自启动单解显式时间积分器的研究进展及性能评估

Direct time integration methods play a critical role in the numerical computation of large-scale nonlinear dynamic systems, particularly in the field of engineering simulation and design. The self-starting single-solve explicit time integration methods have become essential tools in this domain due to their efficiency and reliability in handling complex nonlinear systems. However, as these algorithms continue to evolve and diversify, their performance varies significantly, underscoring the urgent need for a systematic review and in-depth analysis of their capabilities. This paper first introduces the key performance metrics for evaluating time integration methods, including accuracy, stability, amplitude and phase error, providing a theoretical foundation for readers. It then offers a detailed review of the development of self-starting single-solve explicit time integration methods, systematically tracing the evolution of various algorithms. Finally, the performance of several self-starting single-solve explicit methods is compared in terms of spectral properties, accuracy, stability, and error characteristics, with numerical verification performed using typical examples and engineering structures. The paper highlights two explicit methods that currently exhibit superior performance: The fully explicit GSSE method and the velocity-implicit GSSI method. Both methods are characterized by their self-starting capability, single-solution, explicitness, maximized conditional stability, controllable numerical dissipation (over the full range), and identical second-order accuracy. The primary distinction between the two lies in the computational effort required for damping problems and the size of the conditional stability domain in the presence of damping. The paper also explores future research directions for explicit time integration methods, emphasizing the potential for further optimization and development.