Developing high-performance preconditioners based on multiscale domain decomposition methods

• Grant number: 25/09743-3
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: September 01, 2025
• End date: August 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Fabrício Simeoni de Sousa
• Grantee: Dilong Zhou
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

This research project aims to develop efficient preconditioners based on multiscale domain decomposition methods, with a focus on the Multiscale Robin Coupled Method (MRCM), for the numerical simulation of subsurface flows in porous media. These flows are governed by complex models such as Darcy flow and multiphase transport and have critical applications in fields like petroleum reservoir simulation, groundwater contamination, and carbon sequestration. The project will involve the design and implementation of novel interface spaces and adaptive coupling strategies to improve the accuracy and scalability of simulations, particularly in the presence of heterogeneous and fractured media. These advancements will be integrated into an existing high-performance 3D parallel simulation framework and tested using large-scale computations on the Euler/CeMEAI cluster. In addition to methodological development, the project will explore the use of multiscale techniques as preconditioners for general linear solvers, enhancing the efficiency of Krylov-based iterative methods. The research will contribute to both theoretical and computational advancements in numerical methods for partial differential equations, with results disseminated through scientific publications and conferences. (AU)