The Complex Envelope Vectorization

Low-frequency problems in dynamics are comfortably tackled with the standard numerical approaches, like FEM or BEM, at a reasonable computational cost. In the high-frequency and vibro-acoustic problems, that is for short wavelength, the number of degrees of freedom becomes indeed very high. As a consequence, the computational results obtained by these standard discretization techniques, may yield no more valid results, both in terms of computational costs as well as in terms of error propagation in the model. To tackle these problems, a class of new methods has been developed in the past years and, these are matter of investigation in the context of the Mid-Frequency project. Among others, CEV, the Complex Envelope Vectorization method, proved to be successful. The development of CEV began in 1997 by Antonio Carcaterra introducing the Complex Envelope Displacement Analysis (CEDA) [2, 3] and, until now, several extensions followed its application to different academic problems. CEDA was developed as a suitable technique for high frequency problems with the ability to solve the low-frequency problems as well. CEV makes use of standard discretization schemes such as FEM or BEM and operates as a combined pre- and postprocessing layer that can be embedded in other softwares. In the present chapter we present three main advances developed in the context of Mid-Frequency: (i) CEV application to vibro-acoustic problems starting from FE formulation (ii) CEV application to external problems starting from BE discretization, and (iii) CEV generalization to transient problems.