Improved conditioning of infinite elements for exterior acoustics

An optimized version of the so-called mapped wave envelope elements, also known as Astley–Leis elements, is introduced. These elements extend to in nity in one dimension and therefore provide an approach to the simulation of exterior acoustical problems in both frequency and time domains. Their formulation is improved signi cantly through the proper choice of polynomial bases in the direction of radiation. In particular, certain Jacobi polynomials are identi ed which behave well with respect to conditioning of the system matrices. As a consequence, the size of the nite element discretization may reduce considerably without any loss of accuracy. In addition, the new polynomial bases lead to superior performance of the in nite elements in conjunction with iterative solvers