On an accurate A-posteriori error estimator and adaptive time stepping for the implicit and explicit composite time integration algorithms - Wang, Yazhou; Zhang, Tong; Zhang, Xuelin; Mei, Shengwei; Xie, Ningning; Xue, Xiaodai; Tamma, Kumar (Computers & structures, 2022)
•The novel design of A-posteriori error estimator based on the generalized polynomial is demonstrated for composite time integration methods.•The proposed error estimators, Disp/P3 and Disp/P4, have generalized compact single-step representations and work for the entire subsites in both implicit and explicit composite schemes.•Validation tests of linear and nonlinear, damped and undamped cases demonstrate the accurate estimation of the local error with arbitrary time steps, and the effectivity index is close to unity.•The adaptive time stepping procedure based on the proposed error estimator is utilized for efficient transient simulations, benefiting to the computational expense. This paper focuses on the design of an accurate and versatile A-posteriori error estimation and adaptive time stepping for general composite schemes and typical of the implicit ρ∞-Bathe and explicit Noh-Bathe composite methods for time integration in second-order transient systems. Two novel error estimators, Disp/P3 and Disp/P4, are newly proposed based on the generalized polynomials. They have generalized compact single-step representations and work for both implicit and explicit, dissipative and non-dissipative composite schemes. Validation tests of linear and nonlinear problems show that the estimated local error reaches excellent agreement with the exact local error, and the third-order convergence rates of the local error are obtained. Besides, the Disp/P4 is more accurate than Disp/P3 as the effectivity index is almost identical to unity when random time steps are taken into consideration, and hence the Disp/P4 is highly recommended to be merged to the adaptive time stepping procedure. Three examples encompassing the wave propagation, damped/undamped spring-pendulum, and nonlinear spring-mass system are solved by implicit and explicit composite methods via the adaptive time stepping. Numerical results show the advantage of adaptive time stepping based on the proposed error estimator in contrast to constant time stepping regarding the CPU cost.