A performance study of NURBS-based isogeometric analysis for interior two-dimensional time-harmonic acoustics

This work evaluates the performance of a NURBS-based isogeometric finite element formulation for solving stationary acoustic problems in two dimensions. An initial assessment is made by studying eigenvalue problems for a square and a circular domain. The spectral approximation properties of NURBS functions of varying order are compared to those of conventional polynomials and are found to be superior, yielding more accurate representations of eigenvalues as well as eigenmodes. The higher smoothness of NURBS shape functions yields better approximations over an extended frequency range when compared to conventional polynomials. Two numerical case studies, including a geometrically complex domain, are used to benchmark the method versus the traditional finite element method. A convergence analysis confirms the higher efficiency of the isogeometric method on a per-degree-of-freedom basis. Simulations over a wider frequency range also illustrate that the method suffers less from the dispersion effects that deteriorate the acoustic response towards higher frequencies. The tensor product structure of NURBS, however, also imposes practical considerations when modelling a complex geometry consisting of multiple patches.