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The semianalytical analysis of nearly singular integrals in 2D potential problem by isogeometric boundary element method
Author(s) -
Han Zhilin,
Huang Yifan,
Cheng Changzheng,
Liang Yongcheng,
Hu Zongjun,
Niu Zhongrong
Publication year - 2020
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6370
Subject(s) - boundary element method , discretization , singular integral , mathematics , mathematical analysis , invertible matrix , quadrature (astronomy) , singular boundary method , isogeometric analysis , numerical analysis , volume integral , exponential function , transformation (genetics) , boundary (topology) , numerical integration , boundary value problem , finite element method , integral equation , physics , pure mathematics , biochemistry , chemistry , gene , optics , thermodynamics
Benefited from the accuracy improvement in modeling physical problem of complex geometry and integrating the discretization and simulation, the isogeometric analysis in boundary element method (IGABEM) has been drawn a great deal of attention. The nearly singular integrals of 2D potential problem in the IGABEM are addressed by a semianalytical scheme in the present work. We use the subtraction technique to separate the integrals to singular and nonsingular parts, where the singular parts can be calculated by the analytical formulae derived by utilizing a series of integration by parts, while the nonsingular parts are calculated numerically with fewer quadrature points. Comparing the present semianalytical results with the ones of exact solutions, we find that the present method can obtain precise potential and flux densities of inner points much closer to the boundary without refining the elements nearby. Sufficient comparisons with other regularization schemes, such as the exponential and sinh transformation methods, are also conducted. The results in the numerical examples show the competitiveness of the present method, especially when calculating the nearly strongly and highly singular integrals during the simulation of the flux density.