Efficient evaluation of weakly/strongly singular domain integrals in the BEM using a singular nodal integration method

In many analyses of engineering problems based on boundary element methods, a large number of regular and/or singular domain integrals must be accurately evaluated over a single domain. Evaluation of such domain integrals is very time-consuming and is frequently the main source of errors and loss of accuracy in the solutions. Previous efforts have been constantly made in order to facilitate or overcome such shortcomings. In this article, we propose novel and efficient approaches in the framework of Cartesian transformation method (CTM) and the radial integration method (RIM) that can be used for fast evaluation of numerous weakly/strongly singular two-dimensional domain integrals over a single domain. The domain integrals essentially are expressed in terms of some coefficient matrices and vectors, most of which are independent of the integrand of the domain integrals and are dependent only on the geometry. Several examples for the evaluation of weakly/strongly singular domain integrals and two examples for the flow field analysis in micro-channels are presented and the accuracy and convergence of the proposed approaches are investigated.