Implementation and application of elastodynamic boundary element discretizations with improved stability properties

Abstract

Direct and indirect time marching boundary element methods often become numerically unstable. Evidence of, and reasons for, these instabilities is provided in this paper. Two new time stepping schemes are presented, both of which are more stable than the existing standard schemes available. In particular, we introduce the Half‐step scheme, which is more accurate and far more stable than existing methods. This scheme, which is demonstrated on a simple crack problem for the displacement discontinuity method, can also be introduced into the direct boundary element method. Implementation of the Half‐step scheme into existing boundary element codes will allow researchers to attack more challenging problems than before.

Citation

Siebrits, E. and Peirce, A.P. (1997), "Implementation and application of elastodynamic boundary element discretizations with improved stability properties", Engineering Computations, Vol. 14 No. 6, pp. 669-695. https://doi.org/10.1108/02644409710180770