A domain decomposition method with Lagrange multipliers for the Stokes problem is developed and analysed. A common approach to solve the Stokes problem, termed the Uzawa algorithm, is to decouple the velocity and the pressure. This approach yields the Schur complement system for the pressure Lagrange multiplier which is solved with an iterative solver. Each outer iteration of the Uzawa procedur...

Abstract. We propose and study, for structural dynamic problems, a domain decomposition method based on an augmented Lagrangian formulation. This method uses an inexact Uzawa algorithm to solve the linear system required at any time increment. The proposed algorithm is interesting, for parallel and vector applications, because it doesn’t need scalar products and has less operations by iteration...

We propose a Uzawa block relaxation domain decomposition method for a two-body contact problem with Tresca friction. We introduce auxiliary interface unknowns to transform the variational problem into a saddle-point problem. Applying a Uzawa block relaxation algorithm to the corresponding augmented Lagrangian functional we obtain a domain decomposition algorithm in which we have to solve two un...

In this paper two classes of iterative methods for saddle point problems are considered: inexact Uzawa algorithms and a class of methods with symmetric preconditioners. In both cases the iteration matrix can be transformed to a symmetric matrix by block diagonal matrices, a simple but essential observation which allows one to estimate the convergence rate of both classes by studying associated ...

In this work, we propose three novel block-structured multigrid relaxation schemes based on distributive relaxation, Braess–Sarazin and Uzawa for solving the Stokes equations discretized by marker-and-cell scheme. The mass matrix obtained from bilinear finite element method is directly used to approximate inverse of scalar Laplacian operator in schemes. Using local Fourier analysis, theoretical...

In this paper we present an adaptive strategy to obtain an incompressible wind field that adjusts to an experimental one, and verify boundary conditions of physical interest. We use an Augmented Lagrangian formulation for solving this problem. Our method is based on an Uzawa iteration to update the Lagrange multiplier and on an elliptic adaptive inner iteration for velocity. Several examples sh...