A comparison of high-order and plane wave enriched boundary element basis functions for Helmholtz problems

When undertaking a numerical solution of Helmholtz problems using the Boundary Element Method (BEM) it is common to employ low-order Lagrange polynomials, or more recently Non-Uniform Rational B-Splines (NURBS), as basis functions. A popular alternative for high frequency use an enriched basis, such plane wave used in Partition Unity (PUBEM). To authors’ knowledge there yet be thorough quantification error incurred result employing high-order NURBS and polynomials wave-based BEM setting. This focus current work, along with comparison results against PUBEM. The show expected improvements convergence rates scheme order functions increased, slightly outperforming basis. High-order formulations can compare favourably PUBEM certain cases. In addition, observed pollution effect studied travelling duct dispersion presented all three sets