QUADRATURE METHODS FOR HIGHLY OSCILLATORY SINGULAR INTEGRALS

作     者：Jing Gao Marissa Condon Arieh Iserles Benjamin Gilvey Jon Trevelyan Jing Gao;Marissa Condon;Arieh Iserles;Benjamin Gilvey;Jon Trevelyan

作者机构：School of Mathematics and StatisticsXi'an Jiaotong UniversityXi'an 710049China School of Electronic EngineeringDublin City UniversityIreland DAMTPCentre for Mathematical SciencesUniversity of CambridgeUK Department of EngineeringDurham UniversityUK 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2021年第39卷第2期

页      面：227-260页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：The work is supported by Royal Society International Exchanges(grant IE141214) the Projects of International Cooperation and Exchanges NSFC-RS(Grant No.11511130052) the Key Science and Technology Program of Shaanxi Province of China(Grant No.2016GY-080) the Fundamental Research Funds for the Central Universities 

主　　题：Numerical quadrature Singular highly oscillatory integrals Asymptotic analysis Boundary Element Method Plane wave enrichment Partition of Unity 

摘      要：We address the evaluation of highly oscillatory integrals,with power-law and logarithmic *** problems arise in numerical methods in ***,the evaluation of oscillatory integrals dominates the run-time for wave-enriched boundary integral formulations for wave scattering,and many of these exhibit *** show that the asymptotic behaviour of the integral depends on the integrand and its derivatives at the singular point of the integrand,the stationary points and the endpoints of the integral.A truncated asymptotic expansion achieves an error that decays faster for increasing *** on the asymptotic analysis,a Filon-type method is constructed to approximate the *** an asymptotic expansion,the Filon method achieves high accuracy for both small and large ***-valued quadrature involves interpolation at the zeros of polynomials orthogonal to a complex weight *** results indicate that the complex-valued Gaussian quadrature achieves the highest accuracy when the three methods are ***,while it achieves higher accuracy for the same number of function evaluations,it requires signi cant additional cost of computation of orthogonal polynomials and their zeros.