Outward Wave Favouring Formulation in Exterior Acoustics: An Assessment of Its High Frequency Performance

While solving harmonic exterior acoustics problems using the traditional finite element method, we truncate the domain at some finite radius on which appropriate absorbing boundary conditions, like spherical damping condition, approximate the Sommerfeld radiation condition. In exterior domain acoustic wave propagation, there are no incoming waves as the propagating wave does not meet any surface to be reflected. Jog [8] used this physical fact in formulating the Outward wave favouring (OWF) strategy in [8]. He assumed the acoustic pressure in a unique form favourable to simulate the ‘Outgoing’ nature of the acoustic wave in the exterior domain. In that unique form, the highly oscillatory part of the acoustic wave, which is common to all exterior harmonic acoustics problems, is separated. As we separate the highly oscillatory part apriori, the frequency term is contained in that separated known oscillatory term. Therefore, the finite element method (FEM) has to capture the relatively gentle unknown part, which is problem-specific. Hence, this strategy is highly effective for high-frequency exterior domain problems. In this work, we have demonstrated the coarse mesh accuracy of the OWF formulations with various examples running at higher frequencies. We have compared OWF formulations with their conventional counterpart in terms of \(L_2\) error norm over a range of frequencies. Also, we have done a detailed mesh analysis for various benchmark problems over different frequencies. Also, for achieving some expected level of accuracy compared to the analytical benchmark solutions, the required time has been compared between conventional and OWF elements.