A fast adaptive algorithm for scattering from a two dimensional radially-symmetric potential
A fast adaptive algorithm for scattering from a two dimensional radially-symmetric potential
复制标题
二维径向对称势散射的快速自适应算法
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
V. Rokhlin
中科院分区：
文献类型：
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作者：
J. Hoskins;V. Rokhlin
在本文中，我们描述了一种简单的黑盒算法，用于有效且准确地解决与二维径向对称势的时谐波波散射相关的散射问题。该方法使用 FFT 将问题转换为散射场傅里叶系数的一组解耦第二类 Fredholm 积分方程。这些积分方程中的每一个都使用散射矩阵来求解，该矩阵利用了与积分方程相关的积分算子的某些低阶性质。该算法的性能通过几个数值示例进行了说明，包括奇异势和不连续势的散射。最后，上述方法可以很容易地扩展到与时间相关的问题。在概述了必要的修改之后，我们展示了数值实验，说明了算法在此设置下的性能。
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.
影响因子：
1.7
作者：
J. Bremer
通讯作者：
J. Bremer