An adaptive numerical strategy for the medium-frequency analysis of Helmholtz's problem

Overview & Synopsis

The variational theory of complex rays (VTCR) is a wave-based predictive numerical tool for medium-frequency problems. In order to describe the dynamic field variables within the substruc-tures, this approach uses wave shape functions which are exact solutions of the governing differential equation. The discretized parameters are the number of substructures (h) and the number of wave-bands (p) which describe the amplitude portraits. Its capability to produce an accurate solution with only a few degrees of freedom and the absence of pollution error make the VTCR a suitable numerical strategy for the analysis of vibration problems in the medium-frequency range. This approach has been developed for structural and acoustic vibration problems. In this paper, an error indicator which characterizes the accuracy of the solution is introduced and is used to define an adaptive version of the VTCR. Numerical illustrations are given.