Software: GAIO, PARTY and GADS
GAIO - Global Analysis of Invariant Objects
GAIO is a software package for the global numerical analysis of dynamical systems and optimization problems based on set oriented techniques. It may e.g. be used to compute invariant sets, invariant manifolds, invariant measures and almost invariant sets in dynamical systems and to compute the globally optimal solutions of both scalar and multiobjective problems.For further information, in particular on how to obtain it, please contact gaio@djs2.de.
Example: An Unstable Manifold in the Restricted Three Body Problem
GAIO is © 1995-2000 Chair of Applied Mathematics, 2001-2003 djs2 GmbH
PARTY
The problem of partitioning a graph into a number of pieces is one of the fundamental tasks in computer science and occurs
in several applications like parallel programming or VLSI design.Finding optimal partitions
according to different measures is in most cases NP-complete.
A large number of efficient partitioning heuristics have been
developed, but their performance in terms of computation time as well
as solution quality is heavily influenced by choices of parameters and
certain implementation details. Fortunately, the partitioning problem
itself is clearly defined and its description leads to a small
interface.
The PARTY partitioning library serves a variety of different
partitioning methods. Instead of implementing the methods by himself,
the user may take advantage of the PARTY implementations. The
performance of the code has been improved over several years and the
default setting of the library enables a fast and easy start for the
user. Two kinds of interfaces allow the use as stand-alone tool as well
as the inclusion into application codes. Several research projects
currently use the PARTY partitioning library successfully to solve
their partitioning problem.
For further information, in particular on how to obtain it, please contact Robert Preis.
PARTY is © 1995-2004 Robert Preis
GADS - Graph Algorithms for Dynamical Systems
GADS is a toolbox of graph algorithms for the analysis of dynamical systems. It is based on the tools GAIO and PARTY and has interfaces to both tools. The set-oriented methods from GAIO are used to construct a discretized graph of the system. The graph algorithms of GADS and also from PARTY are used to describe the key characteristics of the dynamical system.
For further information, in particular on how to obtain it, please contact Robert Preis.
GADS is © 2003-2004 Chair of Applied Mathematics