Efficient Computation of Highly Oscillatory Fourier Transforms with Nearly Singular Amplitudes over Rectangle Domains
Efficient Computation of Highly Oscillatory Fourier Transforms with Nearly Singular Amplitudes over Rectangle Domains
复制标题
矩形域上具有近奇异振幅的高振荡傅里叶变换的高效计算
DOI：
10.3390/math8111930
复制
发表时间：
2020-11-01
期刊：
影响因子：
2.4
通讯作者：
Ma, Junjie
中科院分区：
文献类型：
--
作者：
Yang, Zhen;Ma, Junjie
In this paper, we consider fast and high-order algorithms for calculation of highly oscillatory and nearly singular integrals. Based on operators with regard to Chebyshev polynomials, we propose a class of spectral efficient Levin quadrature for oscillatory integrals over rectangle domains, and give detailed convergence analysis. Furthermore, with the help of adaptive mesh refinement, we are able to develop an efficient algorithm to compute highly oscillatory and nearly singular integrals. In contrast to existing methods, approximations derived from the new approach do not suffer from high oscillatory and singularity. Finally, several numerical experiments are included to illustrate the performance of given quadrature rules.
