无界区域上波导问题的有效谱迦略金方法(英文)  

Efficient spectral-Galerkin method for waveguide problem in infinite domain

作　　者：赵晓丹[1] 王立联[1] 

机构地区：[1]南洋理工大学物理与数学科学学院数学科学系,新加坡637371

出　　处：《应用数学与计算数学学报》2013年第1期87-100,共14页Communication on Applied Mathematics and Computation

基　　金：supported by the Singapore MOE Academic Research Fund Tier 1(RG58/08);the Singapore A*Star-SERC-PSF(122-PSF-007)

摘　　要：旨在求解二维无界区域上的波导问题.通过在人工边界施加精确非反射边界条件(nonreflecting boundary condition,NRBC),可以将无界问题截断为有界问题,然后,给出了在空间上用傅里叶谱迦略金方法、时间上用Newmark格式和Richardson外插技巧的数值格式来求解该有界问题.介绍了一个快速的时间行进格式来处理包含在NRBC中的时间方向的卷积.提出的算法在空间和时间上都可以达到高阶精度.另外,也证明了该截断问题的适定性.This paper aims to solve a two-dimensional waveguide problem in an infinite domain. The unbounded problem is truncated into a bounded problem us- ing the exact nonreflecting boundary condition （NRBC） at the artificial boundary, and then a Fourier-Legendre spectral-Galerkin method in space and the Newmark scheme with a Richardson extrapolation technique in time are proposed for solving the truncated problem. A fast marching technique is introduced to deal with the temporal convolution in the NRBC. The proposed method can achieve high-order accuracy in both space and time. In addition, the well-posedness of the truncated problem is proved.

关 键 词：无界区域 非反射边界条件 卷积 谱迦略金方法 

分 类 号：O175[理学—数学] TN252[理学—基础数学]