Numerical evaluation of two-dimensional singular boundary integrals—Theory and Fortran code

• Published in: Journal of computational and applied mathematics Vol. 188; no. 1; pp. 44 - 64
• Main Author: Gao, Xiao-Wei
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2006; Elsevier
• Subjects: Approximations and expansions; Boundary element; Boundary integral; Exact sciences and technology; Fortran subroutine; Gaussian quadrature; Mathematical analysis; Mathematics; Measure and integration; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Sciences and techniques of general use; Singular integrals; Singular integrals; Boundary integral; Boundary element; Gaussian quadrature; Fortran subroutine; Boundary integral method; Numerical approximation; Numerical analysis; Cubature; Applied mathematics; Cauchy principal value; FORTRAN; Two-dimensional calculations; Quadrature formula; Cauchy integral; Boundary element method
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2005.03.051

In this paper, an approach is presented for the numerical evaluation of weakly, strongly, hyper- and super-singular boundary integrals which exist in the Cauchy principal value sense in two-dimensional problems. In this approach, the singularities involved in integration kernels are analytically removed by expressing the nonsingular parts of the integration kernels as polynomials of the distance r . A self-contained Fortran code is listed and described for implementation of the proposed approach. The attached code is also able to evaluate general regular integrals using Gaussian quadrature, which enables the code to evaluate any two-dimensional boundary integral. Some examples are provided to verify the correctness of the presented formulations and the included code.