多维超奇异积分的近似计算
APPROXIMATE CALCULATION OF MULTI-DIMENSIONAL HYPERSINGULAR INTEGRALS
李金 1张宇鑫1
作者信息
- 1. 华北理工大学理学院,唐山 063000
- 折叠
摘要
多维超奇异积分在弹性力学和电磁场的散射问题等诸多工程领域中有广泛应用.考虑构造二维、三维面型超奇异积分的求积公式,同时提高误差精度.利用复合矩形求积公式在划分的N个子区间内近似计算被积函数中无奇异性的部分,剩余部分通过超奇异积分的解析式求解.根据外推思想,构造一维超奇异积分的修正复合矩形求积公式.最后将带有外推的求积公式推广到二维、三维面型超奇异积分中.文章结尾的数值算例验证了方法的可行性.
Abstract
Multi-dimensional hypersingular integrals are widely used in many engineering fields such as elasticity and scattering of electromagnetic fields.In order to improve the calculation accuracy,we construct the formula of two-dimensional and three-dimensional hypersingular integrals.In this paper,the composite rectangle quadrature formula is used to approximate the part without singularity in the divided N subinterval and the remaining part is solved by the analytic expression of the hypersingular integral.Based on the extrapolation,the modified composite rectangle quadrature formula of one-dimensional hypersingular integral is constructed.Finally,the modified rectangle quadrature formula is extended to the numer-ical quadrature of two-dimensional and three-dimensional surface hypersingular integrals.Numerical examples at the end of the paper verify the feasibility of the proposed method.
关键词
二维超奇异积分/三维面型超奇异积分/复合矩形求积/外推法Key words
Two-dimensional hypersingular integral/Three-dimensional hypersingular integral,Composite rectangle quadrature/Extrapolation method引用本文复制引用
基金项目
国家自然科学基金(11771398)
河北省自然科学基金(A2019209533)
出版年
2024
NETL
NSTL
万方数据