When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

In this paper we will present a review of recent advances in the application of the augmented
Lagrange multiplier method as a general approach for generating multiplier-free stabilised …

Effective relaxation methods are necessary for good multigrid convergence. For many
equations, standard Jacobi and Gauß–Seidel are inadequate, and more sophisticated …

The magnetohydrodynamics (MHD) equations are generally known to be difficult to solve
numerically, due to their highly nonlinear structure and the strong coupling between the …

Abstract The MOOSE Navier–Stokes module solves mass, momentum, energy, and passive
scalar conservation equations in the context of fluid flow. The module supports solution of …

Augmented Lagrangian preconditioners have successfully yielded Reynolds-robust
preconditioners for the stationary incompressible Navier–Stokes equations, but only for …

Topology optimization problems often support multiple local minima due to a lack of
convexity. Typically, gradient-based techniques combined with continuation in model …

In this work, we propose a novel block preconditioner, labeled Explicit Decoupling Factor
Approximation (EDFA), to accelerate the convergence of Krylov subspace solvers used to …

Most research on preconditioners for time-dependent PDEs has focused on implicit multi-
step or diagonally-implicit multi-stage temporal discretizations. In this paper, we consider …

The Arnold–Winther element successfully discretizes the Hellinger–Reissner variational
formulation of linear elasticity; its development was one of the key early breakthroughs of the …