The radial integration method for evaluation of domain integrals with boundary-only discretization

• Published in: Engineering analysis with boundary elements Vol. 26; no. 10; pp. 905 - 916
• Main Author: Gao, Xiao-Wei
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.12.2002; Elsevier
• Subjects: Boundary element method; Boundary integral; Boundary-integral methods; Computational techniques; Domain integral; Dual reciprocity method; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; Physics; Radial basis function; Radial integration; Solid mechanics; Static elasticity; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Radial basis function; Domain integral; Boundary integral; Radial integration; Dual reciprocity method; Boundary element method; Singularity; Body force; Three dimensional model; Reciprocity theorem; Boundary integral method; Duality; Numerical method; Acceleration; Variable transformation; Structural analysis; Gravity
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/S0955-7997(02)00039-5

In this paper, a simple and robust method, called the radial integration method, is presented for transforming domain integrals into equivalent boundary integrals. Any two- or three-dimensional domain integral can be evaluated in a unified way without the need to discretize the domain into internal cells. Domain integrals consisting of known functions can be directly and accurately transformed to the boundary, while for domain integrals including unknown variables, the transformation is accomplished by approximating these variables using radial basis functions. In the proposed method, weak singularities involved in the domain integrals are also explicitly transformed to the boundary integrals, so no singularities exist at internal points. Some analytical and numerical examples are presented to verify the validity of this method.