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Towards automatic exploration of bifurcation diagrams for large-scale applications

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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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
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Wouters, MichielUniversity of AntwerpUNSPECIFIEDUNSPECIFIED
Date:October 2019
Refereed publication:No
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:No
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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