We proposed a parallel-in-time method based on preconditioner for Biot's consolidation model in poroelasticity. In order to achieve a fast and stable convergence for the matrix system of the Biot's model, we design two preconditioners with approximations of the Schur complement. The parallel-in-time method employs an inverted time-stepping scheme that iterates to solve the preconditioned linear system in the outer loop and advances the time step in the inner loop. This allows us to parallelize the iterations with a theoretical parallel efficiency that approaches 1 as the number of time steps and spatial steps grows. We demonstrate the stability, accuracy, and linear speedup of our method on HPC platform through numerical experiments.

翻译：针对多孔弹性力学中的Biot固结模型，本文提出一种基于预处理器的时空并行方法。为获得Biot模型矩阵系统的快速稳定收敛，我们设计了两种基于Schur补近似形式的预处理器。该时空并行方法采用逆时步进方案，通过外层循环迭代求解预条件线性系统，同时在内层循环中推进时间步长。这种设计使得迭代过程可并行化，其理论并行效率随时间步与空间步数量增加趋近于1。通过在高性能计算平台上的数值实验，我们验证了该方法的稳定性、精度及线性加速比。