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Numerical quadratures for near-singular and near-hypersingular integrals in boundary element methods


Reference:

Carley, M., 2009. Numerical quadratures for near-singular and near-hypersingular integrals in boundary element methods. Mathematical Proceedings of the Royal Irish Academy, 109 (1), pp. 49-60.

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Official URL:

http://dx.doi.org/10.3318/PRIA.2008.109.1.49

Abstract

A method of deriving quadrature rules has been developed which gives nodes and weights for a Gaussian-type rule which integrates functions of the form: \[ f(x,y,t) = \frac{a(x,y,t)}{(x-t)^{2}+y^{2}} + \frac{b(x,y,t)}{[(x-t)^{2}+y^{2}]^{1/2}} + c(x,y,t)\log[(x-t)^{2}+y^{2}]^{1/2} + d(x,y,t), \] without having to explicitly analyze the singularities of $f(x,y,t)$ or separate it into its components. The method extends previous work on a similar technique for the evaluation of Cauchy principal value or Hadamard finite part integrals, in the case when $y\equiv0$. The method is tested by evaluating standard reference integrals and its error is found to be comparable to machine precision in the best case.

Details

Item Type Articles
CreatorsCarley, M.
DOI10.3318/PRIA.2008.109.1.49
DepartmentsFaculty of Engineering & Design > Mechanical Engineering
Research CentresAerospace Engineering Research Centre
RefereedYes
StatusPublished
ID Code13956

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