Evaluation of regular and singular domain integrals with boundary-only discretization—theory and Fortran code

• Published in: Journal of computational and applied mathematics Vol. 175; no. 2; pp. 265 - 290
• Main Author: Gao, Xiao-Wei
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.03.2005; Elsevier
• Subjects: Boundary integral; Domain integral; Exact sciences and technology; Fortran subroutine; Mathematical analysis; Mathematics; Measure and integration; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Radial integration; Sciences and techniques of general use; Singular integrals; Domain integral; Singular integrals; Boundary integral; Radial integration; Fortran subroutine; Numerical integration; Subroutine; Radial integral; Singular integral; FORTRAN; Boundary integral method; Numerical method; Discretization method
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2004.05.012

In this paper, a set of boundary integrals are derived based on a radial integration technique to accurately evaluate two dimensional (2D) and three dimensional (3D), regular and singular domain integrals. A self-contained Fortran code is listed and described for numerical implementation of these boundary integrals. The main feature of the theory is that only the boundary of the integration domain needs to be discretized into elements. This feature cannot only save considerable efforts in discretizing the integration domain into internal cells (as in the conventional method), but also make computational results for singular domain integrals more accurate since the integrals have been regularized. Some examples are provided to verify the correctness of the presented formulations and the included code.