New version pde2path 3.0 (June 2021).
Download: pde2path (software and demos) tar.gz
or zip.
Latest updates:
June 2021: version 3.0, stable version,
associated to the book Numerical continuation and bifurcation in Nonlinear PDEs, SIAM. Also contains a first version of higher order finite elements, following Pozrikidis' FSElib .
See also the pde2path with higher order FEM
tutorial.
January 2021: New tutorial
pde2path without FEM, explaining mods to
run pde2path on "general" right hand sides.
September 2020: most of pde2path now also runs under
octave. See README in the folder
octave of the pde2path download. Otherwise: bug--fixes, and additional
demos (chtor, schnakcone) for problems on curved surfaces,
see Pattern formation tutorial [ยง5 and 6].
pde2path is written and maintained by Hannes deWitt, Tomas Dohnal,
Jens Rademacher, Hannes Uecker, and Daniel Wetzel.
Many thanks to: Francesca Mazzia
for TOM,
to Uwe Prüfert for providing OOPDE,
to Daniel Kressner for pqzschur, and to Kristian Ejlebjaerg Jensen
for trullekrul.
For bugs, questions or remarks please write to:
hannes.uecker -- at -- uol.de, and/or (in particular in case of no response) to
pde2path -- at -- uni-oldenburg.de.
Any feedback is welcome. Abstract.
pde2path is a continuation/bifurcation
package for systems of PDEs over bounded d-dimensional
domains, d=1,2,3, including features such as
nonlinear boundary conditions, cylinder and
torus geometries (i.e., periodic boundary conditions), and a
general interface for adding auxiliary equations like mass
conservation or phase equations for continuation of traveling waves.
The original version 1.0 was for elliptic systems in 2D and based on the Matlab
pdetoolbox, which since v2.3 has been more or less replaced by the free
package
OOPDE. Recent additions (v2.5 and v2.6) include the handling of
multiple steady
bifurcation points, Branch point continuation and Hopf point continuation
via extended systems, continuation of relative equilibria (e.g., traveling waves and rotating waves), branch switching from periodic orbits
(Hopf pitchfork/transcritical bifurcation, and period doubling), and new demos,
for instance on pattern formation on spheres and tori (Pattern formation tutorial, § 6), and on the computation of
coefficients of amplitude equations for Turing bifurcations (ampsys tutorial,
standalone version of ampsys as tar
or zip). In v2.7 we added 2D and 3D
anisotropic mesh adaptation by
trullekrul,
and algorithms for
canonical paths to canonical periodic states in OC problems, in
v2.8 mainly examples of deflation and of periodic orbits in
non-autonomous systems, and since v2.9 we aim to maintain
octave compatibility.
License
pde2path is free software; you can redistribute it and/or modify it under the terms of the GNU GPL as published by the Free Software Foundation. pde2path is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY. See the GNU GPL for more details.
pde2path comes with four third party libraries, OOPDE, pqzschur, TOM,
and trullekrul, with permission, and somewhat modified by the pde2path team.
If you want to redistribute (parts of) these libraries yet again, please first get in touch with the respective author to obtain more information on newer versions.
Your use of pde2path implies that you agree to this License.
References.
A book describing the use of pde2path, and some of the mathematics behind it, is
H. Uecker,
Numerical continuation and bifurcation in Nonlinear PDEs, SIAM, 2021.
A review is given in
H. Uecker,
Numerical continuation and bifurcation in Nonlinear PDEs - Algorithms,
Applications, and Experiments,
Jahresbericht der DMV, 2021.
Here is the old preprint.
It also contains some details of the mathematics behind the
continuation and bifurcation, some mathematical and modeling background
on the example problems, and many references.
v2.0 was first described in
T. Dohnal, J. Rademacher, H. Uecker, D. Wetzel,
pde2path 2.0: multi-parameter continuation and periodic domains, in
Horst Ecker, Alois Steindl, Stefan Jakubek, eds,
ENOC 2014 - Proceedings of 8th European Nonlinear Dynamics Conference.
preprint.
The Hopf algorithms and basic Hopf demos are described in
H. Uecker,
Hopf bifurcation and time periodic orbits with pde2path - algorithms and applications, Communications in Computational Physics, doi: 10.4208/cicp.OA-2017-018, 2018.
preprint. Note that the Hopf algorithms have
since been significantly extended, see the Hopf tutorial
An overview of applications of pde2path to scalar problems is also given
in
S. Engelnkemper, S. V. Gurevich, H. Uecker, D. Wetzel, U. Thiele,
Continuation for thin film hydrodynamics and
related scalar problems, in Comput. Methods Appl. Sci., 50, Springer, Cham, 2019, preprint
