NURBS-enhanced boundary element method based on independent geometry and field approximation for 2D potential problems

Non-uniform rational B-spline (NURBS) in Isogeometric analysis (IGA) is coupled with the boundary element method (BEM) for 2D potential problems in this paper. The geometry and field are usually approximated by the same basis functions in IGA, such as the B-spline or the NURBS basis functions. In the proposed method, these two kinds of approximation are performed independently, i.e. the geometry is reproduced by the NURBS basis functions while the field is approximated by the traditional Lagrangian basis functions which are used in the conventional BEM. The proposed method has the advantage that the geometry can be reproduced exactly at all stages in IGA methods. Actually, one can use the computer aided design (CAD) software or NURBS library to perform the operations related to the geometry. The field approximation is performed in parameter space and separated from the geometry. Thus, it can be implemented easily as the conventional BEM since most algorithms for BEM can be applied directly, such as the methods for treatment of the singular integrals, and the boundary conditions can be imposed directly. Numerical examples have demonstrated the accuracy of the proposed method.