Physics-informed neural networks (PINNs) are a powerful approach for solving problems
involving differential equations, yet they often struggle to solve problems with high frequency …

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 …

One of the state-of-the-art strategies for predicting crack propagation, nucleation, and
interaction is the phase-field approach. Despite its reliability and robustness, the phase-field …

The nonlinear systems obtained by discretizing degenerate parabolic equations may be
hard to solve, especially with Newton's method. In this paper, we apply to the Richards …

Parallel Newton--Krylov FETI-DP (Finite Element Tearing and Interconnecting---Dual-Primal)
domain decomposition methods are fast and robust solvers, eg, for nonlinear implicit …

Nonlinearly preconditioned inexact Newton methods have been applied successfully for
some difficult nonlinear systems of algebraic equations arising from the discretization of …

For linear and nonlinear systems arising from the discretization of PDEs, multiplicative
Schwarz preconditioners can be defined based on subsets of the unknowns that derive from …

Efficient simulation of multiphysics problems is a challenging task. This is often due to the
multiscale nature of the physics and nonlinear coupling between the different processes …

Abstract Development of robust and efficient nonlinear solution strategies for multi-phase
flow and transport within natural porous media is challenging. Fully Implicit Method (FIM) is …

Abstract Domain decomposition methods are widely used as preconditioners for Krylov
subspace linear solvers. In the simulation of porous media flow there has recently been a …