Adaptive enriched geometry independent field approximation for 2D time-harmonic acoustics

Abstract

Isogeometric Analysis (IGA) provides an alternative to Lagrange based finite element methods by representing the geometry and field with the same Non-Uniform Rational B-Splines (NURBS) shape functions within a weak Galerkin formulation. IGA has proven to be highly efficient in solving the Helmholtz equation, due to the ease with which the order and continuity of the approximation space can be increased, as well as the geometrical exactness enabled by the use of NURBS. In Atroshchenko et al. (2018), we generalize IGA, by allowing an independent representation of the geometry and fields (Geometry Independent Field approximaTion, GIFT or Generalized IGA Marussig et al., 2015). GIFT with NURBS and PHT-splines (for the geometry and the field, respectively) allows to keep original coarse parameterization of CAD geometry and enables adaptive local refinement of the solution. In the present work, we investigate the possibility to further improve the approach by enriching the PHT-splines field approximation with a set of plane-waves propagating in different directions. Plane wave enrichment is commonly used to capture oscillatory behaviour of the solution and achieve smaller error on coarser meshes. The performance of PUPHT-splines for varying frequencies, degree of PHT-splines, number of plane waves, different refinement strategies is demonstrated on three benchmark problems.