Department of Scientific Computing   
Institute for Numerical Simulation   
University of Bonn   
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AWFD - Adaptivity, Wavelets & Finite Differences

In general AWFD (Adaptivity, Wavelets & Finite Differences) is a C++ class library for wavelet based solvers for PDEs and integral equations. The software distribution comes with a number of examples and a complete documentation and user guide.

AWFD Features

The main features of AWFD are:
  • Petrov-Galerkin discretizations of linear and non-linear elliptic and parabolic PDE (scalar as well as systems)
  • Adaptive sparse grid strategy for a higher order interpolet multiscale basis
  • Adaptivity control via thresholding of wavelet coefficients
  • Multilevel lifting-preconditioner for linear systems
  • Neumann and Dirichlet boundary conditions
The software distribution includes:
  1. MATLAB functions for the generation of wavelet filter masks
  2. Data structures for uniform, level-adaptive and fully adaptive trial spaces (i.e. grids)
  3. Algorithms for the initialization and refinement of adaptive grids
  4. Algorithms for (adaptive) wavelet transforms, finite difference-/collocation-/Galerkin-discretizations
  5. Linear Algebra
  6. Solvers / preconditioners
  7. IO functions with interfaces to e.g. MATLAB and VTK
The current release is: v0.95.


  1. F. Koster. Multiskalen-basierte Finite Differenzen Verfahren auf adaptiven dünnen Gittern. Doktorarbeit, Universität Bonn, January 2002.
  2. M. Griebel and F. Koster. Adaptive wavelet solvers for the unsteady incompressible Navier Stokes equations. In J. Malek, J. Necas, and M. Rokyta, editors, Advances in Mathematical Fluid Mechanics, Lecture Notes of the Sixth International School ''Mathematical Theory in Fluid Mechanics'', Paseky, Czech Republic, September 1999. Springer Verlag, 2000. also as Report SFB 256 No. 669, Institut für Angewandte Mathematik, Universität Bonn, 2000.
  3. M. Griebel. Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences. Computing, 61(2):151-179, 1998.
    Also as: Proceedings Large-Scale Scientific Computations of Engineering and Environmental Problems, 7. June - 11. June, 1997, Varna, Bulgaria, Notes on Numerical Fluid Mechanics 62, Vieweg-Verlag, Braunschweig, M. Griebel, O. Iliev, S. Margenov and P. Vassilevski (editors).
  4. T. Schiekofer. Die Methode der Finiten Differenzen auf dünnen Gittern zur Lösung elliptischer und parabolischer partieller Differentialgleichungen. Doktorarbeit, Universität Bonn, 1999.