Stability analysis and design of time-stepping schemes for general elastodynamic boundary element models. Int J Numer Methods Engrg 40(2):319–342

In the literature there is growing evidence of instabilities in standard time-stepping schemes to solve boundary integral elastodynamic models.1{3 However, there has been no theory to support scientists and engineers in assessing the stability of their boundary element algorithms or to help them with the design of new, more stable algorithms. In this paper we present a general framework for the analysis of the stability of any time-domain boundary element model. We illustrate how the stability theory can be used to assess the stability of existing boundary element models and how the insight gained from this analysis can be used to design more stable time-stepping schemes. In particular, we describe a new time-stepping procedure that we have developed, which has substantially enhanced stability characteristics and greater accuracy for the same computational eort. The new scheme, which we have called ‘the half-step scheme’, is shown to have substantially improved performance for the displacement discontinuity boundary element method commonly used to model dynamic fracture interaction and propagation. KEY WORDS: numerical instability; elastodynamics; boundary elements; dynamic fracture 1