An efficient finite element time‐domain formulation for the elastic second‐order wave equation: A non‐split complex frequency shifted convolutional PML

René Matzen

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

The perfectly matched layer (PML) technique has demonstrated very high efficiency as absorbing boundary condition for the elastic wave equation recast as a first‐order system in velocity and stress in attenuating non‐grazing bulk and surface waves. This paper develops a novel convolutional PML formulation based on the second‐order wave equation with displacements as the only unknowns to annihilate spurious reflections from near‐grazing waves. The derived variational form allows for the use of e.g. finite element and the spectral element methods as spatial discretization schemes. A recursive convolution update scheme of second‐order accuracy is employed such that highly stable, effective time integration with the Newmark‐beta (implicit and explicit with mass lumping) method is achieved. The implementation requires minor modifications of existing displacement‐based finite element software, and the stability and efficiency of the proposed formulation is verified by relevant two‐dimensional benchmarks that accommodate bulk and surface waves. Copyright © 2011 John Wiley & Sons, Ltd.
Original languageEnglish
JournalInternational Journal for Numerical Methods in Engineering
Volume88
Issue number10
Pages (from-to)951-973
ISSN0029-5981
DOIs
Publication statusPublished - 2011

Keywords

  • Absorbing boundary conditions
  • Elastic wave equation
  • Finite element time-domain discretization
  • Perfectly matched layers
  • Implicit/explicit time integration

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