On the analysis of block smoothers for saddle point problems
We discuss several Uzawa-type iterations as smoothers in the context of multigrid schemes
for saddle point problems. A unified framework to analyze the smoothing properties is …
for saddle point problems. A unified framework to analyze the smoothing properties is …
Multigrid preconditioning for discontinuous Galerkin discretizations of an elliptic optimal control problem with a convection-dominated state equation
S Liu, V Simoncini - Journal of Scientific Computing, 2024 - Springer
We consider discontinuous Galerkin methods for an elliptic distributed optimal control
problem constrained by a convection-dominated problem. We prove global optimal …
problem constrained by a convection-dominated problem. We prove global optimal …
A matrix-free multilevel preconditioner for the generalized stokes problem with discontinuous viscosity
M Wichrowski, P Krzyżanowski - Journal of Computational Science, 2022 - Elsevier
In this paper we present a matrix-free multilevel solver for the generalized Stokes problem
with discontinuous viscosity. The algorithm is based on the FGMRES iteration …
with discontinuous viscosity. The algorithm is based on the FGMRES iteration …
A scalable preconditioning framework for stabilized contact mechanics with hydraulically active fractures
A preconditioning framework for the coupled problem of frictional contact mechanics and
fluid flow in the fracture network is presented. We focus on a blended finite element/finite …
fluid flow in the fracture network is presented. We focus on a blended finite element/finite …
Robust multigrid methods for discontinuous Galerkin discretizations of an elliptic optimal control problem
S Liu - Computational Methods in Applied Mathematics, 2025 - degruyter.com
We consider discontinuous Galerkin methods for an elliptic distributed optimal control
problem, and we propose multigrid methods to solve the discretized system. We prove that …
problem, and we propose multigrid methods to solve the discretized system. We prove that …
Fast auxiliary space preconditioners for linear elasticity in mixed form
A block-diagonal preconditioner with the minimal residual method and an approximate block-
factorization preconditioner with the generalized minimal residual method are developed for …
factorization preconditioner with the generalized minimal residual method are developed for …
High-order finite element methods for a pressure Poisson equation reformulation of the Navier–Stokes equations with electric boundary conditions
RR Rosales, B Seibold, D Shirokoff, D Zhou - Computer Methods in …, 2021 - Elsevier
Pressure Poisson equation (PPE) reformulations of the incompressible Navier–Stokes
equations (NSE) replace the incompressibility constraint by a Poisson equation for the …
equations (NSE) replace the incompressibility constraint by a Poisson equation for the …
Multigrid methods for saddle point problems: Darcy systems
We design and analyze multigrid methods for the saddle point problems resulting from
Raviart–Thomas–Nédélec mixed finite element methods for the Darcy system in porous …
Raviart–Thomas–Nédélec mixed finite element methods for the Darcy system in porous …
Scalable preconditioning for the stabilized contact mechanics problem
We present a family of preconditioning strategies for the contact problem in fractured and
faulted porous media. We combine low-order continuous finite elements to simulate the bulk …
faulted porous media. We combine low-order continuous finite elements to simulate the bulk …
Multigrid methods for saddle point problems: Optimality systems
We develop multigrid methods for an elliptic distributed optimal control problem on convex
domains that are robust with respect to a regularization parameter. We prove the uniform …
domains that are robust with respect to a regularization parameter. We prove the uniform …