Isogeometric boundary element methods (IGBEM) offer a seamless integration of design and analysis. However, the imposition of the same basis for both geometry and boundary fields results in unnecessary geometric refinement because of high-gradient fields. In this work, an IGBEM is presented for exterior acoustics problems, which is based on an independent approximation for the geometry, acoustic potential, and its normal derivative. It was applied to solve the Burton–Miller (BM) equation, which is required for a stable formulation of acoustic exterior problems. The geometry description is based on Non-Uniform Rational B-splines (NURBS). Independent B-splines are considered as a basis for the boundary fields. The boundary conditions produce the right-hand side vector directly, resulting in a single-matrix formulation, which improves the efficiency and memory storage of the method. Convergence analysis indicates rates of p＋1 for knot insertion, while K-refinement results in hypergeometric convergence. An exterior acoustic problem with an analytic solution validates the method and confirms the well-posedness of the Burton–Miller formulation. Finally, an application regarding an airplane acoustic scattering problem is presented for illustrative purposes. The BM hypersingular integrals were not regularized, relying on the source point distance strategy when needed. Further research is underway to incorporate an effective regularization procedure. • Independent basis approximation applied to Burton–Miller boundary integral equations. • Boundary fields refinements without changes in the geometry. • Convergence analysis with knot insertion, h- and k-refinements. • Single-matrix formulation.
Teixeira et al. (Wed,) studied this question.