Enhancing the scalability of shared-memory finite-element simulations: Application to polymer waterflooding in porous media

This paper presents a new structured workflow aimed at enhancing the efficiency and scalability of finite element simulations on shared-memory architectures, with application to polymer waterflooding in porous media. Parallelization is implemented via OpenMP, focusing on performance optimization across the entire simulation pipeline. Bottlenecks in matrix assembly, linear system resolution, and post-processing of derived unknowns are mitigated through strategies such as graph coloring, mesh reordering, and hardware-aware thread/data mapping. Additionally, a novel thread-aware rebalance coloring algorithm is introduced to redistribute elements across colors in a way that balances the computational load among threads, enhancing parallel efficiency. The mathematical model describes single-phase polymer waterflooding, incorporating non-Newtonian behavior due to the pseudoplastic nature of the aqueous phase, as well as hydrodynamic damage arising from adsorption/desorption and mechanical retention phenomena. The system of equations is discretized using a staggered finite element approach, where the hydrodynamic subsystem is solved with the Galerkin Finite Element Method (GFEM), and the transport equation is approximated through the Streamline-Upwind/Petrov-Galerkin (SUPG) method. Numerical experiments and scalability analyses on a 128-core shared memory AMD EPYC system demonstrate performance gains of up to 23 × , with near-linear scalability up to 32 threads and sustained efficiency across different mesh configurations. The proposed methodology provides a comprehensive and flexible framework for accelerating simulations in hydrodynamics and transport equations on complex porous media, contributing to more efficient reservoir management.