An isogeometric indirect boundary element method for modeling steady-state acoustic problems with open boundaries

This work presents an indirect variational boundary element method for solving steady-state acoustic problems in three dimensions, starting from a NURBS-based isogeometric concept. Aside from having the geometrical flexibility inherent to isogeometric analysis, it has already been shown that NURBS also exhibit advantageous properties as compared to classical polynomial shape function expansions for analysis purposes. Moreover, because CAD geometries are intrinsically boundary descriptions, the use of an isogeometric approach in boundary element analysis comes naturally. The implemented indirect variational formulation allows for the modeling of problems both with open and with closed boundaries and also combined interior/exterior problems, in contrast to direct boundary integral formulations. This is an important asset, since various industrial problems require the modeling of such problems. Additionally, the variational formulation leads to symmetric system matrices, which yields a crucial computational advantage for larger models. The proposed method is verified using analytical solutions, and a numerical example is studied to benchmark it against a conventional polynomial-based boundary element method. The results demonstrate the better performance of the method, yielding a higher accuracy per degree of freedom, also towards higher frequencies of analysis.status: publishe