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Analysis and Computation of Decoupled Algorithm for a Poroelasticity Model

Abstract: By introducing an intermediate variable, the Biot model is reformulated into a 3-by-3 block tri-diagonal system. An alternating positive semidefinite splitting preconditioner is proposed for solving such double saddle point problem. This iteration method is proved to be convergent unconditionally. Moreover, a relaxed variant is established, which results in better spectral distribution and numerical performance. We discuss different preconditioners to accelerate the GMRES method and the results of numerical experiments shown that some of them have better performance in terms of iteration and CPU time.