A Comparative Study of Absorbing Layer Methods to Model Radiating Boundary Conditions for the Wave Propagation in Infinite Medium

  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract

    Radiating boundary condition is an important consideration in the finite element modelling of unbounded media. Absorbing layer techniquessuch as Perfectly Matched Layers (PML) and Absorbing Layers by Increasing Damping (ALID) becoming popular as they are efficient in absorbing outward propagating waves energy. In this study, a comparative analysis has been carried out between PML and ALID+VABC (Absorbing Boundary conditions for Viscoelastic materials) methods. The methods are analyzedusing LS-DYNAexplicit solver and the efficiency is compared with standard solutions.The study concluded that PML requires less number of elements to model the boundary conditions when compared with ALID+VABC. But PMLrequires a smaller element length which increases overall computational time. Both the methods are efficient in absorbing the wave energy. However, PML requires additional implementation cost to solve the complex equations.


  • Keywords

    Radiating Boundary Conditions, Perfectly Match Layers, Absorbing Layer by Increase in Damping, Absorbing Boundary Conditions for Viscoelastic Wave Propagation, Soil-Structure Interaction.

  • References

      [1] Sommerfeld, A., (1949). Partial Differential Equations in Physics (Vol. 1). Academic Press.

      [2] Lysmer J., Kuhlemeyer R.L. (1969). Finite dynamic model for infinite media. Journal of Engineering Mechanics. Div ASCE 95(EM4):859–877.

      [3] Engquist B. and Majda A. Absorbing boundary conditions for the numerical simulation of waves, Mathematics of Computation 1977; 31: 629–651,

      [4] Badry R.S., Ramancharla P., Local absorbing boundary conditions to simulate wave propagation in unbounded viscoelastic domains.Comput Struct2018; 208:1-16.

      [5] Berenger, J.P. A perfectly matched layer for the absorption of electromagnetic waves. Journal of Computing in Physics 1994; 114(2):185–200.

      [6] Chew W.C., Liu Q.H. Perfectly matched layers for elastodynamics: a new absorbing boundary condition, Journal of Computational Acoustics 1996; 4(4): 341-359.

      [7] Collino F., Tsogka C. Application of the PML absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media, Geophysics 2001; 66(1): 294-307.

      [8] Marcinkovich C., Olsen K.B. On the implementation of perfectly matched layers in a three-dimensional fourth-order velocity-stress finite difference scheme, Journal of Geophysical Research 2003; 108(B5): 2276.

      [9] Komatitsch D., Martin R. An unsplit convolutional Perfectly Matched Layer improved at grazing incidence for the seismic wave equation. Geophysics 2007; 72(5): 155-167.

      [10] Meza-Fajardo K.C., Papageorgiou A.S. A Nonconvolutional, Split-Field, Perfectly Matched Layer for Wave Propagation in Isotropic and Anisotropic Elastic Media: Stability Analysis,Bulletin of the Seismological Society of America 2008; 98(4): 1811-1836.

      [11] Basu U. Explicit finite element perfectly matched layer for transient three-dimensional elastic waves. International Journal for Numerical Methods in Engineering 2009; 77(2):151–176.

      [12] Sembalt J.F., Lenti L., Ali G. A simple multi directional Absorbing Layer method to simulate elastic wave propagation in unbounded domains, International Journal for Numerical methods in engineering 2010; 1: 1-22.

      [13] Andre Rodriguesa A. and Zuzana Dimitrovova Z. The Caughey absorbing layer method – implementation and validation in Ansys software, Latin American Journal of Solids and Structures 2015; 12: 540-1564.

      [14] Israeli M. and Orszag S.A., Approximation of radiation boundary conditions, J. Comp. Phys 1981; vol. 41: 115-135.

      [15] P. Rajagopal, M. Drozdz, E.A. Skelton, M.J.S. Lowe, R.V. Craster, On the use of absorbing layers to simulate the propagation of elastic waves in unbounded isotropic media using commercially available finite element packages, NDT&E Int. 51 (2012) 30–40.

      [16] Pettit J. R., Walker A., Cawley P., and Lowe M. J. S. A Stiffness Reduction Method for efficient absorption of waves at boundaries for use in commercial Finite Element codes, Ultrasonics 2014; 54(7): 1868-1879.

      [17] Banerjee, P.K., Butterfield, R., (1981). Boundary element methods in engineering science. McGraw-Hill Book Co.

      [18] Bettess P. Infinite elements, International Journal for Numerical Methods in Engineering 1978; 11:54-64.

      [19] Zienkiewicz O. C., Bando K., Bettess P., Emson C. and Chiam T. C., Mapped infinite elements for exterior wave problems. International Journal for Numerical Methods in Engineering, 1985; 21:1229–1251.

      [20] Yun C. B., Kim J.M., Yao Z.H., Yuan M.W. Dynamic Infinite Elements for Soil-Structure Interaction Analysis in a Layered Soil Medium, Comp. Methods in Engg and Science 2007;153-167

      [21] Chen Xiamoing, Duan Jin, Li Yungui. Mass proportional damping in nonlinear time-history analysis, 3rd International Conference on Material, Mechanical and Manufacturing Engineering (IC3ME 2015) 2015; 567-571

      [22] Badry R.S., Ramancharla P.K., (2018); Numerical Modelling of Radiating Boundary Conditions Combined with Modified Absorbing Boundary Condition for Viscoelastic Wave Propagation.International Conference on CST-2018. Sitges, Spain, Barcelona, 4-6 Sep, 2018.

      [23] Ls-DYNA, Livermore Software Technology Corporation.2018.




Article ID: 29141
DOI: 10.14419/ijet.v7i3.35.29141

Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.