Some numerical aspects of the PUFEM for efficient solution of 2D Helmholtz problems

The Partition of Unity Finite Element Method is used to solve wave scattering problems governed by the Helmholtz equation, involving one or more scatterers, in two dimensions. The method allows us to relax the traditional requirement of around ten nodal points per wavelength used in the Finite Element Method. Therefore the elements are multi-wavelength sized and the mesh of the computational domain may be kept unchanged for increasing wave numbers. As a result, the total number of degrees of freedom is drastically reduced. In this work, various numerical aspects affecting the efficiency of the method are investigated by considering an interior Helmhlotz problem. Those include the plane wave enrichment, the h-refinement, the geometry description, and the conjugated or unconjugated type of formulation. The method is then used to solve problems involving multiple scatterers. Last, an exterior scattering problem by a non-smooth rigid body is presented.