High-efficient decoupling method for coupling systems with multiple subdomains and time steps

This paper proposes a high-efficient decoupling method with energy conservation property to solve a coupling system with multiple subdomains and time steps using arbitrary Newmark schemes. Moreover, new General-α integration schemes with desirable algorithmic damping and accuracy are investigated and incorporated in the proposed method to filter spurious high-frequency vibration contents and retain the second-order accuracy. The proposed method can decompose the coupling system into several independent subdomains with different time steps, and different integration schemes can be employed to solve various subdomains independently. Accuracy and stability for each decoupling subdomain are ensured and adjusted using its integration parameters. The complicated and time-consuming border program is not used in the calculation process, and all subdomain vibrations are not split into link vibrations and free vibrations, therefore, computational efficiency is improved significantly compared with existing coupling methods. To conveniently derive the decoupling method, the coupling dynamic system with two subdomains and different time steps is established using the Newmark compact form firstly. Subsequently, a decoupling strategy is formulated to decompose and solve the coupling system, and its stability is proved by using the pseudo-energy method and classic mechanical energy method. Accordingly, New General-α schemes are investigated and incorporated in the proposed method to obtain desirable algorithmic damping and accuracy. Three illustrative examples are employed to demonstrate the accuracy, efficiency, energy property, and adaptability for multi-subdomains (≥3) of the proposed method.