Some Optimally Convergent Algorithms for Decoupling the Computation of Biot's Model

We study numerical algorithms for solving Biot's model. Based on a three-field reformulation, we present some algorithms that are inspired by the work of Chaabane et al. (Comput Math Appl 75(7):2328-2337) and Lee (Unconditionally stable second order convergent partitioned methods for multiple-network poroelasticity arXiv:1901.06078, 2019) for decoupling the computation of Biot's model. A new theoretical framework is developed to analyze the algorithms. Considering a uniform temporal discretization, these algorithms solve the coupled model on the first time level. On the remaining time levels, one algorithm solves a reaction-diffusion subproblem first and then solves a generalized Stokes subproblem. Another algorithm reverses the order of solving the two subproblems. Our algorithms manage to decouple the numerical computation of the coupled system while retaining the convergence properties of the original coupled algorithm. Theoretical analysis is conducted to show that these algorithms are unconditionally stable and optimally convergent. Numerical experiments are also carried out to validate the theoretical analysis and demonstrate the advantages of the proposed algorithms.