We propose a collocation-based NURBS-enhanced boundary element method in which NURBS surfaces are directly used for exact geometry representation, while piecewise-constant basis functions are employed for field approximation. In three-dimensional boundary element analyses, the accuracy of conventional BEM with piecewise-linear shape functions is often limited by geometric approximation errors. Although isogeometric BEM (IGBEM) naturally combines NURBS geometry with smooth basis functions, it encounters difficulties, for example, in Dirichlet problems when the unknown density is discontinuous at geometric singularities such as edges and corners. These discontinuities might not be handled naturally by smooth basis functions typically used in IGBEM. The proposed method resolves this issue through a simple strategy that adopts constant basis functions for the unknown density while preserving the exact CAD geometry via NURBS surfaces, allowing discontinuities to be represented accurately without special treatments. Numerical experiments demonstrate that the proposed BEM achieves substantially higher accuracy than the conventional one for a fixed number of degrees of freedom (DoFs) and improves the convergence rate of the solution from (DoFs)−1/2 to (DoFs)−1. Furthermore, the proposed method provides accurate solutions for scatterers with non-smooth edges without requiring additional treatments, making it a practical and efficient alternative to traditional BEM implementations.
Tomoyasu et al. (Thu,) studied this question.