Linear solvers for reservoir simulation applications are the objective of this review.
Specifically, we focus on techniques for Fully Implicit (FI) solution methods, in which the set …

In this article, a two-level overlap** domain decomposition preconditioner is developed for
solving linear algebraic systems obtained from simulating Darcy flow in high-contrast media …

In this paper, we develop a multigrid preconditioner to solve Darcy flow in highly
heterogeneous porous media. The key component of the preconditioner is to construct a …

We consider a numerical solution of the mixed dimensional discrete fracture model with
highly conductive fractures. We construct an unstructured mesh that resolves lower …

In this paper, we develop a highly parallelized preconditioner based on multiscale space to
tackle Darcy flow in highly heterogeneous porous media. The crucial component of this …

We propose an efficient and robust multiscale preconditioner for large-scale incompressible
flow in highly heterogeneous porous media. We start from the discretization of the first-order …

In this paper, we study two-grid preconditioners for three-dimensional single-phase
nonlinear compressible flow in highly heterogeneous porous media arising from reservoir …

In this paper, we propose an efficient and robust two-grid preconditioner for the linear
elasticity equation with high contrasts. To tackle the challenges imposed by multiple scales …

We study a method based on Balancing Domain Decomposition by Constraints (BDDC) for
numerical solution of a single-phase flow in heterogeneous porous media. The method …

Being able to reproduce the complex flow dynamics that take place in the subsurface is a
key requirement for efficient hydrocarbon recovery and other field operations, including …