Numerical modelling of wave propagation in the medium frequency range: Overview and trends

The computational simulation of structural vibrations and acoustic radiation or scattering has become one of the major field of interest in computational mechanics. However, simulating accurately waves in the medium frequency range is still an unsolved problem of the computational mechanics community. Despite considerable efforts to extend the possible frequency range of existing numerical methods (FEM, BEM or SEA), no fully satisfactory numerical procedures allow to cover the medium frequency range. The key issue to improve the accuracy of the approximate numerical solution is to control the dispersion error. It is particularly crucial for industrial purpose which request robust methods within a reasonable computational cost. The paper objective is to review the main numerical methods which are under development to model the wave propagation, with a special emphasis on the medium frequency range. It focuses on Galerkin based methods, i.e. finite element type methods. The paper shows that the issue of computing short wave still seems to be unsolved as none of the methods is really 'dispersion-free' or outperforms the other ones. Some topics criteria an objective comparison. A first criterion is based on the answer to the following questions: (i) is the method general for any geometry? (ii) does the method allow a coupling for an infinite medium? (iii) does the method allow a vibro-acoustic coupling ? Secondly, the following criteria are of importance: the accuracy, the maximum frequency range, the computational time. A special attention should also be paid to the fact that the materials exhibit frequency dependent properties.