The regularising transformation integration method for boundary element kernels. Comparison with series expansion and weighted Gaussian integration methods

• Published in: Engineering analysis with boundary elements Vol. 6; no. 2; pp. 66 - 71
• Main Authors: Aliabadi, M.H., Hall, W.S.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.06.1989; Elsevier
• Subjects: boundary element method; Exact sciences and technology; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis. Scientific computation; potential problems; Sciences and techniques of general use; series expansion integration method; singular kernel integration; transformation integration method; weighted Gaussian integration method; singular kernel integration; weighted Gaussian integration method; transformation integration method; boundary element method; series expansion integration method; potential problems; Singularity; Three dimensional model; Weighting; Series expansion; Gauss method; Three dimensional space; Numerical method; Comparative study; Boundary element method
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/0955-7997(89)90001-5

The paper is concerned with singular integrands arising from three dimensional potential problems in the Boundary Element Method. These consist of the product of a shape function, a Jacobian and kernel which is singular at points on the boundary. Three schemes for dealing with such integrands are considered; the triangle to square regularising transformation, series expansions combined with subtraction out of the singularities, and weighted Gaussian integration formulae. Integrations using these schemes for plane parallelogram and spherical patch test elements for which exact integrals are known show that the Gaussian formulae do not give good results whereas the expansion/subtraction and regularising transformation schemes give very accurate integrations. It is suggested that the expansion/subtraction method would apply to a wider variety of kernels than the regularising transformation method.