrally accurate and employ a fast multipole based iterative solution procedure which requires only o n operations where n is the number of nodes in the discretization of the interface the interface is described spectrally and we use evolution equations that preserve equal spacing in arclength of the marker points a small scale decomposition is performed to extract the dominant term in the evolution of the interface and we show that this dominant term leads to a cfl type stability constraint when in an equal arclength frame this term is linear and we show that implicit time integration schemes that are explicit in fourier space can be formulated we verify this analysis through several numerical examples

the discrete fourier transform method of solving differential integral equations in scattering theory an accurate and efficient numerical method is presented for solving many differential integral equations arising from electromagnetic scattering theory it uses the discrete fourier transform technique to treat both the derivatives and the convolution integrals which often appear in these equations as a consequence this method is extremely simple to implement uses less computer memory than comparable methods and yields accurate predictions the differential integral equation is recast into a periodic form conducive to application of the discrete fourier convolution theorem the differential operators are approximated by appropriate finite difference and discrete convolution operators all these quantities are computed by using the fast fourier transform an approximate solution is obtained by using the conjugate gradient method results are compared to experimental data or analytical solutions for a 3 lambda 3 lambda metal plate where lambda is the wavelength a homogeneous and a layered infinite circular dielectric cylinder and a dielectric sphere the accuracy of the method is further illustrated by comparing predictions with independent measurements by r a ross 1966 on a 2 lambda 1 lambda metal plate at grazing incidence in all cases agreement is excellent

an improved multilevel green s function interpolation method with adaptive phase compensation an improved multilevel green s function interpolation method mlgfim with adaptive phase compensation apc is proposed the difficulty in applying interpolation approaches to the fast varying phase term in the integral equation kernel for full wave electromagnetic em simulations is eradicated by using the phase compensation and adaptive direction separation ads the multilevel tree structure in mlgfim keeps the number of direction separation invariant at all levels attributing to the recursive interpolation with multilevel phase compensation the proposed mlgfim apc in conjunction with the lagrange chebyshev interpolation yield an o n log n cpu time and o n computer memory requirement for surface scattering problems by introducing a transition level the mlgfim apc can adaptively incorporate interpolation techniques of conventional interpolation ci transition interpolation ti and phase compensation interpolation pi corresponding to electromagnetic simulation of problems of small moderate and large electrical sizes respectively large scale microstrip antenna arrays are simulated to illustrate the accuracy and efficiency of the proposed method it is found that the cpu time scales better than o n log n for these co planar problems

regular article a fast adaptive multipole algorithm in three dimensions we present an adaptive fast multipole method for the laplace equation in three dimensions it uses both new compression techniques and diagonal forms for translation operators to achieve high accuracy at a reasonable cost

a fast analysis of scattering and radiation of large microstrip antenna arrays an accurate and efficient method that combines the precorrected fast fourier transform fft method and the discrete complex image method dcim is presented to characterize the scattering and radiation properties of arbitrarily shaped microstrip patch antennas in this method the mixed potential integral equation mpie is discretized in the spatial domain by means of the discrete complex image method the resultant system is solved iteratively using the generalized conjugate residual method gcr and the precorrected fft technique is used to speed up the matrix vector multiplication the precorrected fft eliminates the need to generate and store the usual square impedance matrix and thus leads to a significant reduction in memory requirement and computational cost numerical results are presented for arbitrarily shaped microstrip antenna arrays to demonstrate the accuracy and efficiency of this technique

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

a mixed form thin stratified medium fast multipole algorithm for both low and mid frequency problems a mixed form thin stratified medium fast multipole algorithm is proposed for fast simulation of general microstrip structures at both low and mid frequencies the newly developed matrix friendly formula of layered medium green s function is applied in this algorithm for well separated interactions the path deformation technique is implemented to achieve a smoother and exponentially convergent integral the two dimensional addition theorem is then incorporated into the integrand to expedite the matrix vector product in our approach multipole expansion low frequency fast multiple algorithm as well as the plane wave expansion mid frequency fast multipole algorithm of the translational addition theorem are combined into a single multilevel tree to capture quasi static physics and wave physics simultaneously the outgoing wave is represented first in terms of multipole expansion at leafy levels and then switched to plane wave expansion automatically at higher levels this seamless connection makes the algorithm applicable in simulations where subwavelength interaction and wave physics both exist

comments on application of fft and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies in the original paper ibid vol ap 34 no 5 p 635 40 1986 t k sarkar et al describe how the fast fourier transform fft and the conjugate gradient method cgm can be used to efficiently make use of the convolutional form of the electric field integral equation for straight wire antennas the commentators agree that the cgm converges more rapidly than the previously used method of steepest descent and the spectral iteration technique they also point out that experience with the dyadic green s function encountered in the two dimensional transverse electric te and three dimensional equations for dielectric bodies is not so encouraging it is found that for these cases the cgm convergence can be quite slow degrading the efficiency of the algorithm in addition the solution obtained using the pulse basis point matching method to discretize the integral equation are very inaccurate for the two dimensional te and three dimensional cases a reply to these comments from the authors of the original paper is included

a fast full wave analysis of scattering and radiation from large finite arrays of microstrip antennas a fast full wave analysis technique that can be used to analyze the scattering and radiation from large finite arrays of microstrip antennas is presented the technique discretizes the mixed potential integral equation mpie in the spatial domain by means of a full wave discrete complex image method the del operators on the green s functions are transferred from the singular kernel to the expansion and testing functions the resultant system of equations is solved using the biconjugate gradient bcg method in which the matrix vector product is evaluated efficiently using the fast fourier transform fft this results in an efficient and accurate computation of the scattering and radiation from finite arrays of microstrip antennas several numerical results are presented demonstrating the accuracy efficiency and capability of this technique

multiple correction and continued fraction approximation ii the main aim of this paper is to further develop the multiple correction method formulated in our previous works cao et al 2015 cao 2015 as applications we establish a kind of hybrid type finite continued fraction approximations related to bbp type series of the constant and other classical constants such as catalan constant or 2

a novel numerical model for simulating three dimensional mimo channels with complex antenna arrays we develop a novel three dimensional 3d numerical model for rigorously simulating mutual coupling effects on the channel capacity of the multiple input multiple output mimo systems in this model the efficient integral equation method mutlilevel green s function interpolation method mlgfim is for the first time employed to calculate the input admittances and radiation patterns of the transmit and receive antennas of mimos comparing with the method of moments whose complexity is o n2 mlgfim has an efficiency of o nlogn and is suitable for efficiently solving antenna arrays problems to accurately model the em wave propagation we 1 use the ray tracing method to obtain the multi paths and 2 rigorously obtain the dyadic path loss factor model from which a novel stochastic path loss model that is flexible for both the environments with pec walls and that with infinite thick lossless dielectric walls is devised using the proposed model we successfully analyze mutual coupling effects on the 3d correlation of a 2 by 2 monopole array and the indoor channel capacity of a 20 by 20 planar array and a 20 by 20 icosahedron array the numerical examples in this paper demonstrate the efficiency of our model for simulating the mimo system with complex radiators

an adaptive mesh algorithm for evolving surfaces simulation of drop breakup and coalescence abstract an algorithm is presented for the adaptive restructuring of meshes on evolving surfaces the resolution of the relevant local length scale is maintained everywhere with prescribed accuracy through the minimization of an appropriate mesh energy function by a sequence of local restructuring operations the resulting discretization depends on the instantaneous configuration of the surface but is insensitive to the deformation history application of the adaptive discretization algorithm is illustrated with three dimensional boundary integral simulations of deformable drops in stokes flow the results show that the algorithm can accurately resolve detailed features of deformed fluid interfaces including slender filaments associated with drop breakup and dimpled regions associated with drop coalescence our algorithm should be useful in a variety of fields including computational fluid dynamics image processing geographical information systems and biomedical engineering problems

a hybrid finite element boundary integral method for the analysis of cavity backed antennas of arbitrary shape an edge based hybrid finite element boundary integral fe bi formulation using tetrahedral elements is described for scattering and radiation analysis of arbitrarily shaped cavity backed patch antennas by virtue of the finite element method fem the cavity irregularities the dielectric super substrate inhomogeneities and the diverse excitation schemes inside the cavity may be readily modeled when tetrahedral elements are used to discretize the cavity on the aperture the volume mesh reduces to a triangular grid allowing the modeling of nonrectangular patches without special handling of the boundary integral system this formulation is typically applicable to cavity backed antenna systems with moderate aperture size to retain an o n memory requirement storage of the full matrix due to the boundary integral equation is avoided by resorting to a structured triangular aperture grid and taking advantage of the integral s convolutional property if necessary this is achieved by overlaying a structured triangular grid on the unstructured triangular grid and relating the edge field coefficients between the two grids via two narrow banded transformation matrices the combined linear system of equations is solved via the biconjugate gradient bicg method and the fft algorithm is incorporated to compute the matrix vector product efficiently with minimal storage requirements

null field preconditioner with selected far field contribution for 3 d full wave efie in this paper a stable and effective preconditioner for the method of moments based electric field integral equation matrix based on the null field method is presented to expedite the convergence of krylov subspace based fast iterative solution the preconditioner is computed from all near field blocks and selected far field blocks in accordance with the null field procedure the final form of the preconditioner is block diagonal and therefore generates no additional fill ins in its inverse and is also amenable to parallelization a complexity analysis is presented to show the near linear cost of preconditioner construction and usage in terms of computation time and memory the numerical experiments with a sequential implementation demonstrate on an average 1 5 3 times speed up in the iterative solution time over threshold dependent incomplete lu based preconditioners

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

higher order interpolatory vector bases for computational electromagnetics low order vector basis functions compatible with the nedelec 1980 representations are widely used for electromagnetic field problems higher order functions are receiving wider application but their development is hampered by the complex procedures used to generate them and lack of a consistent notation for both elements and bases in this paper fully interpolatory higher order vector basis functions of the nedelec type are defined in a unified and consistent manner for the most common element shapes it is shown that these functions can be obtained as the product of zeroth order nedelec representations and interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties of the vector functions are discussed and expressions for the vector functions of arbitrary polynomial order are presented sample numerical results confirm the faster convergence of the higher order functions

fast delaunay triangulation in three dimensions abstract an efficient algorithm for delaunay triangulation of a given set of points in three dimensions based on the point insertion technique is presented various steps of the triangulation algorithm are reviewed and many acceleration procedures are devised to speed up the triangulation process new features include the search of a neighbouring point by the layering scheme locating the containing tetrahedron by random walk formulas of important geometrical quantities of a new tetrahedron based on those of an existing one a novel approach in establishing the adjacency relationship the use of adjacency table and the management of memory the resulting scheme is one of the fastest triangulation algorithms known to the authors which is able to generate tetrahedra generation rate of 15 000 tetrahedra per second for randomly generated points on a hp 735 machine

multilayered media green s functions in integral equation formulations a compact representation is given of the electric and magnetic type dyadic green s functions for plane stratified multilayered uniaxial media based on the transmission line network analog along the aids normal to the stratification furthermore mixed potential integral equations are derived within the framework of this transmission line formalism for arbitrarily shaped conducting or penetrable objects embedded in the multilayered medium the development emphasizes laterally unbounded environments but an extension to the case of a medium enclosed by a rectangular shield is also included

inequalities for the constants of landau and lebesgue the constants of landau and lebesgue are defined for all integers n 0 by gn k 0n1 16k 2 and ln 12 sin n t sin t dt respectively we establish sharp inequalities for gn and ln 2 in terms of the logarithmic derivative of the gamma function further we prove that the sequence gn is completely monotonic we provide best possible upper and lower bounds for the ratios gn 1 gn 1 gn and l n 1 2 l n 1 2 ln 2 and we present sharp bounds for ln 2 gn and ln 2 gn

the implementation of multilevel green s function interpolation method for full wave electromagnetic problems we extend the multilevel green s function interpolation method mlgfim developed for quasi electrostatic problems to full wave simulations the difficulty in applying the interpolation approach lies in the additional rapidly changing phase term associated with the full wave green s functions to enhance the efficiency and accuracy of the full wave green s function interpolation a scattered point set consisting of two staggered tartan grids in conjunction with radial basis function interpolation is employed to further reduce the computational complexity the qr factorization technique is applied to compress the low rank green s function matrices for electromagnetic scattering from pec spheres up to a diameter of eight wavelengths the proposed method compares well with mie s scattering in accuracy and shows the o nlogn efficiency as the method is kernel independent its extension to structures in layered medium is straightforward in the numerical simulations of finite microstrip patch arrays up to 11 by 11 elements the proposed method demonstrates very favorable dependencies of cpu time and memory storage requirement versus the number of unknowns

asymptotic expansions for the constants of landau and lebesgue the constants of landau and lebesgue are defined for all integers n 0 in order by gn k 0n116k 2kk 2andln 12 sin n 12 t sin 12t dt which play important roles in the theories of complex analysis and fourier series respectively certain inequalities and asymptotic expansions for the constants gn and ln have been investigated by many authors here we aim at establishing new asymptotic expansions for the constants gn and ln of landau and lebesgue respectively by mainly using bell polynomials and the partition function

qualitative measures for initial meshes this paper reviews geometric measures used to assess the shape of finite elements in two and three dimensional meshes measures have been normalized and made scale invariant whenever possible this paper also introduces a universal similarity region that enhances comparisons of triangles and their measures as a byproduct the usr provides a dynamic way to compare improved triangular meshes copyright 2000 john wiley sons ltd

adaptive finite element methods for elliptic pdes based on conforming centroidal voronoi delaunay triangulations a new triangular mesh adaptivity algorithm for elliptic pdes that combines a posteriori error estimation with centroidal voronoi delaunay tessellations of domains in two dimensions is proposed and tested the ability of the first ingredient to detect local regions of large error and the ability of the second ingredient to generate superior unstructured grids result in a mesh adaptivity algorithm that has several very desirable features including the following errors are very well equidistributed over the triangles at all levels of refinement the triangles remain very well shaped even if the grid size at any particular refinement level when viewed globally varies by several orders of magnitude and the convergence rates achieved are the best obtainable using piecewise linear finite elements this methodology can be easily extended to higher order finite element approximations or mixed finite element formulations although only the linear approximation is considered in this paper

efficient solution of efie via low rank compression of multilevel predetermined interactions this paper describes the predetermined interaction list oct tree pilot algorithm and its application in expediting the solution of full wave electric field integral equation efie based scattering problems for three dimensional arbitrarily shaped conductors pilot combines features of the fast multipole method fmm and qr decomposition based matrix compression techniques to optimize setup times solve times and memory requirements the method is kernel independent and stable for electrically small structures unlike traditional fmm the novel features of the algorithm namely the mixed potential compression scheme and the hierarchical multilevel predetermined matrix structure are explained in detail a complexity estimate is presented to demonstrate the scaling in time and memory requirements examples exhibiting the accuracy and the time and memory performances are also presented finally a quantitative study is included to address the expected but gradual degradation of qr based compression techniques for electrically large structures

the fast solution of poisson s and the biharmonic equations on irregular regions we present fast methods for solving laplace s and the biharmonic equations on irregular regions with smooth boundaries the methods used for solving both equations make use of fast poisson solvers on a rectangular region in which the irregular region is embedded they also both use an integral equation formulation of the problem where the integral equations are fredholm integral equations of the second kind the main idea is to use the integral equation formulation to define a discontinuous extension of the solution to the rest of the rectangular region fast solvers are then used to compute the extended solution aside from solving the equations we have also been able to compute derivatives of the solutions with little loss of accuracy when the data was sufficiently smooth

rcs computation for a large array of waveguide slots with finite wall thickness using the mom accelerated by p fft algorithm this correspondence presents an accurate and efficient method of moments mom for analyzing electromagnetic scattering by a large finite array of waveguide slots with finite thickness in this method the mixed potential integral equation mpie is utilized onto both upper and lower surfaces of the slots and the subdomain mom procedure is implemented to obtain the equivalent magnetic current distributions the precorrected fast fourier transform p fft method is employed to accelerate the entire computational process to reduce significantly the memory requirements for large arrays during the mom procedure the rao wilton glisson rwg functions are used as the basis and testing functions with both z and x directional magnetic currents considered this approach extends applicability of the present method to solve the mpie for characterizing waveguide slots of arbitrary shape and distribution and the capability of the integral equation based fast algorithm numerical results are obtained and compared with the experimental results to verify the accuracy and efficiency of this technique

fast directional multilevel algorithm for analyzing wave scattering a new method named fast directional multilevel algorithm is proposed for analyzing wave scattering similar to a fast multipole method an oct tree structure is used in the new method unlike the conventional mlfma the kernel is evaluated by a new method instead of approximating the green s function by multipole expansion the fast directional multilevel algorithm is first used to solve the wave scattering problem via combined field integral equation cfie using rao wilton glisson rwg basis functions the low rank representations are extended to apply in the low frequency regime which is proved efficient and stable the numerical results demonstrate that the computational complexity of this new multilevel algorithm can achieve the complexity of o n log n this algorithm is robust and performs well on other oscillatory kernels because of its not depending on the explicit form of kernels

delaunay triangulation in computational fluid dynamics abstract a method which utilises the delaunay criterion is described by which computational grids consisting of assemblies of triangles or tetrahedra can be constructed an algorithm is briefly outlined to construct the triangulation and its dual the voronoi diagram issues related to how to construct boundary conforming grids from such a triangulation are addressed and details are presented of how grid points within the domain can be generated automatically the point generation algorithm utilises either the given boundary point distribution or for grid adaption a background mesh computational aspects of constructing the triangulation in both 2 and 3 dimensions are covered examples of meshes and flow computations for a range of aerospace geometries are presented

a combined full wave cg fft method for rigorous analysis of large microstrip antenna arrays an accurate and efficient technique is presented for the analysis of large microstrip antenna arrays the technique consists of an amalgamation of a spatially discrete scheme consisting of the cg fft method and the complex discrete image cdi technique the unique feature of this approach is the use of the spatially discrete cg fft for analyzing microstrip structures the aliasing and truncation errors are thoroughly eliminated in this approach in addition the grad div operators are transformed from singular green s functions to differentiable expansion and testing functions by using galerkin s procedure thereby improving the accuracy and the rate of convergence to show the accuracy and efficiency of this technique a number of microstrip arrays including a large microstrip reflectarray have been studied it is found that the simulations carried out using this technique are in very good agreement with measurements

optimal rate of convergence for sequences of a prescribed form abstract we provide a highly convergent version of the generalized euler sequence and we determine the element with the optimal rate of convergence in several classes of sequences of a prescribed form the new approach extends and unifies many previous efforts in this direction in addition we answer an open problem on the asymptotic expansion of the harmonic number sequence

grid generation and optimization based on centroidal voronoi tessellations centroidal voronoi tessellations cvts are voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding voronoi regions such tessellations are of use in very diverse applications including data compression clustering analysis cell biology territorial behavior of animals and optimal allocation of resources in this paper we explore the use of cvts in grid generation in connection with finite element approximations of partial differential equations we being by describing these tessellations and methods for their determination we then discuss their application to mesh generation and finish with some examples of their use for the solution of partial differential equations

contour fft based spectral domain mbf analysis of large printed antenna arrays a fast spectral domain method is proposed to evaluate the reaction terms between the macro basis functions in regular and non regular arrays made of identical printed antennas the presented technique first exploits the filtering capabilities of the macro basis functions in the spectral domain the method is then strongly accelerated with the help of a newly formulated fast fourier transform fft based technique which is applicable to a contour integration in the complex plane we name the method as contour fft c fft besides an effective homogeneous medium term treated with multipoles a computational complexity of order n log2 n is achieved for the tabulation of substrate related reaction terms for any possible relative positions the complexity of the proposed method is independent from the complexity of the elements numerical results obtained with the proposed method are compared with those from a pre validated reference solution based on the traditional macro basis functions technique an excellent agreement is observed

a multilevel matrix decomposition algorithm for analyzing scattering from large structures a multilevel algorithm is presented for analyzing scattering from electrically large surfaces the algorithm accelerates the iterative solution of integral equations that arise in computational electromagnetics the algorithm permits a fast matrix vector multiplication by decomposing the traditional method of moment matrix into a large number of blocks with each describing the interaction between distant scatterers the multiplication of each block by a trial solution vector is executed using a multilevel scheme that resembles a fast fourier transform fft and that only relies on well known algebraic techniques the computational complexity and the memory requirements of the proposed algorithm are o n log sup 2 n

precorrected fft solution of the volume integral equation for 3 d inhomogeneous dielectric objects this work presents a fast solution to the volume integral equation for electromagnetic scattering from three dimensional inhomogeneous dielectric bodies by using the precorrected fast fourier transform fft method the object is modeled using tetrahedral volume elements and the basis functions proposed by schaubert et al are employed to expand the unknown electric flux density the basis functions are then projected onto a fictitious uniform grid surrounding the nonuniform mesh enabling the fft to be used to speed up the matrix vector multiplies in the iterative solution of the matrix equation the resultant method greatly reduces the memory requirement to o n and the computational complexity to o nlogn where n is the number of unknowns as a result this method is capable of computing electromagnetic scattering from large complex dielectric objects

inequalities and asymptotic expansions for the constants of landau and lebesgue the constants of landau and lebesgue are defined for all integers n 0 in order by g n k 0 n 1 16 k 2 k k 2 and l n 1 2 sin n 1 2 t sin 1 2 t d t which play important roles in the theories of complex analysis and fourier series respectively diverse inequalities and approximations for these constants have been investigated and developed by many authors here in this paper we establish new asymptotic expansions for the constants g n and l n 2 of landau and lebesgue respectively in terms of the digamma and polygamma functions based on our expansion for the landau constants g n we present new bounds for the landau constants g n in terms of the digamma and polygamma functions we also establish inequalities for the lebesgue constants l n 2 which are applied to derive an asymptotic expansion for l n 2 in terms of 1 n 1 furthermore by giving numerical calculations to be compared among several developed asymptotic expansions for the constants g n and l n 2 it is shown that our expansions presented here would be best ones

surface electric fields and impedance matrix elements of stratified media for the various geometrical configurations of waves in stratified media we consider the important case when both source and field points are located on the same interface separating two different dielectric media we denote this configuration as surface electric field case in this paper the electric fields are calculated numerically without using potentials for the surface electric field case the integrand of the electric field grows with k sub spl rho sup 3 2 for large spl kappa sub spl rho making the sommerfeld integral singular to calculate the surface electric fields in the spatial domain we previously applied a technique of higher order asymptotic extraction in the higher order asymptotic extraction the higher order asymptotic parts were calculated analytically the remainder which has an integrand decays as spl kappa sub spl rho sup 3 2 was calculated numerically along the sommerfeld contour path of integration in this paper we use a different extraction technique the half space extraction after the half space extraction the integrand of the sommerfeld integral of stratified media decays exponentially and the integral is calculated along the sommerfeld integration path the half space extraction part is calculated by numerical integration along the vertical branch cuts the surface electric fields for stratified media using half space extraction and higher order asymptotic extraction are in good agreement to validate the accuracy of the solution we also compute the impedance matrix elements using surface electric fields testing and basis functions all in the spatial domain the results are then compared with the results of the spectral domain method the comparisons of the complex impedance matrix elements are tabulated and show that the difference is less than 2

comparison of interpolating functions and interpolating points in full wave multilevel green s function interpolation method the difficulty for the solution of full wave electromagnetic problems using multilevel green s function interpolation method mlgfim lies in applying interpolating approaches to efficiently and accurately approximate green s function with rapidly changing phase term we compare various interpolating schemes when radial basis function rbf is employed for the interpolation of scattered data of green s function we show that the infinitely smooth gaussian ga rbf has the best interpolation accuracy in order to improve the interpolation efficiency a new kind of staggered tartan grid is proposed a good calculation method for the shape parameter in ga rbf is given to solve its sensitivity to the group size and the number of interpolation points based on the analysis of variation of the number of interpolation points with electric length of the group adaptive choice of the types of interpolation functions and interpolation points are employed numerical examples show that the computational efficiency of this new interpolation scheme is much improved over the previously reported ones

convergence of the lloyd algorithm for computing centroidal voronoi tessellations centroidal voronoi tessellations cvts are voronoi tessellations of a bounded geometric domain such that the generating points of the tessellations are also the centroids mass centers of the corresponding voronoi regions with respect to a given density function centroidal voronoi tessellations may also be defined in more abstract and more general settings due to the natural optimization properties enjoyed by cvts they have many applications in diverse fields the lloyd algorithm is one of the most popular iterative schemes for computing the cvts but its theoretical analysis is far from complete in this paper some new analytical results on the local and global convergence of the lloyd algorithm are presented these results are derived through careful utilization of the optimization properties shared by cvts numerical experiments are also provided to substantiate the theoretical analysis

a simple mesh generator in matlab creating a mesh is the first step in a wide range of applications including scientific computing and computer graphics an unstructured simplex mesh requires a choice of meshpoints vertex nodes

new bounds and asymptotic expansions for the constants of landau and lebesgue abstract the constants of landau and lebesgue are defined for all integers n 0 in order by g n k 0 n 1 16 k 2 k k 2 and l n 1 2 sin n 1 2 t sin 1 2 t d t which play important roles in the theories of complex analysis and fourier series respectively in this paper we establish new bounds and asymptotic expansions for the constants of landau and lebesgue

learning based fast iterative convergence of 3 d mom via eigen agmres method three dimensional 3 d full wave electromagnetic simulation using method of moments mom under the framework of fast solver algorithms like fast multipole method fmm is often bottlenecked by the speed of convergence of the krylov subspace based iterative process this is primarily because the electric field integral equation efie matrix even with cutting edge preconditioning techniques often exhibits bad spectral properties arising from frequency or geometry based ill conditioning which render iterative solvers slow to converge or stagnate occasionally in this communication a novel technique to expedite the convergence of mom matrix solution at a specific frequency is proposed by extracting and applying eigen vectors from a previously solved neighboring frequency in an augmented generalized minimum residual agmres iterative framework this technique can be applied in unison with any preconditioner numerical results demonstrate up to 40 speed up in convergence using the proposed eigen agmres method

on the use of the singular value decomposition in the fast multipole method the authors present a new matrix compression algorithm to improve the efficiency of the fast multipole method fmm the method is based on the application of the singular value decomposition svd to the plane wave fmm aggregation matrices these matrices are low ranked which is exploited to provide alternative sets of orthonormal singular basis functions obtained as linear combinations of the original basis by choosing only the most relevant singular functions a much more compact representation is obtained to accurately handle the interactions between the fmm groups the new formulation provides a reduction close to one order of magnitude both in computational cost and memory requirements with a moderate impact on the accuracy of the solution

some sharp estimates of the constants of landau and lebesgue we establish several sharp two sided inequalities involving the constants of landau and lebesgue which occur and play important roles in two related extremal problems in complex analysis and in fourier analysis respectively the main results improves essentially the watson asymptotic expansion formulas for these constants

fast centroidal voronoi delaunay triangulation for unstructured mesh generation a fast unstructured mesh generation algorithm based on conforming centroidal voronoi delaunay triangulation cfcvdt algorithm ju 2007 is proposed in this paper in the new algorithm the constrained delaunay triangulation cdt algorithm is used only for the generation of the initial mesh the mesh quality shall be continuously improved by updating the positions of vertices and flipping edges in a number of iterations since the most time consuming procedure in cfcvdt algorithm is the cdt in each iteration which has been successfully avoided in this new algorithm the efficiency has been significantly improved furthermore the meshes generated by this algorithm have similar high quality features as that generated by cfcvdt when complex interfaces are involved our algorithm can keep the mesh conforming to the interfaces very efficiently by using various density functions this algorithm can produce high quality non uniform meshes for potentially many applications a fast high quality triangular mesh generation algorithm fcfcvdt is proposed based on the cfcvdt algorithm the fcfcvdt algorithm significantly improves the efficiency of cfcvdt algorithm at the same time maintains the mesh quality it is capable of generating high quality body interface fitted meshes for complicate domains interfaces

an openmp parallelized multilevel green s function interpolation method accelerated by fast fourier transform technique a parallelized multilevel green s function interpolation method mlgfim accelerated by fast fourier transform fft technique is proposed the difficulties in applying various improved interpolation schemes to effectively reduce the number of interpolation points are overcome by using the fft technique in order to accelerate the convergence property of the iterative solution using the proposed algorithm a recently proposed preconditioning scheme i e multiplicative calderon preconditioner is adopted to transform the first kind integral operator to the second kind albeit an increase of computer memory storage requirement an openmp parallel implementation of the mlgfim fft algorithm on a share memory computer system is developed to analyze various electrically large electromagnetic scattering problems including a nasa almond a 20 wavelength cylinder capped with two half spheres and a 37 wavelength cylinder array numerical results illustrate good computational performance of the proposed algorithm

centroidal voronoi tessellations applications and algorithms a centroidal voronoi tessellation is a voronoi tessellation whose generating points are the centroids centers of mass of the corresponding voronoi regions we give some applications of such tessellations to problems in image compression quadrature finite difference methods distribution of resources cellular biology statistics and the territorial behavior of animals we discuss methods for computing these tessellations provide some analyses concerning both the tessellations and the methods for their determination and finally present the results of some numerical experiments