Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 245, Issue -, Pages 148-161Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2012.12.018
Keywords
Numerical integration; Nearly singular integrals; Boundary element method; Sinh transformation
Categories
Ask authors/readers for more resources
A new method (the sinh-sigmoidal method) is proposed for the numerical evaluation of both nearly weakly and nearly strongly singular integrals on triangular boundary elements. These integrals arise in the 3D boundary element method when the source point is very close to the element of integration. The new polar coordinate-based method introduces a sinh transformation in the radial direction and a sigmoidal transformation in the angular direction, before the application of Gaussian quadrature. It also uses approximately twice as many quadrature points in the angular direction as in the radial direction, in response to a finding that the evaluation of these types of integrals is particularly sensitive to the placement of the quadrature points in the angular direction. Comparisons with various other methods demonstrate its accuracy and competitiveness. A major advantage of the new method is its ease of implementation and applicability to a wide class of integrals. (C) 2013 Elsevier B.V. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available