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Numerical studies on desingularized Cauchy's formula with applications to interior potential problems
Author(s) -
Chuang J. M.
Publication year - 1999
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/(sici)1097-0207(19991030)46:6<805::aid-nme681>3.0.co;2-n
Subject(s) - gaussian quadrature , cauchy distribution , mathematics , classification of discontinuities , discretization , mathematical analysis , collocation (remote sensing) , boundary value problem , numerical integration , quadrature (astronomy) , integral equation , numerical analysis , nyström method , cauchy's integral formula , cauchy problem , gaussian , collocation method , initial value problem , differential equation , ordinary differential equation , computer science , physics , quantum mechanics , machine learning , electrical engineering , engineering
Abstract Based on the Cauchy's formula, a pair of fully desingularized real boundary integral equations is proposed for solving interior boundary value problems in the potential theory. With Gaussian points as the collocation points of the boundary integral equation, an arbitrary high‐order Gaussian quadrature can be used globally to discretize the integral equations. The numerical scheme is simple, efficient and accurate. Moreover, using Hölder's condition of the analytic function, the discontinuities of the tangential derivatives of the analytic function across the corner point is studied in detail. A numerical treatment for using corner point as a collocation point of the Gaussian quadrature is also developed. Two examples are included to demonstrate the superiority of usage of the desingularized Cauchy's formula and the developed numerical scheme. Copyright © 1999 John Wiley & Sons, Ltd.