Efficient evaluation of integrals in three-dimensional boundary element method using linear shape functions over plane triangular elements (Q1208812)

The proposed scheme appears to be more accurate and less computationally intensive than the schemes proposed earlier: the basic idea to evaluate double integrals appearing in the boundary element method - expressed by the shape functions for a linear triangle --- is to determine analytically one integration (thus contributing heavily to the accuracy) and to evaluate the remaining line integral by a Gaussian quadrature chosen especially. Results are discussed for the singular case where the source point is at a node (resulting in a fully analytical integration), for the nonsingular case otherwise, and for ``nearly singular'' cases. Examples (integration of \(1/R\) and \(1/R^ 3\) with the distance \(R\) between the source point and the field point) show advantages (with respect to the number of integration points required to get a certain accuracy) and limitations (an extra effort in function evaluation arising from analytical integration) of the method.