An isogeometric indirect boundary element method for Helmholtz problems

Isogeometric Analysis (IGA) is a recently introduced concept that tries to bridge the gap between Computer Aided Engineering (CAE) and Computer Aided Design (CAD). It does so by generalising the Finite Element Method (FEM) to describe the problem geometry with functions that are typically used in CAD environments (such as NURBS) and then using the same type of functions to represent the field variables - often invoking the isoparametric paradigm. This concept allows to bypass the labor-intensive step of converting a CAD geometry to an analysis-suitable geometry description, which is usually a huge bottleneck in the conventional FEM. Moreover, IGA has been shown to exhibit several advantageous approximation properties over the FEM for analysing problems in various fields of research. This paper studies whether these interesting results can be extended to Helmholtz problems using a boundary element formulation. More specifically, this work integrates the isogeometric idea in an indirect variational Boundary Element Method (BEM) for steady-state acoustic problems involving surfaces with open boundaries. The numerical results show that the proposed method compares favorably to a traditional Lagrangian BEM, exhibiting a significantly higher accuracy per degree of freedom.