共查询到20条相似文献,搜索用时 437 毫秒
1.
We present a second kind integral equation (SKIE) formulation for calculating the electromagnetic modes of optical waveguides, where the unknowns are only on material interfaces. The resulting numerical algorithm can handle optical waveguides with a large number of inclusions of arbitrary irregular cross section. It is capable of finding the bound, leaky, and complex modes for optical fibers and waveguides including photonic crystal fibers (PCF), dielectric fibers and waveguides. Most importantly, the formulation is well conditioned even in the case of nonsmooth geometries. Our method is highly accurate and thus can be used to calculate the propagation loss of the electromagnetic modes accurately, which provides the photonics industry a reliable tool for the design of more compact and efficient photonic devices. We illustrate and validate the performance of our method through extensive numerical studies and by comparison with semi-analytical results and previously published results. 相似文献
2.
Eliseo Hernandez-MartinezFrancisco J. Valdes-Parada Jose Alvarez-Ramirez 《Journal of Computational and Applied Mathematics》2011,235(9):3096-3103
Reaction-diffusion equations are commonly used in different science and engineering fields to describe spatial patterns arising from the interaction of chemical or biochemical reactions and diffusive transport mechanisms. The aim of this work is to show that a Green’s function formulation of reaction-diffusion PDEs is a suitable framework to derive FD schemes incorporating both O(h2) accuracy and nonlocal approximations in the whole domain (including boundary nodes). By doing so, the approach departs from a Green’s function formulation of the boundary-value problem to pose an approximation problem based on a domain decomposition. Within each subdomain, the corresponding integral equation is forced to have zero residual at given grid points. Different FD schemes are obtained depending on the numerical scheme used for computing the Green’s integral over each subdomain. Dirichlet and Neumann boundary conditions are considered, showing that the FD scheme based on the Green’s function formulation incorporates, in a natural way, the effects of boundary nodes in the discretization approximation. 相似文献
3.
V. A. Titarev S. V. Utyuzhnikov E. M. Shakhov 《Computational Mathematics and Mathematical Physics》2013,53(8):1221-1230
The kinetic S-model is used to study the steady rarefied gas flow through a long pipe of variable cross section joining two tanks with arbitrary differences in pressure and temperature. The kinetic equation is solved numerically by applying a second-order accurate conservative method on an unstructured mesh. The basic quantity to be computed is the gas flow rate through the pipe. The possibility of finding a solution based on the assumption of the plane cross sectional flow is also explored. The resulting solutions are compared with previously known results. 相似文献
4.
A. V. Vinogradov A. V. Popov D. V. Prokopovich 《Computational Mathematics and Mathematical Physics》2009,49(6):1069-1079
A method for the parameterization of the one-dimensional wave equation is proposed that makes it possible to find its solution by quadratures under an arbitrary dependence of the refraction index on the current wave phase. The form of the solution found is used to investigate the structure of the wave function for a periodic refraction index. Explicit expressions for the fundamental system of solutions and for the Floquet index are obtained. Examples of applying the proposed method to the optimal synthesis of multilayer interference mirrors and Bragg waveguides are discussed. 相似文献
5.
Habib Ammari Alexander Dabrowski Brian Fitzpatrick Pierre Millien Mourad Sini 《Mathematical Methods in the Applied Sciences》2019,42(18):6567-6579
This paper aims at understanding the nature of the subwavelength resonant frequencies of dielectric particles with high refractive indices. It is proved that for an arbitrary shaped particle, these subwavelength resonant frequencies can be expressed in terms of the eigenvalues of the Newtonian potential associated with its shape. The enhancement of the scattered field at the resonant frequencies is shown. The hybridization of the subwavelength resonant frequencies of a dimer consisting of high refractive index dielectric nanoparticles is also characterized. 相似文献
6.
Approximate expressions are obtained for the field producedwhen an electromagnetic source field is diffracted by a dielectricwedge. The boundary value problem, of the diffraction of an E-or H-pokarizedelectromagnetic line source by an arbitrary angled dielectricwedgeis formulated, and its solution is given in the form ofa Fredholm integral equation. The solution of the integral equationis obtained by a standard perturbation technique. The perturbationparameter is dependent on the refractive index of the dielectricwedge. The right angle dielectric wedge, which is illuminatedby an E-polarized plane wate, and whose refractive index (=n)is such that 1<n < 2, is considered in detail. 相似文献
7.
A new finite difference (FD) method, referred to as "Cartesian cut-stencil
FD", is introduced to obtain the numerical solution of partial differential equations
on any arbitrary irregular shaped domain. The 2nd-order accurate two-dimensional
Cartesian cut-stencil FD method utilizes a 5-point stencil and relies on the construction of a unique mapping of each physical stencil, rather than a cell, in any arbitrary
domain to a generic uniform computational stencil. The treatment of boundary conditions and quantification of the solution accuracy using the local truncation error
are discussed. Numerical solutions of the steady convection-diffusion equation on
sample complex domains have been obtained and the results have been compared
to exact solutions for manufactured partial differential equations (PDEs) and other
numerical solutions. 相似文献
8.
The problem of the nonrectilinear steady-state flow of a nonlinear viscoelastic liquid in cylindrical channels is considered. It is established that in channels whose cross sections form an equilateral triangle or an isosceles right-angled triangle there are six transverse currents (eddies) in a plane perpendicular to the main longitudinal flow. In cylinders with cross sections in the form of an arbitrary triangle there may be four or six eddies, depending on the shape of the triangle. 相似文献
9.
The inverse problem of electromagnetic sounding of the shape of a conducting body is considered in the framework of the two-dimensional
model with E-polarization, assuming a cylindrical body of an arbitrary cross section embedded in a layered medium. The integral
equations are obtained for the case of an ideally conducting body and a body of finite conductivity. The linearization method
is applied to obtain an iterative method that finds a correction to the initial shape.
Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 96–103. 相似文献
10.
Yu. K. Podlipenko 《Ukrainian Mathematical Journal》1993,45(4):535-557
We investigate boundary-value problems that appear in the study of the diffraction of acoustic waves on an infinite cylinder (with a cross section of an arbitrary shape) placed inside a wedge so that the axis of the cylinder is parallel to the edge of the wedge. The potential theory which enables one to reduce these boundary-value problems to integral equations is elaborated.Translated from Ukrainskii Matematicheskii Zhumal, Vol. 45, No. 4, pp. 500–519, April, 1993. 相似文献
11.
Luis A. Florit 《Differential Geometry and its Applications》2007,25(1):23-28
By means of a simple warped product construction we obtain examples of submanifolds with nonpositive extrinsic curvature and minimal index of relative nullity in any space form. We then use this to extend to arbitrary space forms four known splitting results for Euclidean submanifolds with nonpositive sectional curvature. 相似文献
12.
The authors study a one-dimensional model for optical tunnellingwith a refractive index in the shape of a square well. The relevanceof the model and its limiting cases are discussed. The mainresult is the leading behaviour of the exponentially small imaginarypart of the eigenvalue which determines the radiation loss.The leading behaviour of the imaginary part is calculated usingBerry's formula which controls the asymptotic expansion of theAiry function Bi(z) to better-than-exponential accuracy. 相似文献
13.
FDI对经济增长是否总是起到正面推进作用?进一步,该作用的发挥在多大程度上依赖于当地的金融发展水平?这是我国当前修订对外开放政策框架前所必须要考虑的问题。本文使用Hansen非动态面板门槛回归模型、采用我国1992-2012年省际面板数据对FDI对经济增长作用的金融发展门槛进行了实证分析。研究发现,与一般认为的FDI总能促进地区经济增长的观点不同,FDI对经济增长的作用具有明显的金融发展门槛效应,而且是双重门槛:当金融发展水平低于低门槛时,FDI对地区经济会有抑制作用;在高低门槛之间,FDI对经济增长会有比较显著的促进作用;高于高门槛时,FDI对地区经济的促进作用将逐步回落;金融发展双重门槛的存在使得FDI对经济增长的作用整体呈现倒U型。论文最后据此提出应根据地区金融发展程度实行差异性政策等相关的政策建议。 相似文献
14.
V. G. Litvinov 《Mechanics of Composite Materials》1967,3(2):224-228
The problem of the shape of a drawn viscoelastic extrudate of arbitrary cross section is investigated. The solution of the problem is represented as a superposition of the nonstationary extension under constant load and the motion determined by the throughput of the process. As an example, calculations are made for a circular polyethylene extrudate.Mekhanika Polimerov, Vol. 3, No. 2, pp. 326–333, 1967 相似文献
15.
L. Verhóczki 《Periodica Mathematica Hungarica》1995,31(1):71-83
In the present paper parallel submanifolds and focal points of a given submanifold with flat normal bundle are discussed provided that the ambient space has constant sectional curvature. We present shape operators of parallel submanifolds with respect to arbitrary normal vectors. Furthermore, we prove that the focal points of a submanifold with flat normal bundle form totally geodesic hypersurfaces in the normal submanifolds.Supported by Hungarian Nat. Found. for Sci. Research Grant No. 1615 (1991).Dedicated to Professor J. Strommer on the occasion of his 75th birthday 相似文献
16.
Fuhrmann’s state-space construction (in its generalized form) is used to obtain a general theory of first order representations of Fliess models defined over an arbitrary noetherian commutative ring. The case of arbitrary linear delay differential equations is involved. 相似文献
17.
In this article, homotopy analysis method (HAM) is employed to investigate non-linear large deformation of Euler–Bernoulli beams subjected to an arbitrary distributed load. Constitutive equations of the problem are obtained. It is assumed that the length of the beam remains constant after applying external loads. Different auxiliary parameters and functions of the HAM and the extra auxiliary parameter, which is applied to initial guess of the solution, are employed to procure better convergence rate of the solution. The results of the solution are obtained for two different examples including constant cross sectional beam subjected to constant distributed load and periodic distributed load. Special base functions, orthogonal polynomials e.g. Chebyshev expansion, are employed as a tool to improve the convergence of the solution. The general solution, presented in this paper, can be used to attain the solution of the beam under arbitrary distributed load and flexural stiffness. Ultimately, it is shown that small deformation theory overestimates different quantities such as bending moment, shear force, etc. for large deflection of the beams in comparison with large deformation theory. Finally, it is concluded that solution of small deformation theory is far from reality for large deflection of straight Euler–Bernoulli beams. 相似文献
18.
本文研究长波在三维变截面弯管中的传播问题.通过建立正交曲线坐标系,以波数k和管道横截面的特征半径a的乘积ka作为小参数,对波动方程进行无量纲处理,用正则摄动法,把三维的Helmholtz方程化为二维的Laplace(或Poisson)方程和一维的Webster方程.并分析了管道的几何参数(横截面面积、管道中心线的曲率和挠度)对复速度势渐近展开的各阶项的影响.文中指出,横截面面积的变化首先影响浙近解的零阶项.在横截面的形状具有某种对称性时,管道中心线的曲率首先影响渐近解的二阶项,而挠度首先影响渐近解的三阶项.最后,给出了长波在弯曲圆管中传播的实例. 相似文献
19.
20.
A. N. Agalakov S. B. Raevskii A. A. Titarenko 《Computational Mathematics and Mathematical Physics》2013,53(7):937-946
A rectangular shielded waveguide with arbitrary anisotropic filling is used to describe a spectral approach to the computation of longitudinal regular shielded waveguides filled in part with a nonreciprocal medium whose parameters have an arbitrary dependence on the transverse coordinates. Numerical results are presented that confirm the validity of the algorithms developed. 相似文献