Domain decomposition with local time discretization for the nonlinear Stokes–Biot system

Abstract

This work presents a domain decomposition method for the fluid-poroelastic structure interaction (FPSI) system, which utilizes local time integration for subproblems. To derive the domain decomposition scheme, we introduce a Lagrange multiplier and define time-dependent Steklov–Poincaré-type operators based on the interface conditions. These operators are employed to transform the coupled system into an evolutionary nonlinear interface problem, which is then solved using an iterative algorithm. This approach provides the flexibility to use different time discretization schemes and step sizes in subdomains, making it an efficient method for simulating multiphysics systems. We present numerical tests for both non-physical and physical problems to demonstrate the accuracy and efficiency of this method.