Optimized mapped wave envelope elements for exterior acoustics

In the simulation of exterior acoustical problems using the Finite Element Method (FEM), infinite elements are an effective approach. Among several possible formulations, the Mapped Wave Envelope Elements or Astley-Leis Elements turned out to be rather promising. Problems 'involving severe ill-conditioning of the elements due to ineffective polynomial spaces seem to be overcome by introducing Legendre polynomials for radial approximation. The behavior of these elements in conjunction with iterative solvers, though, still remains difficult, especially in frequency domain. In this contribution Astley-Leis Elements with Jacobi polynomials as radial basis are presented, which are well suited to be employed in conjunction with iterative solvers. Numerical examples with using three different solvers, namely GMRES, QMR, and BiCGSTAB, are presented. An inspection of the eigenvalue distribution of the system matrices explains the good characteristics of the new elements.