An assessment of two popular Padé-based approaches for fast frequency sweeps of time-harmonic finite element problems.

Abstract

Several Padé-based computational methods have been recently combined with the finite element method for the efficient solution of complex time-harmonic acoustic problems. Among these, the component-wise approach, which focuses on the fast-frequency sweep of individual degrees of freedom in the problem, is an alternative to the projection-based approaches. While the former approach allows for piecewise analytical expressions of the solution for targeted degrees of the freedom, the projection-based approaches may offer a wider range of convergence. In this work, the two approaches are compared for a range of problems varying in complexity, size and physics. This includes for instance the modelling of coupled problems with non-trivial frequency dependence such as for the modelling of sound absorbing porous materials. Conclusions are drawn in terms of computational time efficiency, implementation, and suitability of the methods depending on specific scientific problems of interest.