一类介质散射问题的数值算法

针对一类时谐波在非均匀介质中的散射问题提出一种非多项式最小二乘有限元算法.首先应用人工吸收边界将区域截断成有界域,然后选取平面波函数构造逼近空间,最后利用解及其法向导在内边界处的跃度定义目标泛函进行计算.算法不仅能够有效的处理小波数情形,而且适用于大波数情形.算法数值模拟过程易于实现,数值实验检验了算法的有效性.

Numerical Approach to Compute a Kind of Medium Scattering

Focused on a kind of scattering problem of time harmonic wave in inhomogeneous medium,we propose a non-polynomial finite element method. The domain is first truncated into a bounded one by the artificial absorbing boundary. Then plane wave functions are used as the basis functions to construct the discrete space. Finally,the objective functional for computation is defined by the jump of the solution and its normal derivative on the interfaces. The algorithm can not only deal well with the problem with small wave number,but also apply to the case of big wave number. And its implementation is also simple. Numerical simulation for the algorithm is presented to illustrate the effectiveness of the approach.