A comparison of approximate boundary conditions and infinite element methods for exterior Helmholtz problems Original Research Article

We compare the accuracy of a variety of approximate boundary conditions (ABCs) and two versions of an infinite element method (IEM) for approximating solutions of exterior Helmholtz problems. The infinite elements are of variable order in the radial direction and differ only in whether the test functions in the weak formulation are conjugated or not. We find that the accuracy of the ABCs decreases with increasing frequency, and that at higher frequencies their accuracy is several orders of magnitude lower than that obtained with the IEMs. We show that the convergence rate of the conjugated element is slower than the rate for the unconjugated element and that the latter element fails to converge in the far field.