On efficient computation of highly oscillatory retarded potential integral equations
On efficient computation of highly oscillatory retarded potential integral equations
复制标题
高振荡迟缓势积分方程的高效计算
DOI：
10.1080/00207160.2017.1380192
复制
发表时间：
2018-01-01
影响因子：
1.8
通讯作者：
Liu, Guidong
中科院分区：
文献类型：
--
作者：
Xiang, Shuhuang;Li, Bin;Liu, Guidong
本文基于高振荡的第一类沃尔泰拉积分方程的傅里叶逆变换和高效算法，提出了一种求解具有高振荡空间时谐入射波的延迟型位势积分方程的高效数值方法。从积分方程，它导致一个有效的近似，通过应用克伦肖-柯蒂斯型方法，成本相同的操作独立的大值的频率。应用傅里叶逆变换求解延迟势积分方程得到了数值结果。初步的数值结果表明了近似的效率和精度。
ABSTRACT This paper presents an efficient numerical method for retarded potential integral equations with highly oscillatory spatially time-harmonic incident waves, which is based on inverse Fourier transforms and efficient algorithms for the highly oscillatory Volterra integral equation of the first kind. From the integral equation, it leads to an efficient approximation by applying the Clenshaw–Curtis-type method which costs the same operations independent of large values of frequencies. Applying inverse Fourier transforms yields numerical results on solving the retarded potential integral equations. Preliminary numerical results show the efficiency and accuracy of the approximations.