Overview of the discontinuous enrichment method, the ultra-weak variational formulation, and the partition of unity method for acoustic scattering in the medium frequency regime and performance comparisons

Abstract

The efficient finite element discretization of the Helmholtz equation becomes challenging in the medium frequency regime because of numerical dispersion, or what is often referred to in the literature as the pollution effect. A number of FEMs with plane wave basis functions have been proposed to alleviate this effect, and improve on the unsatisfactory preasymptotic convergence of the polynomial FEM. These include the partition of unity method, the ultra-weak variational formulation, and the discontinuous enrichment method. A previous comparative study of the performance of such methods focused on the first two aforementioned methods only. By contrast, this paper provides an overview of all three methods and compares several aspects of their performance for an acoustic scattering benchmark problem in the medium frequency regime. It is found that the discontinuous enrichment method outperforms both the partition of unity method and the ultra-weak variational formulation by a significant margin. © 2011 John Wiley & Sons, Ltd.