a novel parallel parabolic equation method for electromagnetic scatterings the alternating group explicit age scheme together with the alternating direction implicit adi scheme is used for the parabolic equation pe method to analyze the electromagnetic scattering from electrically large conducting targets the calculation can be taken plane by plane by using the finite difference scheme along the paraxial direction furthermore each transverse plane is divided into two regions which are a small region around the target and an outer region combined with the air layer and a perfect matching layer the adi scheme is applied to the small region whereas the age scheme is introduced to the outer region in this manner only a few matrix equations are needed to be solved for the small region and the unknowns of the outer region can be directly obtained without solving any matrix equations therefore the cpu time can be reduced significantly by the proposed method and it can be easily adapted to the parallel technology the numerical results verify the accuracy and efficiency of the proposed method compared with the crank nicolson based pe method and the adi based pe method moreover the parallel efficiency is given as the last numerical example

construction of dual b spline functions using new properties of dual functions we show that the method of constructing the dual bases recently presented in p wozny construction of dual bases journal of computational and applied mathematics 245 2013 75 85 can be significantly simplified next we propose a simple algorithm of constructing the dual b spline functions which can be useful in solving some approximation problems related to numerical analysis or computer graphics

a novel marching on in degree solver of time domain parabolic equation for transient em scattering analysis a novel marching on in degree mod solver of 3 d time domain parabolic equation is proposed to solve the transient electromagnetic scattering from electrically large perfect electric conductor pec targets the finite difference fd scheme is applied to the spatial discretization while the weighted laguerre polynomials are used as the temporal basis functions in this way a large number of computational resources can be saved by using the fd scheme along the paraxial direction and the late time stability can be guaranteed by the mod method both the fd schemes of crank nicolson and the alternating direction implicit types are discussed in this communication numerical results are given to demonstrate the accuracy and efficiency of the proposed method

electromagnetic scattering from 3 d targets in a random medium using finite difference frequency domain in this paper a three dimensional 3 d numerical technique based on the finite difference frequency domain fdfd is implemented to calculate the scattering from arbitrary shaped objects embedded in a continuous random medium the total field scattered field tf sf algorithm is integrated with the fdfd to minimize the memory consumption and speed up the calculations for validation purposes the radar cross section of a 2 d conducting cylinder in random medium is calculated using the fdfd technique and compared to previously published data based on the current generator method an upgrade to a 3 d solver was then inspired once the idea of using the multi grid technique was introduced to accelerate the convergence rate of the bicgstab iterative solver thus allowing the fdfd technique to become a robust method to solve the scattering problem from large targets embedded in random medium therefore using the introduced simulating scheme one can easily elucidate any scattering information out of real life targets surrounded by random environmental effects

plane wave scattering from three dimensional multiple objects using the iterative multiregion technique based on the fdfd method an iterative approach using the finite difference frequency domain method is presented in this paper in order to solve the problem of scattering from large three dimensional electromagnetic scatterers the idea of iterative multiregion technique is introduced to divide one computational domain into smaller subregions and solve each subregion separately then the subregion solutions are combined iteratively to obtain a solution for the complete domain as a result a considerable reduction in the computation time and memory has been achieved

on the eigenvalues of the electrostatic integral operator abstract a fundamental result in scattering and potential theory in r 3 states that the spectrum of the electrostatic integral operator lies in the interval 1 1 in the case of a sphere and a prolate spheroid it is known that the spectrum of the operator lies in the interval 1 0 a fundamental question arises whether the spectrum of the operator always lies in this interval or whether there exists a smooth surface for which the electrostatic integral operator has a positive eigenvalue in this paper this question is answered a surface is produced whereby the underlying integral operator has a positive eigenvalue

perfectly matched layer truncation for parabolic wave equation models solutions of the parabolic wave equation are extended to complex values of the height variable the fast decay of the solutions in certain directions of the complex plane is used to improve parabolic wave equation solvers the solution is marched on a suitably chosen contour in the complex plane rather than on the real line this interpretation of berenger s perfectly matched layer allows extremely efficient truncation of the computational domain with a split step fourier algorithm the theory is developed for both the wide angle and narrow angle parabolic wave equations and numerical results are presented

on the magnetostatic integral operator for ellipsoids the magnetostatic integral operator in r3is of considerable interest in both scattering and potential theory as well as for its scalar pendant the electrostatic integral operator its eigenvalues and its eigenfunctions play a fundamental role in the theory of permanent magnetization while the eigenvalues of both operators are closely related explicit expressions for the eigenfunctions of the magnetostatic operator are known only in the case when the underlying surface is a sphere for the cases of ellipsoids and spheroids we present explicit expressions for the eigenvalues in terms of lame functions and associated legendre functions and expressions for eigenfunctions in terms of surface ellipsoidal and surface spheroidal harmonics respectively as an application the permanent magnetization of ellipsoids is discussed

perfectly matched absorbing layers for the paraxial equations a new absorbing boundary technique for the paraxial wave equations is proposed and analyzed numerical results show the efficiency of the method

fully discrete spectral methods for boundary integral equations on slender spheroids we develop fully discrete spectral boundary integral algorithms to solve interior and exterior potential boundary value problems on three dimensional slender spheroids our approach is based on identifying and using analytical solutions of associated generalised eigenvalue problems of boundary integral operators we generalise approximation theory results on the sphere using spheroidally appropriate eigenfunctions and solve an open problem of stability of spectral methods for first kind boundary integral equations on spheroids

numerical simulation of bor scattering and radiation using a higher order fem numerical simulations of body of revolution geometries for scattering and radiation problems are presented the formulation consists of a finite element boundary integral fe bi method which is based on a finite element method that uses higher order nodal based scalar basis functions for the azimuthal field component and higher order edge based vector basis functions for the transverse field this formulation when combined with a symmetric fe bi hybridization scheme yields a final system of equations that is more accurate than earlier first order formulations numerical examples are given to demonstrate the accuracy and capabilities of the higher order solution

a finite difference treatment of interface conditions for the parabolic wave equation the irregular interface a finite difference solution to the parabolic wave equation is extended to treat an irregular interface interface conditions are developed to preserve continuity of pressure and continuity of the normal component of particle velocity at the boundary between media having different sound speeds and densities a complete mathematical treatment for the case of an irregular interface is presented to demonstrate the method numerical results are obtained for sound propagation from deep to shallow water

target scattering calculations with the parabolic equation method the parabolic equation technique is used to solve the helmholtz equation in the presence of scatterers of arbitrary shape in two and three dimensions the scattered field is computed directly using non homogeneous boundary conditions on the scattering object to represent the incident field effectively this decouples the pe paraxial direction from the direction of incidence for convex objects the whole range of scattering angles can be covered with a small number of narrow angle calculations finite difference implementations involve tridiagonal matrices in two dimensions and more general sparse matrices in three dimensions the resulting codes can be used to solve scattering problems for objects ranging in size from a few wavelengths to hundreds of wavelengths the method has been tested against analytical solutions for soft and rigid circular cylinders in 2d and soft and rigid spheres in 3d showing good agreement at all scattering angles

a dual functional to the univariate b spline in this paper dual functionals with local supports to the univariate b splines are constructed by symmetrization which are a linear combination of function values

a numerical scheme for the solution of the vector parabolic equation governing the radio wave propagation in straight and curved rectangular tunnels a high frequency field prediction model useful to evaluate the radio wave propagation in realistic tunnels having rectangular cross section is presented the model is based on a hybrid implicit explicit finite difference numerical scheme adopted to solve the vector parabolic equation vpe governing the electromagnetic field propagation in straight and curved tunnels to model the materials forming the tunnel walls mixed dirichlet von neumann boundary conditions are employed in this way all the relevant field propagation processes are properly taken into account to show the feasibility of the proposed numerical method results concerning the spatial distribution of the electromagnetic field and the power flux in straight and curved rectangular tunnels are provided an analysis concerning the convergence properties of the proposed numerical scheme is also reported

a vector meshless parabolic equation method for three dimensional electromagnetic scatterings the three dimensional 3 d vector parabolic equation pe method was used for electromagnetic scattering with reasonable accuracy the algorithm was marched from plane to plane along some preferred directions so that the computational load could be reduced significantly however the traditional 3 d pe method was discretized with the finite difference fd scheme and was not flexible for complex geometries in this paper the radial point interpolation meshless rpim method is used for its flexibility to model complex geometries in each transverse plane when the pe method is applied to analyze the electromagnetic scattering from electrically large objects numerical results demonstrate that the proposed technique can efficiently give reasonably accurate results for the complex objects when compared with both the multilevel fast multipole method mlfmm and the traditional pe method

the method of ordered multiple interactions for closed bodies boundary integral methods for calculating bistatic scatter start with a specified sample grid over the surface that defines the scatterer whereas standard method of moments mom implementations can be applied independent of the mesh structure the method of ordered multiple interactions momi effectively defines a surface trajectory over the sample grid this paper introduces source directed slice sampling whereby a variant of the momi method applied to three dimensional 3d objects becomes a strict forward backward recursion applications of momi to 1d rough surfaces first demonstrated the rapid convergence that can be obtained when the surface sampling follows the projected direction of the incident radiation with a 3d object source directed sampling can be implemented with no projection although the surface must be resampled for each new source direction the first iteration of the momi recursion makes a partial backward correction with strict forward backward sampling the initial forward sweep which we call the forward approximation often provides a good approximation to the source currents the results are demonstrated for the scalar problem but the extension to the vector problem is straightforward

a point interpolation meshless method based on radial basis functions a point interpolation meshless method is proposed based on combining radial and polynomial basis functions involvement of radial basis functions overcomes possible singularity associated with the meshless methods based on only the polynomial basis this non singularity is useful in constructing well performed shape functions furthermore the interpolation function obtained passes through all scattered points in an influence domain and thus shape functions are of delta function property this makes the implementation of essential boundary conditions much easier than the meshless methods based on the moving least squares approximation in addition the partial derivatives of shape functions are easily obtained thus improving computational efficiency examples on curve surface fittings and solid mechanics problems show that the accuracy and convergence rate of the present method is high copyright 2002 john wiley sons ltd

construction of dual bases let b n b 0 b 1 b n n 0 1 n n n be the sets of linearly independent functions we give a simple method of construction the dual functions d n d 0 n d 1 n d n n 0 n n satisfying the following conditions spand n spanb n and d i j 0 i j n n where d i i 1 d i j 0 for i j and is a given inner product the proposed algorithm allows us to construct all the sets of the dual functions d 0 d 1 d n in the time o n 3 where n is a natural number four illustrative examples presenting the possible applications of obtained results are given

electromagnetic uncertainty analysis using stochastic fdfd method this paper presents a novel stochastic finite difference frequency domain s fdfd method that incorporates the statistical variations of electrical properties directly into the fdfd algorithm by using the delta method approximation the method is validated through two examples a 1 d bioelectromagnetic layered model and specific absorption rate in a 2 d slice of a human head model comparisons between the single run s fdfd results and those of the monte carlo method the benchmark in statistical simulations show that the s fdfd method can predict the mean and variance of electromagnetic fields with a fair degree of accuracy in a computationally efficient way our numerical experiment also shows that the accuracy is highly dependent on the approximation for the correlation coefficients of the variance equations

a spectral property of the electrostatic integral operator for an ellipsoid the eigenfunctions of the electrostatic integral operator and its adjoint are governed by the lame polynomials it is shown that the arithmetic mean of the eigenvalues corresponding to the maximum number of linearly independent eigenfunctions of equal order is the same for the ellipsoid as for the sphere

a split step pade solution for the parabolic equation method a split step pade solution is derived for the parabolic equation pe method higher order pade approximations are used to reduce both numerical errors and asymptotic errors e g phase errors due to wide angle propagation this approach is approximately two orders of magnitude faster than solutions based on pade approximations that account for asymptotic errors but not numerical errors in contrast to the split step fourier solution which achieves similar efficiency for some problems the split step pade solution is valid for problems involving very wide propagation angles large depth variations in the properties of the waveguide and elastic ocean bottoms the split step pade solution is practical for global scale problems

an alternative direction decomposition scheme and error analysis for parabolic equation model alternate direction implicit adi method has been widely used to analyze the tunnel propagation or electromagnetic scattering problem for the finite difference method in this paper a novel alternate direction decomposition add scheme is proposed to simplify the split step fourier transform ssft algorithm in parabolic equation pe model the spatial matrix of electric field is decoupled into two subarrays by add ssft algorithm which is used to decrease the computational burden for 3 d pe problems in a large scale environment after the integration order exchanged also the phase error of this approximation is analyzed to show the algorithm performance along with several numerical results including the tunnel cases with traditional modal theory and they are provided to validate and calibrate the pe model and demonstrate the efficiency and accuracy of the proposed algorithm moreover the scattering computation is investigated and compared with multilevel fast multipole method to show that add ssft is appropriate for solving the scattering problems for the electrical large target