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We propose an augmented Lagrangian-based preconditioner to accelerate the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure such as those arising from mixed finite element…

Numerical Analysis · Mathematics 2023-10-26 Fatemeh P. A. Beik , Michele Benzi

We present a novel augmented Lagrangian (AL) preconditioner for the solution of linear systems arising from finite element discretizations of elliptic interface problems with jump coefficients. The method is based on the Fictitious Domain…

Numerical Analysis · Mathematics 2026-03-16 Michele Benzi , Marco Feder , Luca Heltai , Federica Mugnaioni

We address the solution of the distributed control problem for the steady, incompressible Navier--Stokes equations. We propose an inexact Newton linearization of the optimality conditions. Upon discretization by a finite element scheme, we…

Numerical Analysis · Mathematics 2025-04-16 Santolo Leveque , Michele Benzi , Patrick E. Farrell

In this paper, a novel augmented Lagrangian preconditioner based on global Arnoldi for accelerating the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure, these systems…

Numerical Analysis · Mathematics 2024-09-10 A. Badahmane , A. Ratnani , H. Sadok

Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-level domain decomposition preconditioners are based on the…

Numerical Analysis · Mathematics 2018-04-23 Gabriel R. Barrenechea , Michał Bosy , Victorita Dolean

In this article we study a mixed finite element formulation for solving the Stokes problem with general surface forces that induce a jump of the normal trace of the stress tensor, on an interface that splits the domain into two subdomains.…

Numerical Analysis · Mathematics 2019-04-03 Sébastien Court

In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries…

Numerical Analysis · Mathematics 2015-06-15 Sébastien Court , Michel Fournié , Alexei Lozinski

A non-overlapping domain decomposition algorithm is proposed to solve the linear system arising from mixed finite element approximation of incompressible Stokes equations. A continuous finite element space for the pressure is used. In the…

Numerical Analysis · Mathematics 2012-04-10 Jing Li , Xuemin Tu

We present augmented Lagrangian Schur complement preconditioners and robust multigrid methods for incompressible Stokes problems with extreme viscosity variations. Such Stokes systems arise, for instance, upon linearization of nonlinear…

Numerical Analysis · Mathematics 2021-11-03 Yu-hsuan Shih , Georg Stadler , Florian Wechsung

In this paper, we revisit an auxiliary space preconditioning method proposed by Xu [Computing 56, 1996], in which low-order finite element spaces are employed as auxiliary spaces for solving linear algebraic systems arising from high-order…

Numerical Analysis · Mathematics 2012-04-13 Young-Ju Lee , Wei Leng , Chen-Song Zhang

In Benzi & Olshanskii (SIAM J.~Sci.~Comput., 28(6) (2006)) a preconditioner of augmented Lagrangian type was presented for the two-dimensional stationary incompressible Navier--Stokes equations that exhibits convergence almost independent…

Numerical Analysis · Mathematics 2019-10-11 Patrick E. Farrell , Lawrence Mitchell , Florian Wechsung

Topology optimization problems generally support multiple local minima, and real-world applications are typically three-dimensional. In previous work [I. P. A. Papadopoulos, P. E. Farrell, and T. M. Surowiec, Computing multiple solutions of…

Numerical Analysis · Mathematics 2022-11-23 Ioannis P. A. Papadopoulos , Patrick E. Farrell

We study a fictitious domain approach with Lagrange multipliers to discretize Stokes equations on a mesh that does not fit the boundaries. A mixed finite element method is used for fluid flow. Several stabilization terms are added to…

Numerical Analysis · Mathematics 2017-10-24 Michel Fournié , Alexei Lozinski

The aim of this work is to present a parallel solver for a formulation of fluid-structure interaction (FSI) problems which makes use of a distributed Lagrange multiplier in the spirit of the fictitious domain method. The fluid subproblem,…

Numerical Analysis · Mathematics 2025-03-28 Daniele Boffi , Fabio Credali , Lucia Gastaldi , Simone Scacchi

We consider the problem of iteratively solving large and sparse double saddle-point systems arising from the stationary Stokes-Darcy equations in two dimensions, discretized by the Marker-and-Cell (MAC) finite difference method. We analyze…

Numerical Analysis · Mathematics 2023-02-28 Chen Greif , Yunhui He

We study a recently introduced formulation for fluid-structure interaction problems which makes use of a distributed Lagrange multiplier in the spirit of the fictitious domain method. The time discretization of the problem leads to a mixed…

Numerical Analysis · Mathematics 2017-05-01 Daniele Boffi , Lucia Gastaldi

A preconditioning strategy for the Powell-Hestenes-Rockafellar Augmented Lagrangian method (ALM) is presented. The scheme exploits the structure of the Augmented Lagrangian Hessian. It is a modular preconditioner consisting of two blocks.…

Optimization and Control · Mathematics 2017-02-24 AM Sajo-Castelli

We investigate the performance of multigrid preconditioners for solving linear systems arising from finite element discretizations of elliptic interface problems using the Fictitious Domain with Distributed Lagrange Multipliers (FD-DLM)…

Numerical Analysis · Mathematics 2025-03-04 Najwa Alshehri , Daniele Boffi , Chayapol Chaoveeraprasit

We propose an augmented Lagrangian preconditioner for a three-field stress-velocity-pressure discretization of stationary non-Newtonian incompressible flow with an implicit constitutive relation of power-law type. The discretization…

Numerical Analysis · Mathematics 2020-08-11 P. E. Farrell , P. A. Gazca-Orozco

In this research, to solve the large indefinite least squares problem, we firstly transform its normal equation into a sparse block three-by-three linear systems, then use GMRES method with an accelerated preconditioner to solve it. The…

Numerical Analysis · Mathematics 2025-05-26 Jun Li , Lingsheng Meng
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