Thies, Jonas and Hennig, Rebekka-Sarah and Wouters, Michiel (2019) Towards automatic exploration of bifurcation diagrams for large-scale applications. ENUMATH 2019, 2019-09-30 - 2019-10-04, Egmont aan Zee, the Netherlands.
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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/ | ||||||||||||||||
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Document Type: | Conference or Workshop Item (Speech) | ||||||||||||||||
Title: | Towards automatic exploration of bifurcation diagrams for large-scale applications | ||||||||||||||||
Authors: |
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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 Start Date: | 30 September 2019 | ||||||||||||||||
Event End Date: | 4 October 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: | 24 Apr 2024 20:34 |
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