论文标题
快速自适应算法，用于从二维径向对称电势散射的快速自适应算法
A fast adaptive algorithm for scattering from a two dimensional radially-symmetric potential
论文作者
论文摘要
在本文中，我们描述了一种简单的黑匣子算法，用于有效，准确地求解与二维中径向对称电势的时谐波散射有关的散射问题。该方法使用FFT将问题转换为一组散射场傅立叶系数的脱钩的第二种弗雷姆积分方程。这些积分方程中的每一个都使用散射矩阵求解，该矩阵利用了与积分方程相关的积分运算符的某些低级别属性。用几个数值示例说明了算法的性能，包括来自奇异和不连续电位的散射。最后，上述方法可以很容易地扩展到时间依赖的问题。概述了必要的修改后，我们显示了数字实验，以说明在这种情况下算法的性能。
In the present paper we describe a simple black box algorithm for efficiently and accurately solving scattering problems related to the scattering of time-harmonic waves from radially-symmetric potentials in two dimensions. The method uses FFTs to convert the problem into a set of decoupled second-kind Fredholm integral equations for the Fourier coefficients of the scattered field. Each of these integral equations are solved using scattering matrices, which exploit certain low-rank properties of the integral operators associated with the integral equations. The performance of the algorithm is illustrated with several numerical examples including scattering from singular and discontinuous potentials. Finally, the above approach can be easily extended to time-dependent problems. After outlining the necessary modifications we show numerical experiments illustrating the performance of the algorithm in this setting.
