TY - GEN
T1 - Towards Scalable Automatic Exploration of Bifurcation Diagrams for Large-Scale Applications
AU - Thies, Jonas
AU - Wouters, Michiel
AU - Hennig, Rebekka Sarah
AU - Vanroose, Wim
PY - 2021
Y1 - 2021
N2 - The Trilinos library LOCA (http://www.cs.sandia.gov/LOCA/ ) allows computing branches of steady states of large-scale dynamical systems like (discretized) 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 PyNCT (https://pypi.org/project/PyNCT/ ). The scope of this algorithmically versatile software is, however, limited to relatively small (e.g. 2D) problems because it relies on linear algebra from Python libraries like NumPy. Furthermore, PyNCT currently does not support problems with a non-Hermitian Jacobian matrix, which rules out interesting applications in chemistry and fluid dynamics. In this paper we aim to combine the best of both worlds: a high-level implementation of algorithms in PyNCT with parallel models and linear algebra implemented in Trilinos. PyNCT is extended to non-symmetric systems and its complete backend is replaced by the PHIST library (https://bitbucket.org/essex/phist ), which allows us to use the same underlying HPC libraries as LOCA does. We then apply the new code to a reaction-diffusion model to demonstrate its potential of enabling fully automatic bifurcation analysis on parallel computers.
AB - The Trilinos library LOCA (http://www.cs.sandia.gov/LOCA/ ) allows computing branches of steady states of large-scale dynamical systems like (discretized) 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 PyNCT (https://pypi.org/project/PyNCT/ ). The scope of this algorithmically versatile software is, however, limited to relatively small (e.g. 2D) problems because it relies on linear algebra from Python libraries like NumPy. Furthermore, PyNCT currently does not support problems with a non-Hermitian Jacobian matrix, which rules out interesting applications in chemistry and fluid dynamics. In this paper we aim to combine the best of both worlds: a high-level implementation of algorithms in PyNCT with parallel models and linear algebra implemented in Trilinos. PyNCT is extended to non-symmetric systems and its complete backend is replaced by the PHIST library (https://bitbucket.org/essex/phist ), which allows us to use the same underlying HPC libraries as LOCA does. We then apply the new code to a reaction-diffusion model to demonstrate its potential of enabling fully automatic bifurcation analysis on parallel computers.
UR - http://www.scopus.com/inward/record.url?scp=85106451813&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-55874-1_97
DO - 10.1007/978-3-030-55874-1_97
M3 - Conference contribution
AN - SCOPUS:85106451813
SN - 9783030558734
T3 - Lecture Notes in Computational Science and Engineering
SP - 981
EP - 989
BT - Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference
A2 - Vermolen, Fred J.
A2 - Vuik, Cornelis
PB - Springer
T2 - European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019
Y2 - 30 September 2019 through 4 October 2019
ER -