Scalable linear solvers for sparse linear systems from large-scale numerical simulations

TL;DR

This paper develops scalable parallel linear solvers for large sparse systems in reservoir simulations, enabling efficient computation on distributed-memory systems with thousands of CPU cores.

Contribution

It introduces a comprehensive framework of distributed matrix/vector modules, Krylov solvers, and preconditioners optimized for large-scale reservoir simulations on parallel systems.

Findings

Solvers demonstrate excellent scalability on thousands of CPU cores.

Integration with HYPRE's BoomerAMG enhances multigrid performance.

Parallel implementation supports efficient large-scale reservoir simulations.

Abstract

This paper presents our work on designing scalable linear solvers for large-scale reservoir simulations. The main objective is to support implementation of parallel reservoir simulators on distributed-memory parallel systems, where MPI (Message Passing Interface) is employed for communications among computation nodes. Distributed matrix and vector modules are designed, which are the base of our parallel linear systems. Commonly-used Krylov subspace linear solvers are implemented, including the restarted GMRES method, the LGMRES method, and the BiCGSTAB method. It also has an interface to a parallel algebraic multigrid solver, BoomerAMG from HYPRE. Parallel general-purpose preconditioners and special preconditioners for reservoir simulations are also developed. The numerical experiments show that our linear solvers have excellent scalability using thousands of CPU cores.