On some results about the variational theory of complex rays used close to the high frequency regime

This work presents some results about the variational theory of complex rays (VTCR) when the frequency increases. This numerical strategy has indeed be mainly only used in the literature on examples where there were about 10–20 wavelengths in the characteristic length of the problem. Few works concerned its use on examples with at least two or three times more wavelengths than that, then close to the high frequency regime, which is the case here. This work tries to show how to bypass the numerical difficulties one can suffer from when using the VTCR on examples with so many wavelengths. It also studies the evolution of the variational formulation of the VTCR when the frequency increases, which leads to some interesting physical interpretations and draws relations with some high frequency vibrations strategies.