Crank-Nicolson-type iterative decoupled algorithms for Biot's consolidation model using total pressure
<|reference_start|>Crank-Nicolson-type iterative decoupled algorithms for Biot's consolidation model using total pressure: In this work, we develop Crank-Nicolson-type iterative decoupled algorithms for a three-field formulation of Biot's consolidation model using total pressure. We begin by constructing an equivalent fully implicit coupled algorithm using the standard Crank-Nicolson method for the three-field formulation of Biot's model. Employing an iterative decoupled scheme to decompose the resulting coupled system, we derive two distinctive forms of Crank-Nicolson-type iterative decoupled algorithms based on the order of temporal computation and iteration: a time-stepping iterative decoupled algorithm and a global-in-time iterative decoupled algorithm. Notably, the proposed global-in-time algorithm supports a partially parallel-in-time feature. Capitalizing on the convergence properties of the iterative decoupled scheme, both algorithms exhibit second-order time accuracy and unconditional stability. Through numerical experiments, we validate theoretical predictions and demonstrate the effectiveness and efficiency of these novel approaches.<|reference_end|>
@article{gu2024crank-nicolson-type,
    title={Crank-Nicolson-type iterative decoupled algorithms for Biot's
  consolidation model using total pressure},
    author={Huipeng Gu and Mingchao Cai and Jingzhi Li},
    journal={arXiv preprint arXiv:2409.18391},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.18391},
    primaryClass={math.NA cs.NA}
}