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- Joachim Schöberl, Walter Zulehner
- SIAM J. Matrix Analysis Applications
- 2007

We consider large scale sparse linear systems in saddle point form. A natural property of such indefinite 2-by-2 block systems is the positivity of the (1,1) block on the kernel of the (2,1) block. Many solution methods, however, require that the positivity of the (1,1) block is satisfied everywhere. To enforce the positivity everywhere, an augmented… (More)

- Walter Zulehner
- Math. Comput.
- 2002

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… (More)

- Walter Zulehner
- Computing
- 2000

In this paper smoothing properties are shown for a class of iterative methods for saddle point problems with smoothing rates of the order 1/m, where m is the number of smoothing steps. This generalizes recent results by Braess and Sarazin, who could prove this rates for methods where, in the context of the Stokes problem, the pressure correction equation is… (More)

- Walter Zulehner
- SIAM J. Matrix Analysis Applications
- 2011

In this paper we discuss how to find norms for parameter-dependent saddle point problems which lead to robust (i.e.: parameter-independent) estimates of the solution in terms of the data. In a first step a characterization of such norms is given for a general class of symmetric saddle point problems. Then, for special cases, explicit formulas for these… (More)

- Joachim Schöberl, Walter Zulehner
- Numerische Mathematik
- 2003

- Joachim Schöberl, René Simon, Walter Zulehner
- SIAM J. Numerical Analysis
- 2011

We consider the discretized optimality system of a special class of elliptic optimal control problems and propose an all-at-once multigrid method for solving this discretized system. Under standard assumptions the convergence of the multigrid method and the robustness of the convergence rates with respect to the involved parameter are shown. Numerical… (More)

- Huidong Yang, Walter Zulehner
- LSSC
- 2009

Fluid-structure interaction problems arise in many fields of application such as flows around elastic structures or blood flow in arteries. The method presented in this paper for solving such a problem is based on a reduction to an equation at the interface, involving the so-called Steklov-Poincaré operators. This interface equation is solved by a Newton… (More)

- Wolfgang Krendl, Valeria Simoncini, Walter Zulehner
- Numerische Mathematik
- 2013

For a general class of saddle point problems sharp estimates for Babuška's inf-sup stability constants are derived in terms of the constants in Brezzi's theory. In the finite-dimensional Hermitian case more detailed spectral properties of preconditioned saddle point matrices are presented, which are helpful for the convergence analysis of common Krylov… (More)

- Ulrich Langer, Günther Of, Olaf Steinbach, Walter Zulehner
- SIAM J. Scientific Computing
- 2007

The Boundary Element Tearing and Interconnecting (BETI) methods have recently been introduced as boundary element counterparts of the well–established Finite Element Tearing and Interconnecting (FETI) methods. In this paper we present inexact data–sparse versions of the BETI methods which avoid the elimination of the primal unknowns and dense matrices.… (More)

- Wolfgang Krendl, Valeria Simoncini, Walter Zulehner
- ENUMATH
- 2013

For the optimal control problem with time-periodic Stokes equations a practical robust preconditioner is presented. The discretization of the corresponding optimality system leads to a linear system with a large, sparse and complex 4-by-4 block matrix in saddle point form. We present a decoupling strategy, which reduces the system to two linear systems with… (More)