A New Approach for Numerical Evaluation of High Order 3D Singular Boundary Integrals

2010 ◽  
Author(s):  
Xiao-Wei Gao ◽  
Jane W. Z. Lu ◽  
Andrew Y. T. Leung ◽  
Vai Pan Iu ◽  
Kai Meng Mok
Keyword(s):  
Numerical Evaluation ◽  
High Order ◽  
Singular Boundary ◽  
Boundary Integrals ◽  
New Approach

scholarly journals Numerical Evaluation of Arbitrary Singular Domain Integrals Using Third-Degree B-Spline Basis Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Jin-Xiu Hu ◽  
Hai-Feng Peng ◽  
Xiao-Wei Gao
Keyword(s):  
Numerical Evaluation ◽  
Boundary Integral ◽  
Basis Functions ◽  
Boundary Integrals ◽  
New Approach ◽  
B Spline ◽  
Radial Integral ◽  
Integral Formulas ◽  
Spline Basis ◽  
Singular Domain

A new approach is presented for the numerical evaluation of arbitrary singular domain integrals. In this method, singular domain integrals are transformed into a boundary integral and a radial integral which contains singularities by using the radial integration method. The analytical elimination of singularities condensed in the radial integral formulas can be accomplished by expressing the nonsingular part of the integration kernels as a series of cubic B-spline basis functions of the distancerand using the intrinsic features of the radial integral. In the proposed method, singularities involved in the domain integrals are explicitly transformed to the boundary integrals, so no singularities exist at internal points. A few numerical examples are provided to verify the correctness and robustness of the presented method.

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