【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.更多还原

【Abstract】 We discussed the numerical computation of the scattering problems for two-dimensional Schrdinger equation(-Δ+V(x)-k2)u=0.For a class of specific potentials,i.e.,V(r)=b/rδ 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 Grding 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.更多还原