Abstract

In this talk, I will present several parallel iterative algorithms for nonlinear thermo-poroelasticity, free of Poisson locking as well as pressure and temperature oscillations.  An auxiliary variable is introduced to transform the original model into a four-field formulation in order to overcome locking-induced oscillations. The iterative idea is extended to linearize and decouple the four-field model. Different coupling strategies are employed among these three subproblems, combined with appropriately designed iteration settings, yielding distinct iterative parallel algorithms. Stabilization terms are incorporated into these algorithms to suppress pressure and temperature oscillations in extreme situations. Error estimates are derived for the nonlinear coupled model, and the convergence of these parallel iterative decoupled algorithms is proved. Finally, numerical experiments are presented to compare the performance of the different parallel algorithms in both weakly and strongly coupled regimes, thereby validating their efficiency and robustness.