IFISS : a computational laboratory for investigating incompressible flow problems

The IFISS Incompressible Flow & Iterative Solver Software package contains software which can be run with MATLAB or Octave to create a computational laboratory for the interactive numerical study of incompressible flow problems. It includes algorithms for discretization by mixed finite element methods and a posteriori error estimation of the computed solutions, together with state-of-the-art preconditioned iterative solvers for the resulting discrete linear equation systems. In this paper we give a flavour of the code's main features and illustrate its applicability using several case studies. We aim to show that IFISS can be a valuable tool in both teaching and research

Preconditioning for nonsymmetry and time-dependence

In this short paper, we decribe at least one simple and frequently arising situation |that of nonsymmetric real Toeplitz (constant diagonal) matrices| where we can guarantee rapid convergence of the appropriate iterative method by manipulating the problem into a symmetric form without recourse to the normal equations. This trick can be applied regardless of the nonnormality of the Toeplitz matrix. We also propose a symmetric and positive definite preconditioner for this situation which is proved to cluster eigenvalues and is by consequence guaranteed to ensure convergence in a number of iterations independent of the matrix dimension

Block Preconditioners for the Incompressible Stokes Problem

Abstract. This paper discusses the solution of the Stokes problem using block preconditioned iterative methods. Block preconditioners are based on the block factorization of the discretized problem. We focus on two specific types: SIMPLE-type preconditioners and the LSC preconditioner. Both methods use scaling to improve their performance. We test convergence of GCR in combination with these preconditioners both for a constant and a non-constant viscosity Stokes problem.