Assessment of finite and spectral element shape functions for efficient iterative simulations of interior acoustics

Several shape function families currently used in the spectral element and the finite element method (FEM) are reviewed. Widely known shape functions such as the conventional Lagrange functions, various p-FEM shapes, and recent developments in the area of spectral methods are compared. Especially, shape functions derived from Bernstein polynomials are discussed, due to their ease of formulation for almost any geometric entity. Their applicability and efficiency for acoustic simulations are assessed. In particular, the efficiency is measured in terms of performance of current Krylov solvers.