The Spectral Cell Method for Ultrasonic Guided Wave Propagation Problems

Abstract : In the current paper we present a fast and robust numerical tool for the simulation of ultrasonic guided waves in heterogeneous structures. The proposed approach, the so-called spectral cell method (SCM), combines the fundamental ideas of the spectral element method (SEM) with the fictitious domain concept. The SCM accordingly retains the high convergence rates known from high-order finite element methods and circumvents the need for body-fitted discretizations. Mass-lumping techniques being available for the SEM can also be applied for the SCM, which offers benefits when explicit time integration methods such as the central difference method (CDM) are employed. Due to these properties both memory requirements and computational time can be notably reduced. The SCM therefore paves the way for an efficient simulation of ultrasonic guided waves. In the first part of the paper we introduce the basic principles of high-order finite element methods (for multi-physics applications - piezoelectricity) and the fictitious domain approach to illustrate the behaviour of the proposed method. The second part contains numerical examples showing that the performance of the SCM is comparable to other (established) high-order methods.