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.

翻译：本文针对采用总压力的三场Biot固结模型，提出了Crank-Nicolson型迭代解耦算法。首先，我们采用标准Crank-Nicolson方法为Biot模型的三场表述构建了等效的完全隐式耦合算法。通过运用迭代解耦方案分解所得耦合系统，我们根据时间计算与迭代的次序推导出两种不同形式的Crank-Nicolson型迭代解耦算法：时间步进迭代解耦算法与全局时间迭代解耦算法。值得注意的是，所提出的全局时间算法支持部分时间并行特性。得益于迭代解耦方案的收敛特性，两种算法均表现出二阶时间精度与无条件稳定性。通过数值实验，我们验证了理论预测，并证明了这些新方法的有效性与计算效率。