2025/07/03 by Jong-Ho Park, Park, Jongho, S. Majid Hassanizadeh +1 · 1 citation
Mathematics · #65N20 #65N55 #76S05 #90C25 #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2507.03192
openalex publication_date 2025/07/03 · openalex created_date 2025/10/20 · openalex updated_date 2026/07/28
High-velocity fluid flow through porous media is modeled by prescribing a nonlinear relationship between the flow rate and the pressure gradient, called the Darcy--Forchheimer equation. This paper is concerned with the analysis of parallel multilevel methods for solving the Darcy--Forchheimer model. We begin by reformulating the Darcy--Forchheimer model as a nearly semicoercive convex optimization problem via the augmented Lagrangian method. Building on this formulation, we develop a parallel multilevel method, also known as a multilevel additive Schwarz method, within the framework of subspace correction for nearly semicoercive convex problems, yielding a theoretically supported and computationally efficient solver for the Darcy--Forchheimer model. The convergence analysis establishes robustness with respect to the augmented Lagrangian parameter ε. To further enhance convergence, we incorporate a backtracking line search and a full approximation scheme. Numerical results support the theoretical findings and demonstrate the effectiveness of the proposed approach.