Finite and spectral cell method for wave propagation in heterogeneous materials

摘要

In the current paper we present a fast, reliable technique for simulating wave propagation in complex structures made of heterogeneous materials. The proposed approach, the spectral cell method, is a combination of the finite cellmethod and the spectral element method that significantly lowers preprocessing and computational expenditure. The spectral cell method takes advantage of explicit timeintegration schemes coupled with a diagonal mass matrix to reduce the time spent on solving the equation system. By employing a fictitious domain approach, this method also helps to eliminate some of the difficulties associated with mesh generation. Besides introducing a proper, specific mass lumping technique, we also study the performance of the low-order and high-order versions of this approach based on several numerical examples. Our results show that the highorder version of the spectral cell method together requires less memory storage and less CPU time than other possible versions, when combined simultaneously with explicit timeintegration algorithms. Moreover, as the implementation of the proposed method in available finite element programs is straightforward, these properties turn the method into a viable tool for practical applications such as structural health monitoring 1–3, quantitative ultrasound applications 4, or the active control of vibrations and noise 5,6.