Software

1. FLENS - A Flexible Library for Efficient Numerical Solutions

FLENS is an open source software project developed at the Department of Numerical Mathematics at the University of Ulm (Michael Lehn, Alexander Stippler, Sebastian Singer, Karsten Urban). A detailed documetntation and the download sources can be found on sourceforge.
FLENS is used both in teaching and research.

2. Wavelet Software

Here you will find:

• Registration and access to the software
• Library MSLib
• Wavelet methods for the Stokes problem
• Demo gallery of adaptive wavelet methods

Registration and access

To download the software you need to register via this webpage

Library MSLib

The software package MSLib (MultiScale Library) includes the following routines:
- basic linear algebra tools for vector-matrix-calculations
- standard solvers for linear systems
- data structures for refinable functions and wavelets
- construction of divergence free wavelets
- construction of wavelet based trial spaces that fulfill LBB
- evaluation of integrals of (derivatives of) refinable functions
- setup of the corresponding stiffness matrices
- multiscale transformations
- multilevel preconditioners for pcg methods

You can find an overview of the software in the following papers:

• "Towards Object Oriented Software Tools for Numerical Multiscale Methods for P.D.E.s using Wavelets"
  - Titus Barsch, Angela Kunoth, Karsten Urban,
  In: Multiscale Methods for Partial Differential Equations, W. Dahmen, A. Kurdilla, P. Oswald (eds.), Academic Press, 1997, 383-412.
• "Software Tools for using wavelets on the interval for the numerical solution of operator equations"
  - Titus Barsch, Karsten Urban, In Concepts of Numerical Software, W. Hackbusch and G. Wittum (eds.), 2000, 13-25.
• There is also a detailed documentation for version 1.0 available:
  "The Multilevel Library: Software Tools for Multiscale Methods and Wavelets, Version 1.0, Documentation"
  - Arne Barinka, Titus Barsch, Karsten Urban, Jürgen Vorloeper, IGPM-Report 156, RWTH Aachen, 1996.
  as well as for version 2.1:
  "The Multilevel Library: Software Tools for Multiscale Methods and Wavelets, Version 2.1, Documentation"
  - Arne Barinka, Titus Barsch, Karsten Urban, Jürgen Vorloeper
  RWTH Aachen, IGPM report 205, 2001.

Wavelet methods for the Stokes problem

This software package provides routines for solving the Stokes problem with adapted wavelet bases (divergence-free wavelets as well as with wavelet trial spaces fulfilling the LBB condition). The figures show the velocity field for a 3d (left) and a 2d (right) cavity.

References:

• "A Wavelet-Galerkin Method for the Stokes-Equations"
  - Wolfgang Dahmen, Angela Kunoth, Karsten Urban
  Computing, 56, No. 3 (1996), 259-302.
  
• "Using divergence free wavelets for the numerical solution of the Stokes problem"
  - Karsten Urban
  In Algebraic Multilevel Iterations, O. Axelsson, B. Polman (ed.), Nijmegen, 1996, 259-278.
  
• "On Divergence-free Wavelets"
  - Karsten Urban
  Advances in Computational Mathematics 4, No. 1,2, 51-82, 1995, Abstract.
  
• "Multiskalenverfahren für das Stokes-Problem und angepaßte Wavelet-Basen" (PhD thesis, in german)
  - Karsten Urban
  Verlag der Augustinus-Buchhandlung, Aachen, 1995. ISBN 3-86073-424-5.
  Zusammenfassung
  

Demo gallery of adaptive wavelet methods

The gallery contains some demos for adaptive wavelet methods in 1d and 2d. For example, it contains the following movie of an adaptive Wavelet-Galerkin method on the L-shaped domain.

References:

• "Adaptive Wavelet Schemes for Elliptic Problems - Implementation and Numerical Experiments"
  (Revised Version, Nov. `99)
  - Arne Barinka, Titus Barsch, Philippe Charton, Albert Cohen, Stephan Dahlke, Wolfgang Dahmen, Karsten Urban
  RWTH Aachen, IGPM report 173, 1999.