Time‐dependent absorbing boundary conditions for elastic wave propagation

This paper develops a finite element scheme to generate the spatial- and time-dependent absorbing boundary conditions for unbounded elastic-wave problems. This scheme first calculates the spatial- and time-dependent wave speed over the cosine of the direction angle using the Higdon's one-way first-order boundary operator, and then this operator is used again along the absorbing boundary in order to simulate the behaviour of unbounded problems. Different from other methods, the estimation of the wave speed and directions is not necessary in this method, since the wave speed over the cosine of the direction angle is calculated automatically. Two- and three-dimensional numerical simulations indicate that the accuracy of this scheme is acceptable if the finite element analysis is appropriately arranged. Moreover, only the displacements along absorbing boundary nodes need to be set in this method, so the standard finite element method can still be used. Copyright © 2001 John Wiley & Sons, Ltd.

[1]  Rosemary A. Renaut,et al.  Abstract of papers to appear in future issuesAbsorbing boundary conditions, difference operators, and stability , 1992 .

[2]  D. Givoli.  A spatially exact non-reflecting boundary condition for time dependent problems , 1992 .

[3]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[4]  Robert L. Higdon,et al.  Numerical absorbing boundary conditions for the wave equation , 1987 .

[5]  I. Orlanski.  A Simple Boundary Condition for Unbounded Hyperbolic Flows , 1976 .

[6]  Shen-Haw Ju,et al.  Mass types, element orders and solution schemes for the Richards equation , 1997 .

[7]  D. Givoli,et al.  Nonreflecting boundary conditions based on Kirchhoff-type formulae , 1995 .

[8]  Dale R. Durran,et al.  Toward More Accurate Wave-Permeable Boundary Conditions , 1993 .

[9]  Robert L. Higdon,et al.  Radiation boundary conditions for elastic wave propagation , 1990 .

[10]  Robert L. Higdon,et al.  Absorbing boundary conditions for acoustic and elastic waves in stratified media , 1992 .

[11]  A. Majda,et al.  Absorbing boundary conditions for the numerical simulation of waves , 1977 .

[12]  Josef Ballmann,et al.  Two techniques for the absorption of elastic waves using an artificial transition layer , 1997 .

[13]  William H. Raymond,et al.  A radiation boundary condition for multi‐dimensional flows , 1984 .

[14]  Shen-Haw Ju,et al.  Simulating three-dimensional stress intensity factors by the least-squares method , 1998 .