A NURBS-enhanced improved interpolating boundary element-free method for 2D potential problems and accelerated by fast multipole method

Isogeometric analysis (IGA) has been widely applied in the finite element method and boundary element method (BEM), in which the geometry discretization error can be avoided. This paper proposes a NURBS-enhanced meshless improved interpolating boundary element-free method for 2D potential problems. In the proposed method, non-uniform rational B-spline (NURBS) basis functions are applied to reproduce the geometry like in IGA, and the boundary integral cells, called isogeometric cells, are defined by the knot vector of NURBS in parameter space. Thus, the geometry can remain the same at all stages because refining a NURBS curve will not change its shape. An improved interpolating moving least-square (IIMLS) method is applied to approximate the field in parameter space, and the boundary nodes can be defined using Greville abscissae definition. Compared with IGA in BEM, the shape functions obtained by IIMLS in the proposed method have the delta function property, and the boundary conditions can be applied directly. In addition, most methods for the treatment of the singular integrals in BEM can be applied easily in the proposed method. Fast multipole method is further coupled with the proposed method for large-scale computation.