A Review on Techniques of Domain Integrals Computation in Boundary Elements Method

In this article, a review of the evaluation methods of the domain integrals in the boundary element method will be presented. The emergence of domain integrals in the formulation of the boundary element method mainly originates from the inertia term in dynamic problems, body forces in static problems or the effects of material heterogeneity. There are several approaches to calculate boundary and domain integrals in boundary element methods. Choosing the type of integration method has a prominent effect on the accuracy of the numerical solution. In this research, a comprehensive review on the techniques of domain integrals computation will be presented based on two approaches, i.e. domain splitting, and converting the domain integrals to boundary ones. The review focuses primarily on the formulation of approaches without requiring domain splitting, because of their popularity. Among them, the dual reciprocity method and the radial integration method have been described as the most efficient. At the end, the details of the modified radial integration method for calculating the integrals within non-convex domains will be stated.