Journal ArticleDOI
Downwind Gauß-Seidel-Smoothing for Convection-Dominated Problems
Hackbusch Wolfgang,Probst Thomas +1 more
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This paper deals with an appropriate ordering strategy and block partitioning of the Gauß‐Seidel iteration and its application to multigrid methods for convection‐dominated problems.Abstract:
Due to the vanishing ellipticity, multigrid methods for convection-dominated problems tend to loose their good convergence properties. With a suited discretisation, an appropriate ordering of the unknowns and, if necessary, a special block partitioning, the smoothing property of the Gaus-Seidel iteration and therefore good convergence can be regained. This paper deals with such an ordering strategy and block partitionings.read more
Citations
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Journal ArticleDOI
An Augmented Lagrangian-Based Approach to the Oseen Problem
TL;DR: An effective solver for the discrete Oseen problem based on an augmented Lagrangian formulation of the corresponding saddle point system based on a block triangular preconditioner used with a Krylov subspace iteration like BiCGStab is described.
Book
Iterative Methods for Linear Systems: Theory and Applications
TL;DR: This book distinguishes itself from other texts on the topic by providing a straightforward yet comprehensive analysis of the Krylov subspace methods, approaching the development and analysis of algorithms from various algorithmic and mathematical perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning.
Journal ArticleDOI
Analysis of tensor product multigrid
Steffen Börm,Ralf Hiptmair +1 more
TL;DR: This work considers anisotropic second order elliptic boundary value problems in two dimensions, for which the anisotropy is exactly aligned with the coordinate axes, and employs eigenspace techniques to separate the coordinate directions.
Journal ArticleDOI
Navier--Stokes Equations in Rotation Form: A Robust Multigrid Solver for the Velocity Problem
TL;DR: This paper analyzes a standard finite element method for the discretization of a coupled nonsymmetric system of linear equations of diffusion-reaction type, and introduces and analyze a multigrid solver for the discrete problem.
Journal ArticleDOI
Robust smoothers for high-order discontinuous Galerkin discretizations of advection-diffusion problems
TL;DR: It is demonstrated that multilevel methods with suitably chosen smoothers can provide such solvers, even in the presence of non self-adjoint advection terms and locally refined meshes.
References
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Journal ArticleDOI
Downwind Gauß‐Seidel Smoothing for Convection Dominated Problems
Wolfgang Hackbusch,Thomas Probst +1 more
TL;DR: Numerical experiments show that, in the case of general convection directions, the multigrid algorithms obtained in this way have the same properties as in the model situation.
Journal ArticleDOI
On the feedback vertex set problem for a planar graph
TL;DR: An algorithm solving the feedback-vertex-set problem for planar digraphs is described and a side-product is a decomposition of the graph into subsets that are of interest for block-Gauß-Seidel smoothers in multi-grid methods.