Numerical investigation on the fixed-stress splitting scheme for Biot's equations: Optimality of the tuning parameter
For researchers using iterative coupling methods in poroelasticity, this work shows that existing optimal parameter formulas are incomplete, motivating more comprehensive mathematical analyses.
The paper numerically investigates the optimal tuning parameter for the fixed-stress splitting scheme in solving Biot's equations, finding that the optimal value depends not only on mechanical parameters but also on boundary conditions and fluid flow parameters.
We study the numerical solution of the quasi-static linear Biot's equations solved iteratively by the fixed-stress splitting scheme. In each iteration the mechanical and flow problems are decoupled, where the flow problem is solved by keeping an artificial mean stress fixed. This introduces a numerical tuning parameter which can be optimized. We investigate numerically the optimality of the parameter and compare our results with physically and mathematically motivated values from the literature, which commonly only depend on mechanical material parameters. We demonstrate, that the optimal value of the tuning parameter is also affected by the boundary conditions and material parameters associated to the fluid flow problem suggesting the need for the integration of those in further mathematical analyses optimizing the tuning parameter.