求解一类二维Schrdinger方程散射问题的PML方法  

PML Method for Solving the Scattering Problems for a Class of Two-dimensional Schrdinger Equations

作　　者：李媛[1] 马富明[1] 

机构地区：[1]吉林大学数学研究所,长春130012

出　　处：《吉林大学学报（理学版）》2009年第2期233-239,共7页Journal of Jilin University:Science Edition

基　　金：国家重点基础研究发展计划973项目基金(批准号:2005CB321701)

摘　　要：讨论二维Schrdinger方程(-Δ+V(x)-k2)u=0散射问题的数值计算.针对一类特殊的位势,即在某一圆域Br0外,位势V(r)=b/rδ,其中b>0,δ>1均为常数,提出一种PML方法.首先通过复化极径得到PML方程,然后在关于吸收参数的假设下,证明了PML问题变分形式中的半双线性形式满足Grding不等式,进而证明了PML问题解的存在惟一性,并给出了数值实验.实验结果表明,该方法有一定的可行性.We discussed the numerical computation of the scattering problems for two-dimensional Schrodinger equation （ -△ ＋ V（x） - k^2 ） u = 0. For a class of specific potentials, i. e. , V（r） = b/r^δ outside a circular domain Br0, where both b 〉 0 and δ 〉 1 are constants, we presented a PML method. We first got the PML equations by making the radius complex, and then proved that the sesquilinear form in the weak formulation of the PML problem satisfies the Gotrding inequality under the hypothesis of the absorption factor, and further could prove the existence and uniqueness of the solutions of the PML problem, finally, we gave the numerical experiments which show that this method is feasible to a certain extent.

关 键 词：Schrdinger方程 散射问题 PML方法 

分 类 号：O241.82[理学—计算数学]