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quadrature METHODS FOR HIGHLY OSCILLATORY SINGULAR INTEGRALS

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Journal of Computational Mathematics 2021年第2期39卷 227-260页

作者： Jing Gao Marissa Condon Arieh Iserles Benjamin Gilvey Jon Trevelyan School of Mathematics and Statistics Xi'an Jiaotong UniversityXi'an 710049China School of Electronic Engineering Dublin City UniversityIreland DAMTP Centre for Mathematical SciencesUniversity of CambridgeUK Department of Engineering Durham UniversityUK

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.

关键词： numerical quadrature Singular highly oscillatory integrals Asymptotic analysis Boundary Element Method Plane wave enrichment Partition of Unity

GALERKIN MESHLESS METHODS BASED ON PARTITION OF UNITY quadrature

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Applied Mathematics and Mechanics(English Edition) 2005年第7期26卷 893-899页

作者：曾清红卢德唐 Department of Mechanics and Mechanic Engineering University of Science and Technology of China Hefei 230027 P.R.China

numerical quadrature is an important ingredient of Galerkin meshless methods. A new numerical quadrature technique, partition of unity quadrature （PUQ）,for Galerkin meshless methods was presented. The technique is based on finite covering and partition of unity. There is no need to decompose the physical domain into small cell. It possesses remarkable integration accuracy. Using Element-free Galerkin methods as example, Galerkin meshless methods based on PUQ were studied in detail. Meshing is always not required in the procedure of constitution of approximate function or numerical quadrature, so Galerkin meshless methods based on PUQ are “truly” meshless methods.

关键词： Galerkin meshless method finite cover partition of unity numerical quadrature

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Efficient and accurate numerical-projection of electromagnetic multipoles for scattering objects

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Frontiers of Optoelectronics 2023年第4期16卷 215-226页

作者： Wenfei Guo Zizhe Cai Zhongfei Xiong Weijin Chen Yuntian Chen School of Optical and Electronic Information Huazhong University of Science and TechnologyWuhan 430074China Department of Electrical and Computer Engineering National University of SingaporeSingapore 117576Singapore Wuhan National Laboratory of Optoelectronics Huazhong University of Science and TechnologyWuhan 430074China Optics Valley Laboratory Wuhan 430074China

In this paper,we develop an efcient and accurate procedure of electromagnetic multipole decomposition by using the Lebedev and Gaussian quadrature methods to perform the numerical ***,we briefy review the principles of multipole decomposition,highlighting two numerical projection methods including surface and volume ***,we discuss the Lebedev and Gaussian quadrature methods,provide a detailed recipe to select the quadrature points and the corresponding weighting factor,and illustrate the integration accuracy and numerical efciency(that is,with very few sampling points)using a unit sphere surface and regular *** the demonstrations of an isotropic dielectric nanosphere,a symmetric scatterer,and an anisotropic nanosphere,we perform multipole decomposition and validate our numerical projection *** obtained results from our procedure are all consistent with those from Mie theory,symmetry constraints,and fnite element simulations.

关键词： Multipole decomposition numerical quadrature Light scattering

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A Kind of Algorithm on B-Spline Wavelet-BEM

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Wuhan University Journal of Natural Sciences 1999年第3期4卷 265-268页

作者： Cheng Yong-jun Yi Xu-ming Ye Bi-quan Shen Yuan-tong College of Mathematical and Computer Sciences Wuhan University Wuhan China Department of Mathematics and Physics China University of Geosciences Wuhan China

B-Spline wavelet-BEM numerical algorithm is presented. To avoid to treating singular integrals in wavelet-BEM, a method of putting source points out of the domain is used and discussed. Meanwhile, two higher effective numerical quadrature formulae are suggested. Finally, an example in mechanics is given and numerical results show that this method is effective. In addition, this method can be extended to manipulate problems, especially, with singularity.

关键词： Key words B Spline wavelet BEM numerical quadrature

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