摘要：The boundary integral equation method (BIEM) is one of the important numerical techniques used to simulate geophysical phenomena including dynamic propagation, nucleation, and sequence of earthquake ruptures.We studied the stability and convergence of two time-marching schemes numerically for 2-D problems in Mode I, II, and III conditions.One was a conventional method based on piecewise-constant spatiotemporal distribution of the rate of displacement gap V (CM), and the other was a slightly modifed scheme from a predictor–corrector method previously applied to a spectral BIEM (NL).In the stability analysis, we simulated behavior of a traction-free fault under uncorrelated random distributions of initial traction.The growth rate of the perturbation is negative in a parameter regime of complex shape with CM, which has two numerical parameters, and the intersection for all the modes is very restricted as reported previously.In contrast, NL has only one parameter and yields simpler and a wide parameter regime of stability, conceivably allowing more fexible meshing on the fault.In the convergence analysis in which a smooth problem was solved, CM resulted in a numerical error scaled as x1 while NL led to the scaling of x2 typically or of x1.5 under certain conditions in Mode II problems.NL requires negligible additional computational costs and modifcation of the code is quite straightforward relative to CM.Therefore, we conclude that NL is a useful timemarching scheme that has wide applicability in simulations of earthquake ruptures although the reason for the rather complicated convergence behavior and verifcation of the fndings here to more general conditions deserve further study.
