Convergence results of a heterogeneous asynchronous newmark time integrators

Abstract

This paper is concerned with the convergence analysis of the PH heterogeneous asynchronous time integrators algorithm, proposed by Prakash and Hjelmstad [Int. J. Numer. Methods Eng. 61 (2004) 2183–2204], and devoted to transient dynamic problems for structural analysis. According to PH method, the time discretization is performed using the well-known Newmark schemes, where the time step ratio, i.e., the ratio of the macro time step to the micro time step, of two subdomains separated by an interface is a positive integer. The analysis is restricted to linear problems with two subdomains for simplification. We show that L∞-uniform convergence of the approximated solutions is achieved taking into account damping terms and suitable regularities on load terms. We shall also give some error estimates of the method.