Non‐Intrusive Global‐Local Method for Poroelasticity Problems With Localized Pressure Effects

ABSTRACT In many poroelasticity applications, pressure effects are confined to a small region, making it inefficient and possibly unnecessary to solve the full system across the entire domain. Instead, we propose to solve the poroelasticity problem locally, where pressure effects are significant, and use a simpler linear elasticity model elsewhere. This creates a coupled elasticity–poroelasticity problem with transmission conditions. To solve this coupled problem, we propose a new non‐intrusive global–local algorithm that iteratively solves the elasticity problem in the entire (global) domain and the poroelasticity problem only in a local domain, ensuring proper transmission conditions across the interface. This approach, which extends the existing global–local concept applied to single‐physics problems to multiphysics systems, significantly reduces computational cost, especially when the local domain is much smaller than the global one. Numerical experiments demonstrate the robustness and efficiency of the method, showcasing its potential for providing an efficient solution for more complex multi‐physics problems with localized effects of a single physical process.