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Finite and spectral cell method for wave propagation in heterogeneous materials

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Abstract

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 cell method and the spectral element method that significantly lowers preprocessing and computational expenditure. The spectral cell method takes advantage of explicit time-integration 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 high-order version of the spectral cell method together requires less memory storage and less CPU time than other possible versions, when combined simultaneously with explicit time-integration 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].

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Acknowledgments

The first and last authors gratefully acknowledge the support provided by the German Research Foundation (DFG) under Grant DU405/4. The second and the third authors would like to express their gratitude to the DFG for the support received under Grant GA 480/13-3.

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Authors and Affiliations

  1. Numerical Structural Analysis with Application in Ship Technology, Hamburg University of Technology, Schwarzenbergstr. 95c, 21073,  Hamburg, Germany

    Meysam Joulaian & Alexander Düster

  2. Faculty of Mechanical Engineering, Computational Mechanics, Otto-von-Guericke-University Magdeburg, Universitätsplatz 2, 39106,  Magdeburg, Germany

    Sascha Duczek & Ulrich Gabbert

Authors
  1. Meysam Joulaian
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  2. Sascha Duczek
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  3. Ulrich Gabbert
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  4. Alexander Düster
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Correspondence to Meysam Joulaian.

Additional information

Dedicated to Professor Dr.rer.nat. Ernst Rank on the occasion of his 60th birthday.

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Joulaian, M., Duczek, S., Gabbert, U. et al. Finite and spectral cell method for wave propagation in heterogeneous materials. Comput Mech 54, 661–675 (2014). https://doi.org/10.1007/s00466-014-1019-z

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