### Abstract

The numerical analysis of the wave propagation problem, from elastic to electromagnetic waves, is often faced with the problem of dealing with unbounded media. Since the domain of finite-difference and finite element methods must be itself finite, various truncation techniques have been proposed over the last decades, such as absorbing boundary conditions (Lysmer and Kuhlemeyer[1]), infinite elements (Bettess [2]) and absorbing boundary layers (such as the Perfectly Matched Layer, or PML, introduced by Bérenger [3]). In this paper, the Caughey Absorbing Layer Method (CALM), proposed by Semblat et al. [4], is implemented in the commercial finite element software Ansys, using an implicit dynamics formulation. It is tested for one- and two-dimensional problems and its efficiency is compared with that of the Lysmer-Kuhlemeyer absorbing boundaries. The dependency on material parameters, loss factor and load frequency is also tested. To mitigate the problem of wave reflection at the interface between the medium of interest and the absorbing layer, different variations of damping along the layer's length are tested and their efficiency compared. By analysing the maximum displacement and the L^{2}-norm of the displacement field, the implementation of the CALM in Ansys is shown to be effective at mitigating the problem of spurious wave reflection at the boundaries. Their performance is clearly superior to the Lysmer absorbing boundary conditions, but at a greater computational cost due to the additional degrees of freedom. The quadratic variation of the Rayleigh damping has proved to be the most effective, and an estimate of the optimum loss factor as a function of the length of the layer in relation to the wavelength to absorb was proposed. Although the optimal damping is frequency dependent, it was shown to work well even if the frequency is overestimated or greatly underestimated.

Original language | English |
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Title of host publication | 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014 |

Publisher | International Center for Numerical Methods in Engineering |

Pages | 557-568 |

Number of pages | 12 |

ISBN (Electronic) | 9788494284472 |

Publication status | Published - 1 Jul 2014 |

Event | Joint 11th World Congress on Computational Mechanics, WCCM 2014, the 5th European Conference on Computational Mechanics, ECCM 2014 and the 6th European Conference on Computational Fluid Dynamics, ECFD 2014 - Barcelona, Spain Duration: 20 Jul 2014 → 25 Jul 2014 |

### Conference

Conference | Joint 11th World Congress on Computational Mechanics, WCCM 2014, the 5th European Conference on Computational Mechanics, ECCM 2014 and the 6th European Conference on Computational Fluid Dynamics, ECFD 2014 |
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Country | Spain |

City | Barcelona |

Period | 20/07/14 → 25/07/14 |

### Keywords

- Absorbing boundary layer
- Elastic wave propagation
- Finite element method
- Spurious reflections
- Unbounded domains

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## Cite this

*11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014*(pp. 557-568). International Center for Numerical Methods in Engineering.