Thies, Jonas and Hennig, Rebekka-Sarah and Wouters, Michiel (2019) Towards automatic exploration of bifurcation diagrams for large-scale applications. ENUMATH 2019, 30. Sept. - 4. Okt. 2019, Egmont aan Zee, the Netherlands.
![]() |
PDF
2MB |
Abstract
There are several libraries for computing branches of steady states of dynamical systems, e.g. LOCA (http://www.cs.sandia.gov/LOCA/) for large-scale problems like nonlinear PDEs. The core algorithms typically are (pseudo-)arclength continuation, Newton-Krylov methods and (sparse) eigenvalue solvers. While LOCA includes some basic techniques for computing bifurcation points and switching branches, the exploration of a complete bifurcation diagram still takes a lot of programming effort and manual interference. On the other hand, recent developments in algorithms for fully automatic exploration are condensed in a Python tool called PyNCT (https://pypi.org/project/PyNCT/). The scope of this algorithmically versatile software is, however, limited to relatively small (e.g. 2D) problems because of the lack of a high-performance linear algebra implementation of the numerical core. In this talk we aim to combine the best of both worlds: a high-level implementations of algorithms in PyNCT with parallel models and linear algebra implemented in Trilinos (LOCA/Epetra). PyNCT is extended to non-symmetric systems and its complete backend is replaced by the phist library (https://bitbucket.org/essex/phist), which allows straight-forwared coupling to Epetra and PDE models implemented originally for LOCA. We apply the new code to reaction-diffusion and fluid dynamics models in three space dimensions to demonstrate its potential. By combining state-of-the-art automatic continuation algorithms from PyNCT with high-performance solvers and preconditioners from phist and Trilinos, we show that fully automatic bifurcation analysis on HPC systems is possible.
Item URL in elib: | https://elib.dlr.de/130650/ | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Document Type: | Conference or Workshop Item (Speech) | ||||||||||||
Title: | Towards automatic exploration of bifurcation diagrams for large-scale applications | ||||||||||||
Authors: |
| ||||||||||||
Date: | October 2019 | ||||||||||||
Refereed publication: | No | ||||||||||||
Open Access: | Yes | ||||||||||||
Gold Open Access: | No | ||||||||||||
In SCOPUS: | No | ||||||||||||
In ISI Web of Science: | No | ||||||||||||
Status: | Published | ||||||||||||
Keywords: | Python, HPC, bifurcation diagrams, sparse linear algebra, parallel computing | ||||||||||||
Event Title: | ENUMATH 2019 | ||||||||||||
Event Location: | Egmont aan Zee, the Netherlands | ||||||||||||
Event Type: | international Conference | ||||||||||||
Event Dates: | 30. Sept. - 4. Okt. 2019 | ||||||||||||
Organizer: | TU Delft | ||||||||||||
HGF - Research field: | Aeronautics, Space and Transport | ||||||||||||
HGF - Program: | Space | ||||||||||||
HGF - Program Themes: | Space System Technology | ||||||||||||
DLR - Research area: | Raumfahrt | ||||||||||||
DLR - Program: | R SY - Space System Technology | ||||||||||||
DLR - Research theme (Project): | R - Vorhaben SISTEC (old) | ||||||||||||
Location: | Köln-Porz | ||||||||||||
Institutes and Institutions: | Institut of Simulation and Software Technology > High Performance Computing Institut of Simulation and Software Technology | ||||||||||||
Deposited By: | Thies, Jonas | ||||||||||||
Deposited On: | 25 Nov 2019 10:05 | ||||||||||||
Last Modified: | 04 Mar 2020 08:38 |
Repository Staff Only: item control page