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

当使用边界元方法（BEM）对Helmholtz问题进行数值求解时，通常将低阶Lagrange多项式或更新的非均匀有理B样条曲线（NURBS）用作基础函数。高频问题的一种流行替代方法是使用丰富的基础，例如在统一边界元方法（PUBEM）划分中使用的平面波基础。据作者所知，由于在BEM环境中对基于波的问题采用高阶NURBS和Lagrange多项式而导致的数值误差尚未得到彻底的量化。这是当前工作的重点，并将结果与​​PUBEM进行比较。结果表明，随着基函数阶数的增加，拉格朗日或NURBS方案的收敛速度有望得到改善，NURBS基础略好于Lagrange基础。在某些情况下，高阶Lagrange和NURBS配方可与PUBEM相比。此外，还针对管道中的行波研究了BEM中最近观察到的污染效应，并为所有三组基函数提供了数值色散。