---
_id: '19945'
abstract:
- lang: eng
text: Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations,
…) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian
systems on manifolds equipped with Poisson brackets. The Poisson structure is
connected to conservation properties and other geometric features of solutions
to the PDE and, therefore, of great interest for numerical integration. For the
example of Burgers' equations and related PDEs we use Clebsch variables to lift
the original system to a collective Hamiltonian system on a symplectic manifold
whose structure is related to the original Lie-Poisson structure. On the collective
Hamiltonian system a symplectic integrator can be applied. Our numerical examples
show excellent conservation properties and indicate that the disadvantage of an
increased phase-space dimension can be outweighed by the advantage of symplectic
integration.
article_type: original
author:
- first_name: Robert I
full_name: McLachlan, Robert I
last_name: McLachlan
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: https://orcid.org/0000-0002-5940-8057
- first_name: Benjamin K
full_name: Tapley, Benjamin K
last_name: Tapley
citation:
ama: McLachlan RI, Offen C, Tapley BK. Symplectic integration of PDEs using Clebsch
variables. Journal of Computational Dynamics. 2019;6(1):111-130. doi:10.3934/jcd.2019005
apa: McLachlan, R. I., Offen, C., & Tapley, B. K. (2019). Symplectic integration
of PDEs using Clebsch variables. Journal of Computational Dynamics, 6(1),
111–130. https://doi.org/10.3934/jcd.2019005
bibtex: '@article{McLachlan_Offen_Tapley_2019, title={Symplectic integration of
PDEs using Clebsch variables}, volume={6}, DOI={10.3934/jcd.2019005},
number={1}, journal={Journal of Computational Dynamics}, publisher={American Institute
of Mathematical Sciences (AIMS)}, author={McLachlan, Robert I and Offen, Christian
and Tapley, Benjamin K}, year={2019}, pages={111–130} }'
chicago: 'McLachlan, Robert I, Christian Offen, and Benjamin K Tapley. “Symplectic
Integration of PDEs Using Clebsch Variables.” Journal of Computational Dynamics
6, no. 1 (2019): 111–30. https://doi.org/10.3934/jcd.2019005.'
ieee: R. I. McLachlan, C. Offen, and B. K. Tapley, “Symplectic integration of PDEs
using Clebsch variables,” Journal of Computational Dynamics, vol. 6, no.
1, pp. 111–130, 2019.
mla: McLachlan, Robert I., et al. “Symplectic Integration of PDEs Using Clebsch
Variables.” Journal of Computational Dynamics, vol. 6, no. 1, American
Institute of Mathematical Sciences (AIMS), 2019, pp. 111–30, doi:10.3934/jcd.2019005.
short: R.I. McLachlan, C. Offen, B.K. Tapley, Journal of Computational Dynamics
6 (2019) 111–130.
date_created: 2020-10-06T16:44:07Z
date_updated: 2022-01-06T06:54:15Z
department:
- _id: '636'
doi: 10.3934/jcd.2019005
extern: '1'
intvolume: ' 6'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.aimsciences.org/article/doi/10.3934/jcd.2019005
oa: '1'
page: 111-130
publication: Journal of Computational Dynamics
publication_identifier:
issn:
- 2158-2505
publisher: American Institute of Mathematical Sciences (AIMS)
status: public
title: Symplectic integration of PDEs using Clebsch variables
type: journal_article
user_id: '85279'
volume: 6
year: '2019'
...
---
_id: '21944'
article_number: '044116'
author:
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Lorenzo
full_name: Boninsegna, Lorenzo
last_name: Boninsegna
- first_name: Cecilia
full_name: Clementi, Cecilia
last_name: Clementi
citation:
ama: Nüske F, Boninsegna L, Clementi C. Coarse-graining molecular systems by spectral
matching. The Journal of Chemical Physics. 2019. doi:10.1063/1.5100131
apa: Nüske, F., Boninsegna, L., & Clementi, C. (2019). Coarse-graining molecular
systems by spectral matching. The Journal of Chemical Physics. https://doi.org/10.1063/1.5100131
bibtex: '@article{Nüske_Boninsegna_Clementi_2019, title={Coarse-graining molecular
systems by spectral matching}, DOI={10.1063/1.5100131},
number={044116}, journal={The Journal of Chemical Physics}, author={Nüske, Feliks
and Boninsegna, Lorenzo and Clementi, Cecilia}, year={2019} }'
chicago: Nüske, Feliks, Lorenzo Boninsegna, and Cecilia Clementi. “Coarse-Graining
Molecular Systems by Spectral Matching.” The Journal of Chemical Physics,
2019. https://doi.org/10.1063/1.5100131.
ieee: F. Nüske, L. Boninsegna, and C. Clementi, “Coarse-graining molecular systems
by spectral matching,” The Journal of Chemical Physics, 2019.
mla: Nüske, Feliks, et al. “Coarse-Graining Molecular Systems by Spectral Matching.”
The Journal of Chemical Physics, 044116, 2019, doi:10.1063/1.5100131.
short: F. Nüske, L. Boninsegna, C. Clementi, The Journal of Chemical Physics (2019).
date_created: 2021-04-30T17:01:13Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1063/1.5100131
extern: '1'
language:
- iso: eng
publication: The Journal of Chemical Physics
publication_identifier:
issn:
- 0021-9606
- 1089-7690
publication_status: published
status: public
title: Coarse-graining molecular systems by spectral matching
type: journal_article
user_id: '81513'
year: '2019'
...
---
_id: '16709'
author:
- first_name: Tuhin
full_name: Sahai, Tuhin
last_name: Sahai
- first_name: Adrian
full_name: Ziessler, Adrian
last_name: Ziessler
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Sahai T, Ziessler A, Klus S, Dellnitz M. Continuous relaxations for the traveling
salesman problem. Nonlinear Dynamics. 2019. doi:10.1007/s11071-019-05092-5
apa: Sahai, T., Ziessler, A., Klus, S., & Dellnitz, M. (2019). Continuous relaxations
for the traveling salesman problem. Nonlinear Dynamics. https://doi.org/10.1007/s11071-019-05092-5
bibtex: '@article{Sahai_Ziessler_Klus_Dellnitz_2019, title={Continuous relaxations
for the traveling salesman problem}, DOI={10.1007/s11071-019-05092-5},
journal={Nonlinear Dynamics}, author={Sahai, Tuhin and Ziessler, Adrian and Klus,
Stefan and Dellnitz, Michael}, year={2019} }'
chicago: Sahai, Tuhin, Adrian Ziessler, Stefan Klus, and Michael Dellnitz. “Continuous
Relaxations for the Traveling Salesman Problem.” Nonlinear Dynamics, 2019.
https://doi.org/10.1007/s11071-019-05092-5.
ieee: T. Sahai, A. Ziessler, S. Klus, and M. Dellnitz, “Continuous relaxations for
the traveling salesman problem,” Nonlinear Dynamics, 2019.
mla: Sahai, Tuhin, et al. “Continuous Relaxations for the Traveling Salesman Problem.”
Nonlinear Dynamics, 2019, doi:10.1007/s11071-019-05092-5.
short: T. Sahai, A. Ziessler, S. Klus, M. Dellnitz, Nonlinear Dynamics (2019).
date_created: 2020-04-16T14:05:04Z
date_updated: 2022-01-06T06:52:55Z
department:
- _id: '101'
doi: 10.1007/s11071-019-05092-5
language:
- iso: eng
publication: Nonlinear Dynamics
publication_identifier:
issn:
- 0924-090X
- 1573-269X
publication_status: published
status: public
title: Continuous relaxations for the traveling salesman problem
type: journal_article
user_id: '47427'
year: '2019'
...
---
_id: '10593'
abstract:
- lang: eng
text: We present a new framework for optimal and feedback control of PDEs using
Koopman operator-based reduced order models (K-ROMs). The Koopman operator is
a linear but infinite-dimensional operator which describes the dynamics of observables.
A numerical approximation of the Koopman operator therefore yields a linear system
for the observation of an autonomous dynamical system. In our approach, by introducing
a finite number of constant controls, the dynamic control system is transformed
into a set of autonomous systems and the corresponding optimal control problem
into a switching time optimization problem. This allows us to replace each of
these systems by a K-ROM which can be solved orders of magnitude faster. By this
approach, a nonlinear infinite-dimensional control problem is transformed into
a low-dimensional linear problem. Using a recent convergence result for the numerical
approximation via Extended Dynamic Mode Decomposition (EDMD), we show that the
value of the K-ROM based objective function converges in measure to the value
of the full objective function. To illustrate the results, we consider the 1D
Burgers equation and the 2D Navier–Stokes equations. The numerical experiments
show remarkable performance concerning both solution times and accuracy.
article_type: original
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
citation:
ama: Peitz S, Klus S. Koopman operator-based model reduction for switched-system
control of PDEs. Automatica. 2019;106:184-191. doi:10.1016/j.automatica.2019.05.016
apa: Peitz, S., & Klus, S. (2019). Koopman operator-based model reduction for
switched-system control of PDEs. Automatica, 106, 184–191. https://doi.org/10.1016/j.automatica.2019.05.016
bibtex: '@article{Peitz_Klus_2019, title={Koopman operator-based model reduction
for switched-system control of PDEs}, volume={106}, DOI={10.1016/j.automatica.2019.05.016},
journal={Automatica}, author={Peitz, Sebastian and Klus, Stefan}, year={2019},
pages={184–191} }'
chicago: 'Peitz, Sebastian, and Stefan Klus. “Koopman Operator-Based Model Reduction
for Switched-System Control of PDEs.” Automatica 106 (2019): 184–91. https://doi.org/10.1016/j.automatica.2019.05.016.'
ieee: S. Peitz and S. Klus, “Koopman operator-based model reduction for switched-system
control of PDEs,” Automatica, vol. 106, pp. 184–191, 2019.
mla: Peitz, Sebastian, and Stefan Klus. “Koopman Operator-Based Model Reduction
for Switched-System Control of PDEs.” Automatica, vol. 106, 2019, pp. 184–91,
doi:10.1016/j.automatica.2019.05.016.
short: S. Peitz, S. Klus, Automatica 106 (2019) 184–191.
date_created: 2019-07-10T08:08:16Z
date_updated: 2022-01-06T06:50:46Z
department:
- _id: '101'
doi: 10.1016/j.automatica.2019.05.016
intvolume: ' 106'
language:
- iso: eng
page: 184-191
publication: Automatica
publication_identifier:
issn:
- 0005-1098
publication_status: published
status: public
title: Koopman operator-based model reduction for switched-system control of PDEs
type: journal_article
user_id: '47427'
volume: 106
year: '2019'
...
---
_id: '10595'
abstract:
- lang: eng
text: In this article we show that the boundary of the Pareto critical set of an
unconstrained multiobjective optimization problem (MOP) consists of Pareto critical
points of subproblems where only a subset of the set of objective functions is
taken into account. If the Pareto critical set is completely described by its
boundary (e.g., if we have more objective functions than dimensions in decision
space), then this can be used to efficiently solve the MOP by solving a number
of MOPs with fewer objective functions. If this is not the case, the results can
still give insight into the structure of the Pareto critical set.
article_type: original
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Gebken B, Peitz S, Dellnitz M. On the hierarchical structure of Pareto critical
sets. Journal of Global Optimization. 2019;73(4):891-913. doi:10.1007/s10898-019-00737-6
apa: Gebken, B., Peitz, S., & Dellnitz, M. (2019). On the hierarchical structure
of Pareto critical sets. Journal of Global Optimization, 73(4),
891–913. https://doi.org/10.1007/s10898-019-00737-6
bibtex: '@article{Gebken_Peitz_Dellnitz_2019, title={On the hierarchical structure
of Pareto critical sets}, volume={73}, DOI={10.1007/s10898-019-00737-6},
number={4}, journal={Journal of Global Optimization}, author={Gebken, Bennet and
Peitz, Sebastian and Dellnitz, Michael}, year={2019}, pages={891–913} }'
chicago: 'Gebken, Bennet, Sebastian Peitz, and Michael Dellnitz. “On the Hierarchical
Structure of Pareto Critical Sets.” Journal of Global Optimization 73,
no. 4 (2019): 891–913. https://doi.org/10.1007/s10898-019-00737-6.'
ieee: B. Gebken, S. Peitz, and M. Dellnitz, “On the hierarchical structure of Pareto
critical sets,” Journal of Global Optimization, vol. 73, no. 4, pp. 891–913,
2019.
mla: Gebken, Bennet, et al. “On the Hierarchical Structure of Pareto Critical Sets.”
Journal of Global Optimization, vol. 73, no. 4, 2019, pp. 891–913, doi:10.1007/s10898-019-00737-6.
short: B. Gebken, S. Peitz, M. Dellnitz, Journal of Global Optimization 73 (2019)
891–913.
date_created: 2019-07-10T08:13:31Z
date_updated: 2022-01-06T06:50:46Z
department:
- _id: '101'
doi: 10.1007/s10898-019-00737-6
intvolume: ' 73'
issue: '4'
language:
- iso: eng
page: 891-913
publication: Journal of Global Optimization
publication_identifier:
issn:
- 0925-5001
- 1573-2916
publication_status: published
status: public
title: On the hierarchical structure of Pareto critical sets
type: journal_article
user_id: '47427'
volume: 73
year: '2019'
...
---
_id: '10597'
abstract:
- lang: eng
text: In comparison to classical control approaches in the field of electrical drives
like the field-oriented control (FOC), model predictive control (MPC) approaches
are able to provide a higher control performance. This refers to shorter settling
times, lower overshoots, and a better decoupling of control variables in case
of multi-variable controls. However, this can only be achieved if the used prediction
model covers the actual behavior of the plant sufficiently well. In case of model
deviations, the performance utilizing MPC remains below its potential. This results
in effects like increased current ripple or steady state setpoint deviations.
In order to achieve a high control performance, it is therefore necessary to adapt
the model to the real plant behavior. When using an online system identification,
a less accurate model is sufficient for commissioning of the drive system. In
this paper, the combination of a finite-control-set MPC (FCS-MPC) with a system
identification is proposed. The method does not require high-frequency signal
injection, but uses the measured values already required for the FCS-MPC. An evaluation
of the least squares-based identification on a laboratory test bench showed that
the model accuracy and thus the control performance could be improved by an online
update of the prediction models.
author:
- first_name: Soren
full_name: Hanke, Soren
last_name: Hanke
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Oliver
full_name: Wallscheid, Oliver
last_name: Wallscheid
- first_name: Joachim
full_name: Böcker, Joachim
last_name: Böcker
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Hanke S, Peitz S, Wallscheid O, Böcker J, Dellnitz M. Finite-Control-Set Model
Predictive Control for a Permanent Magnet Synchronous Motor Application with Online
Least Squares System Identification. In: 2019 IEEE International Symposium
on Predictive Control of Electrical Drives and Power Electronics (PRECEDE).
; 2019. doi:10.1109/precede.2019.8753313'
apa: Hanke, S., Peitz, S., Wallscheid, O., Böcker, J., & Dellnitz, M. (2019).
Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous
Motor Application with Online Least Squares System Identification. In 2019
IEEE International Symposium on Predictive Control of Electrical Drives and Power
Electronics (PRECEDE). https://doi.org/10.1109/precede.2019.8753313
bibtex: '@inproceedings{Hanke_Peitz_Wallscheid_Böcker_Dellnitz_2019, title={Finite-Control-Set
Model Predictive Control for a Permanent Magnet Synchronous Motor Application
with Online Least Squares System Identification}, DOI={10.1109/precede.2019.8753313},
booktitle={2019 IEEE International Symposium on Predictive Control of Electrical
Drives and Power Electronics (PRECEDE)}, author={Hanke, Soren and Peitz, Sebastian
and Wallscheid, Oliver and Böcker, Joachim and Dellnitz, Michael}, year={2019}
}'
chicago: Hanke, Soren, Sebastian Peitz, Oliver Wallscheid, Joachim Böcker, and Michael
Dellnitz. “Finite-Control-Set Model Predictive Control for a Permanent Magnet
Synchronous Motor Application with Online Least Squares System Identification.”
In 2019 IEEE International Symposium on Predictive Control of Electrical Drives
and Power Electronics (PRECEDE), 2019. https://doi.org/10.1109/precede.2019.8753313.
ieee: S. Hanke, S. Peitz, O. Wallscheid, J. Böcker, and M. Dellnitz, “Finite-Control-Set
Model Predictive Control for a Permanent Magnet Synchronous Motor Application
with Online Least Squares System Identification,” in 2019 IEEE International
Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE),
2019.
mla: Hanke, Soren, et al. “Finite-Control-Set Model Predictive Control for a Permanent
Magnet Synchronous Motor Application with Online Least Squares System Identification.”
2019 IEEE International Symposium on Predictive Control of Electrical Drives
and Power Electronics (PRECEDE), 2019, doi:10.1109/precede.2019.8753313.
short: 'S. Hanke, S. Peitz, O. Wallscheid, J. Böcker, M. Dellnitz, in: 2019 IEEE
International Symposium on Predictive Control of Electrical Drives and Power Electronics
(PRECEDE), 2019.'
date_created: 2019-07-10T08:15:23Z
date_updated: 2022-01-06T06:50:46Z
department:
- _id: '101'
doi: 10.1109/precede.2019.8753313
language:
- iso: eng
publication: 2019 IEEE International Symposium on Predictive Control of Electrical
Drives and Power Electronics (PRECEDE)
publication_identifier:
isbn:
- '9781538694145'
publication_status: published
status: public
title: Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous
Motor Application with Online Least Squares System Identification
type: conference
user_id: '47427'
year: '2019'
...
---
_id: '29867'
author:
- first_name: Tim
full_name: Faulwasser, Tim
last_name: Faulwasser
- first_name: K.
full_name: Flaßkamp, K.
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Karl
full_name: Worthmann, Karl
last_name: Worthmann
citation:
ama: 'Faulwasser T, Flaßkamp K, Ober-Blöbaum S, Worthmann K. Towards velocity turnpikes
in optimal control of mechanical systems. In: IFAC-PapersOnLine, ed. Vol 52(16).
; 2019:490-495.'
apa: 'Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., & Worthmann, K. (2019).
Towards velocity turnpikes in optimal control of mechanical systems: Vol. 52(16)
(IFAC-PapersOnLine, Ed.; pp. 490–495).'
bibtex: '@inproceedings{Faulwasser_Flaßkamp_Ober-Blöbaum_Worthmann_2019, title={Towards
velocity turnpikes in optimal control of mechanical systems}, volume={52(16)},
author={Faulwasser, Tim and Flaßkamp, K. and Ober-Blöbaum, Sina and Worthmann,
Karl}, editor={IFAC-PapersOnLine}, year={2019}, pages={490–495} }'
chicago: Faulwasser, Tim, K. Flaßkamp, Sina Ober-Blöbaum, and Karl Worthmann. “Towards
Velocity Turnpikes in Optimal Control of Mechanical Systems.” edited by IFAC-PapersOnLine,
52(16):490–95, 2019.
ieee: T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, and K. Worthmann, “Towards velocity
turnpikes in optimal control of mechanical systems,” 2019, vol. 52(16), pp. 490–495.
mla: Faulwasser, Tim, et al. Towards Velocity Turnpikes in Optimal Control of
Mechanical Systems. Edited by IFAC-PapersOnLine, vol. 52(16), 2019, pp. 490–95.
short: 'T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, K. Worthmann, in: IFAC-PapersOnLine
(Ed.), 2019, pp. 490–495.'
corporate_editor:
- IFAC-PapersOnLine
date_created: 2022-02-17T07:23:52Z
date_updated: 2023-11-08T08:09:01Z
department:
- _id: '636'
language:
- iso: eng
page: 490-495
status: public
title: Towards velocity turnpikes in optimal control of mechanical systems
type: conference
user_id: '15694'
volume: 52(16)
year: '2019'
...
---
_id: '16708'
abstract:
- lang: eng
text: " In this work we extend the novel framework developed by Dellnitz, Hessel-von
Molo, and Ziessler to\r\nthe computation of finite dimensional unstable manifolds
of infinite dimensional dynamical systems.\r\nTo this end, we adapt a set-oriented
continuation technique developed by Dellnitz and Hohmann for\r\nthe computation
of such objects of finite dimensional systems with the results obtained in the
work\r\nof Dellnitz, Hessel-von Molo, and Ziessler. We show how to implement this
approach for the analysis\r\nof partial differential equations and illustrate
its feasibility by computing unstable manifolds of the\r\none-dimensional Kuramoto--Sivashinsky
equation as well as for the Mackey--Glass delay differential\r\nequation.\r\n"
author:
- first_name: Adrian
full_name: Ziessler, Adrian
last_name: Ziessler
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Raphael
full_name: Gerlach, Raphael
id: '32655'
last_name: Gerlach
citation:
ama: Ziessler A, Dellnitz M, Gerlach R. The Numerical Computation of Unstable Manifolds
for Infinite Dimensional Dynamical Systems by Embedding Techniques. SIAM Journal
on Applied Dynamical Systems. 2019;18(3):1265-1292. doi:10.1137/18m1204395
apa: Ziessler, A., Dellnitz, M., & Gerlach, R. (2019). The Numerical Computation
of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding
Techniques. SIAM Journal on Applied Dynamical Systems, 18(3), 1265–1292.
https://doi.org/10.1137/18m1204395
bibtex: '@article{Ziessler_Dellnitz_Gerlach_2019, title={The Numerical Computation
of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding
Techniques}, volume={18}, DOI={10.1137/18m1204395},
number={3}, journal={SIAM Journal on Applied Dynamical Systems}, author={Ziessler,
Adrian and Dellnitz, Michael and Gerlach, Raphael}, year={2019}, pages={1265–1292}
}'
chicago: 'Ziessler, Adrian, Michael Dellnitz, and Raphael Gerlach. “The Numerical
Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by
Embedding Techniques.” SIAM Journal on Applied Dynamical Systems 18, no.
3 (2019): 1265–92. https://doi.org/10.1137/18m1204395.'
ieee: 'A. Ziessler, M. Dellnitz, and R. Gerlach, “The Numerical Computation of Unstable
Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques,”
SIAM Journal on Applied Dynamical Systems, vol. 18, no. 3, pp. 1265–1292,
2019, doi: 10.1137/18m1204395.'
mla: Ziessler, Adrian, et al. “The Numerical Computation of Unstable Manifolds for
Infinite Dimensional Dynamical Systems by Embedding Techniques.” SIAM Journal
on Applied Dynamical Systems, vol. 18, no. 3, 2019, pp. 1265–92, doi:10.1137/18m1204395.
short: A. Ziessler, M. Dellnitz, R. Gerlach, SIAM Journal on Applied Dynamical Systems
18 (2019) 1265–1292.
date_created: 2020-04-16T14:04:20Z
date_updated: 2023-11-17T13:13:09Z
department:
- _id: '101'
doi: 10.1137/18m1204395
intvolume: ' 18'
issue: '3'
language:
- iso: eng
main_file_link:
- url: https://epubs.siam.org/doi/epdf/10.1137/18M1204395
page: 1265-1292
publication: SIAM Journal on Applied Dynamical Systems
publication_identifier:
issn:
- 1536-0040
publication_status: published
status: public
title: The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical
Systems by Embedding Techniques
type: journal_article
user_id: '32655'
volume: 18
year: '2019'
...
---
_id: '34917'
abstract:
- lang: eng
text: We relate proper isometry classes of maximal lattices in a totally definite
quaternary quadratic space (V,q) with trivial discriminant to certain equivalence
classes of ideals in the quaternion algebra representing the Clifford invariant
of (V,q). This yields a good algorithm to enumerate a system of representatives
of proper isometry classes of lattices in genera of maximal lattices in (V,q).
author:
- first_name: Markus
full_name: Kirschmer, Markus
id: '82258'
last_name: Kirschmer
- first_name: Gabriele
full_name: Nebe, Gabriele
last_name: Nebe
citation:
ama: Kirschmer M, Nebe G. Quaternary quadratic lattices over number fields. International
Journal of Number Theory. 2019;15(02):309-325. doi:10.1142/s1793042119500131
apa: Kirschmer, M., & Nebe, G. (2019). Quaternary quadratic lattices over number
fields. International Journal of Number Theory, 15(02), 309–325.
https://doi.org/10.1142/s1793042119500131
bibtex: '@article{Kirschmer_Nebe_2019, title={Quaternary quadratic lattices over
number fields}, volume={15}, DOI={10.1142/s1793042119500131},
number={02}, journal={International Journal of Number Theory}, publisher={World
Scientific Pub Co Pte Lt}, author={Kirschmer, Markus and Nebe, Gabriele}, year={2019},
pages={309–325} }'
chicago: 'Kirschmer, Markus, and Gabriele Nebe. “Quaternary Quadratic Lattices over
Number Fields.” International Journal of Number Theory 15, no. 02 (2019):
309–25. https://doi.org/10.1142/s1793042119500131.'
ieee: 'M. Kirschmer and G. Nebe, “Quaternary quadratic lattices over number fields,”
International Journal of Number Theory, vol. 15, no. 02, pp. 309–325, 2019,
doi: 10.1142/s1793042119500131.'
mla: Kirschmer, Markus, and Gabriele Nebe. “Quaternary Quadratic Lattices over Number
Fields.” International Journal of Number Theory, vol. 15, no. 02, World
Scientific Pub Co Pte Lt, 2019, pp. 309–25, doi:10.1142/s1793042119500131.
short: M. Kirschmer, G. Nebe, International Journal of Number Theory 15 (2019) 309–325.
date_created: 2022-12-23T11:05:09Z
date_updated: 2023-12-06T10:05:59Z
department:
- _id: '102'
doi: 10.1142/s1793042119500131
intvolume: ' 15'
issue: '02'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 309-325
publication: International Journal of Number Theory
publication_identifier:
issn:
- 1793-0421
- 1793-7310
publication_status: published
publisher: World Scientific Pub Co Pte Lt
status: public
title: Quaternary quadratic lattices over number fields
type: journal_article
user_id: '82258'
volume: 15
year: '2019'
...
---
_id: '34916'
abstract:
- lang: eng
text: We describe the powers of irreducible polynomials occurring as characteristic
polynomials of automorphisms of even unimodular lattices over number fields. This
generalizes results of Gross & McMullen and Bayer-Fluckiger & Taelman.
author:
- first_name: Markus
full_name: Kirschmer, Markus
id: '82258'
last_name: Kirschmer
citation:
ama: Kirschmer M. Automorphisms of even unimodular lattices over number fields.
Journal of Number Theory. 2019;197:121-134. doi:10.1016/j.jnt.2018.08.004
apa: Kirschmer, M. (2019). Automorphisms of even unimodular lattices over number
fields. Journal of Number Theory, 197, 121–134. https://doi.org/10.1016/j.jnt.2018.08.004
bibtex: '@article{Kirschmer_2019, title={Automorphisms of even unimodular lattices
over number fields}, volume={197}, DOI={10.1016/j.jnt.2018.08.004},
journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Kirschmer,
Markus}, year={2019}, pages={121–134} }'
chicago: 'Kirschmer, Markus. “Automorphisms of Even Unimodular Lattices over Number
Fields.” Journal of Number Theory 197 (2019): 121–34. https://doi.org/10.1016/j.jnt.2018.08.004.'
ieee: 'M. Kirschmer, “Automorphisms of even unimodular lattices over number fields,”
Journal of Number Theory, vol. 197, pp. 121–134, 2019, doi: 10.1016/j.jnt.2018.08.004.'
mla: Kirschmer, Markus. “Automorphisms of Even Unimodular Lattices over Number Fields.”
Journal of Number Theory, vol. 197, Elsevier BV, 2019, pp. 121–34, doi:10.1016/j.jnt.2018.08.004.
short: M. Kirschmer, Journal of Number Theory 197 (2019) 121–134.
date_created: 2022-12-23T11:04:34Z
date_updated: 2023-12-06T10:07:17Z
department:
- _id: '102'
doi: 10.1016/j.jnt.2018.08.004
intvolume: ' 197'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 121-134
publication: Journal of Number Theory
publication_identifier:
issn:
- 0022-314X
publication_status: published
publisher: Elsevier BV
status: public
title: Automorphisms of even unimodular lattices over number fields
type: journal_article
user_id: '82258'
volume: 197
year: '2019'
...
---
_id: '45948'
author:
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Buyang
full_name: Li, Buyang
last_name: Li
- first_name: Christian
full_name: Lubich, Christian
last_name: Lubich
citation:
ama: Kovács B, Li B, Lubich C. A convergent evolving finite element algorithm for
mean curvature flow of closed surfaces. Numerische Mathematik. 2019;143(4):797-853.
doi:10.1007/s00211-019-01074-2
apa: Kovács, B., Li, B., & Lubich, C. (2019). A convergent evolving finite element
algorithm for mean curvature flow of closed surfaces. Numerische Mathematik,
143(4), 797–853. https://doi.org/10.1007/s00211-019-01074-2
bibtex: '@article{Kovács_Li_Lubich_2019, title={A convergent evolving finite element
algorithm for mean curvature flow of closed surfaces}, volume={143}, DOI={10.1007/s00211-019-01074-2},
number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business
Media LLC}, author={Kovács, Balázs and Li, Buyang and Lubich, Christian}, year={2019},
pages={797–853} }'
chicago: 'Kovács, Balázs, Buyang Li, and Christian Lubich. “A Convergent Evolving
Finite Element Algorithm for Mean Curvature Flow of Closed Surfaces.” Numerische
Mathematik 143, no. 4 (2019): 797–853. https://doi.org/10.1007/s00211-019-01074-2.'
ieee: 'B. Kovács, B. Li, and C. Lubich, “A convergent evolving finite element algorithm
for mean curvature flow of closed surfaces,” Numerische Mathematik, vol.
143, no. 4, pp. 797–853, 2019, doi: 10.1007/s00211-019-01074-2.'
mla: Kovács, Balázs, et al. “A Convergent Evolving Finite Element Algorithm for
Mean Curvature Flow of Closed Surfaces.” Numerische Mathematik, vol. 143,
no. 4, Springer Science and Business Media LLC, 2019, pp. 797–853, doi:10.1007/s00211-019-01074-2.
short: B. Kovács, B. Li, C. Lubich, Numerische Mathematik 143 (2019) 797–853.
date_created: 2023-07-10T11:40:56Z
date_updated: 2024-04-03T09:21:40Z
department:
- _id: '841'
doi: 10.1007/s00211-019-01074-2
intvolume: ' 143'
issue: '4'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 797-853
publication: Numerische Mathematik
publication_identifier:
issn:
- 0029-599X
- 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: A convergent evolving finite element algorithm for mean curvature flow of closed
surfaces
type: journal_article
user_id: '100441'
volume: 143
year: '2019'
...
---
_id: '55284'
author:
- first_name: Ch.
full_name: Elsholtz, Ch.
last_name: Elsholtz
- first_name: Marc
full_name: Technau, Marc
id: '106108'
last_name: Technau
orcid: 0000-0001-9650-2459
- first_name: N.
full_name: Technau, N.
last_name: Technau
citation:
ama: Elsholtz Ch, Technau M, Technau N. The maximal order of iterated multiplicative
functions. Mathematika. 2019;64(4):990–1009. doi:10.1112/S0025579319000214
apa: Elsholtz, Ch., Technau, M., & Technau, N. (2019). The maximal order of
iterated multiplicative functions. Mathematika, 64(4), 990–1009.
https://doi.org/10.1112/S0025579319000214
bibtex: '@article{Elsholtz_Technau_Technau_2019, title={The maximal order of iterated
multiplicative functions}, volume={64}, DOI={10.1112/S0025579319000214},
number={4}, journal={Mathematika}, author={Elsholtz, Ch. and Technau, Marc and
Technau, N.}, year={2019}, pages={990–1009} }'
chicago: 'Elsholtz, Ch., Marc Technau, and N. Technau. “The Maximal Order of Iterated
Multiplicative Functions.” Mathematika 64, no. 4 (2019): 990–1009. https://doi.org/10.1112/S0025579319000214.'
ieee: 'Ch. Elsholtz, M. Technau, and N. Technau, “The maximal order of iterated
multiplicative functions,” Mathematika, vol. 64, no. 4, pp. 990–1009, 2019,
doi: 10.1112/S0025579319000214.'
mla: Elsholtz, Ch., et al. “The Maximal Order of Iterated Multiplicative Functions.”
Mathematika, vol. 64, no. 4, 2019, pp. 990–1009, doi:10.1112/S0025579319000214.
short: Ch. Elsholtz, M. Technau, N. Technau, Mathematika 64 (2019) 990–1009.
date_created: 2024-07-16T11:09:02Z
date_updated: 2024-07-24T07:25:42Z
department:
- _id: '102'
doi: 10.1112/S0025579319000214
extern: '1'
intvolume: ' 64'
issue: '4'
language:
- iso: eng
page: 990–1009
publication: Mathematika
status: public
title: The maximal order of iterated multiplicative functions
type: journal_article
user_id: '106108'
volume: 64
year: '2019'
...
---
_id: '55285'
author:
- first_name: Marc
full_name: Technau, Marc
id: '106108'
last_name: Technau
orcid: 0000-0001-9650-2459
citation:
ama: Technau M. Generalised Beatty sets. Notes Number Theory Discrete Math.
2019;25(2):127–135. doi:10.7546/nntdm.2019.25.2.127-135
apa: Technau, M. (2019). Generalised Beatty sets. Notes Number Theory Discrete
Math., 25(2), 127–135. https://doi.org/10.7546/nntdm.2019.25.2.127-135
bibtex: '@article{Technau_2019, title={Generalised Beatty sets}, volume={25}, DOI={10.7546/nntdm.2019.25.2.127-135},
number={2}, journal={Notes Number Theory Discrete Math.}, author={Technau, Marc},
year={2019}, pages={127–135} }'
chicago: 'Technau, Marc. “Generalised Beatty Sets.” Notes Number Theory Discrete
Math. 25, no. 2 (2019): 127–135. https://doi.org/10.7546/nntdm.2019.25.2.127-135.'
ieee: 'M. Technau, “Generalised Beatty sets,” Notes Number Theory Discrete Math.,
vol. 25, no. 2, pp. 127–135, 2019, doi: 10.7546/nntdm.2019.25.2.127-135.'
mla: Technau, Marc. “Generalised Beatty Sets.” Notes Number Theory Discrete Math.,
vol. 25, no. 2, 2019, pp. 127–135, doi:10.7546/nntdm.2019.25.2.127-135.
short: M. Technau, Notes Number Theory Discrete Math. 25 (2019) 127–135.
date_created: 2024-07-16T11:09:02Z
date_updated: 2024-07-24T07:25:59Z
department:
- _id: '102'
doi: 10.7546/nntdm.2019.25.2.127-135
extern: '1'
intvolume: ' 25'
issue: '2'
language:
- iso: eng
page: 127–135
publication: Notes Number Theory Discrete Math.
status: public
title: Generalised Beatty sets
type: journal_article
user_id: '106108'
volume: 25
year: '2019'
...
---
_id: '34915'
abstract:
- lang: eng
text: We describe the determinants of the automorphism groups of Hermitian lattices
over local fields. Using a result of G. Shimura, this yields an explicit method
to compute the special genera in a given genus of Hermitian lattices over a number
field.
author:
- first_name: Markus
full_name: Kirschmer, Markus
id: '82258'
last_name: Kirschmer
citation:
ama: Kirschmer M. Determinant groups of Hermitian lattices over local fields. Archiv
der Mathematik. 2019;113(4):337-347. doi:10.1007/s00013-019-01348-z
apa: Kirschmer, M. (2019). Determinant groups of Hermitian lattices over local fields.
Archiv Der Mathematik, 113(4), 337–347. https://doi.org/10.1007/s00013-019-01348-z
bibtex: '@article{Kirschmer_2019, title={Determinant groups of Hermitian lattices
over local fields}, volume={113}, DOI={10.1007/s00013-019-01348-z},
number={4}, journal={Archiv der Mathematik}, publisher={Springer Science and Business
Media LLC}, author={Kirschmer, Markus}, year={2019}, pages={337–347} }'
chicago: 'Kirschmer, Markus. “Determinant Groups of Hermitian Lattices over Local
Fields.” Archiv Der Mathematik 113, no. 4 (2019): 337–47. https://doi.org/10.1007/s00013-019-01348-z.'
ieee: 'M. Kirschmer, “Determinant groups of Hermitian lattices over local fields,”
Archiv der Mathematik, vol. 113, no. 4, pp. 337–347, 2019, doi: 10.1007/s00013-019-01348-z.'
mla: Kirschmer, Markus. “Determinant Groups of Hermitian Lattices over Local Fields.”
Archiv Der Mathematik, vol. 113, no. 4, Springer Science and Business Media
LLC, 2019, pp. 337–47, doi:10.1007/s00013-019-01348-z.
short: M. Kirschmer, Archiv Der Mathematik 113 (2019) 337–347.
date_created: 2022-12-23T11:03:41Z
date_updated: 2023-04-04T09:05:04Z
department:
- _id: '102'
doi: 10.1007/s00013-019-01348-z
intvolume: ' 113'
issue: '4'
keyword:
- General Mathematics
language:
- iso: eng
page: 337-347
publication: Archiv der Mathematik
publication_identifier:
issn:
- 0003-889X
- 1420-8938
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Determinant groups of Hermitian lattices over local fields
type: journal_article
user_id: '93826'
volume: 113
year: '2019'
...
---
_id: '21'
abstract:
- lang: eng
text: "We address the general mathematical problem of computing the inverse p-th\r\nroot
of a given matrix in an efficient way. A new method to construct iteration\r\nfunctions
that allow calculating arbitrary p-th roots and their inverses of\r\nsymmetric
positive definite matrices is presented. We show that the order of\r\nconvergence
is at least quadratic and that adaptively adjusting a parameter q\r\nalways leads
to an even faster convergence. In this way, a better performance\r\nthan with
previously known iteration schemes is achieved. The efficiency of the\r\niterative
functions is demonstrated for various matrices with different\r\ndensities, condition
numbers and spectral radii."
author:
- first_name: Dorothee
full_name: Richters, Dorothee
last_name: Richters
- first_name: Michael
full_name: Lass, Michael
id: '24135'
last_name: Lass
orcid: 0000-0002-5708-7632
- first_name: Andrea
full_name: Walther, Andrea
last_name: Walther
- first_name: Christian
full_name: Plessl, Christian
id: '16153'
last_name: Plessl
orcid: 0000-0001-5728-9982
- first_name: Thomas
full_name: Kühne, Thomas
id: '49079'
last_name: Kühne
citation:
ama: Richters D, Lass M, Walther A, Plessl C, Kühne T. A General Algorithm to Calculate
the Inverse Principal p-th Root of Symmetric Positive Definite Matrices. Communications
in Computational Physics. 2019;25(2):564-585. doi:10.4208/cicp.OA-2018-0053
apa: Richters, D., Lass, M., Walther, A., Plessl, C., & Kühne, T. (2019). A
General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive
Definite Matrices. Communications in Computational Physics, 25(2),
564–585. https://doi.org/10.4208/cicp.OA-2018-0053
bibtex: '@article{Richters_Lass_Walther_Plessl_Kühne_2019, title={A General Algorithm
to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices},
volume={25}, DOI={10.4208/cicp.OA-2018-0053},
number={2}, journal={Communications in Computational Physics}, publisher={Global
Science Press}, author={Richters, Dorothee and Lass, Michael and Walther, Andrea
and Plessl, Christian and Kühne, Thomas}, year={2019}, pages={564–585} }'
chicago: 'Richters, Dorothee, Michael Lass, Andrea Walther, Christian Plessl, and
Thomas Kühne. “A General Algorithm to Calculate the Inverse Principal P-Th Root
of Symmetric Positive Definite Matrices.” Communications in Computational Physics
25, no. 2 (2019): 564–85. https://doi.org/10.4208/cicp.OA-2018-0053.'
ieee: 'D. Richters, M. Lass, A. Walther, C. Plessl, and T. Kühne, “A General Algorithm
to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices,”
Communications in Computational Physics, vol. 25, no. 2, pp. 564–585, 2019,
doi: 10.4208/cicp.OA-2018-0053.'
mla: Richters, Dorothee, et al. “A General Algorithm to Calculate the Inverse Principal
P-Th Root of Symmetric Positive Definite Matrices.” Communications in Computational
Physics, vol. 25, no. 2, Global Science Press, 2019, pp. 564–85, doi:10.4208/cicp.OA-2018-0053.
short: D. Richters, M. Lass, A. Walther, C. Plessl, T. Kühne, Communications in
Computational Physics 25 (2019) 564–585.
date_created: 2017-07-25T14:48:26Z
date_updated: 2023-09-26T11:45:02Z
department:
- _id: '27'
- _id: '518'
- _id: '304'
- _id: '104'
doi: 10.4208/cicp.OA-2018-0053
external_id:
arxiv:
- '1703.02456'
intvolume: ' 25'
issue: '2'
language:
- iso: eng
page: 564-585
project:
- _id: '32'
grant_number: PL 595/2-1 / 320898746
name: Performance and Efficiency in HPC with Custom Computing
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: Communications in Computational Physics
publisher: Global Science Press
quality_controlled: '1'
status: public
title: A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric
Positive Definite Matrices
type: journal_article
user_id: '15278'
volume: 25
year: '2019'
...
---
_id: '16711'
abstract:
- lang: eng
text: "Embedding techniques allow the approximations of finite dimensional\r\nattractors
and manifolds of infinite dimensional dynamical systems via\r\nsubdivision and
continuation methods. These approximations give a topological\r\none-to-one image
of the original set. In order to additionally reveal their\r\ngeometry we use
diffusion mapst o find intrinsic coordinates. We illustrate our\r\nresults on
the unstable manifold of the one-dimensional Kuramoto--Sivashinsky\r\nequation,
as well as for the attractor of the Mackey-Glass delay differential\r\nequation."
author:
- first_name: Raphael
full_name: Gerlach, Raphael
id: '32655'
last_name: Gerlach
- first_name: Péter
full_name: Koltai, Péter
last_name: Koltai
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Gerlach R, Koltai P, Dellnitz M. Revealing the intrinsic geometry of finite
dimensional invariant sets of infinite dimensional dynamical systems. arXiv:190208824.
Published online 2019.
apa: Gerlach, R., Koltai, P., & Dellnitz, M. (2019). Revealing the intrinsic
geometry of finite dimensional invariant sets of infinite dimensional dynamical
systems. In arXiv:1902.08824.
bibtex: '@article{Gerlach_Koltai_Dellnitz_2019, title={Revealing the intrinsic geometry
of finite dimensional invariant sets of infinite dimensional dynamical systems},
journal={arXiv:1902.08824}, author={Gerlach, Raphael and Koltai, Péter and Dellnitz,
Michael}, year={2019} }'
chicago: Gerlach, Raphael, Péter Koltai, and Michael Dellnitz. “Revealing the Intrinsic
Geometry of Finite Dimensional Invariant Sets of Infinite Dimensional Dynamical
Systems.” ArXiv:1902.08824, 2019.
ieee: R. Gerlach, P. Koltai, and M. Dellnitz, “Revealing the intrinsic geometry
of finite dimensional invariant sets of infinite dimensional dynamical systems,”
arXiv:1902.08824. 2019.
mla: Gerlach, Raphael, et al. “Revealing the Intrinsic Geometry of Finite Dimensional
Invariant Sets of Infinite Dimensional Dynamical Systems.” ArXiv:1902.08824,
2019.
short: R. Gerlach, P. Koltai, M. Dellnitz, ArXiv:1902.08824 (2019).
date_created: 2020-04-16T14:06:21Z
date_updated: 2024-09-24T12:09:27Z
ddc:
- '510'
department:
- _id: '101'
external_id:
arxiv:
- '1902.08824'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1902.08824
oa: '1'
publication: arXiv:1902.08824
status: public
title: Revealing the intrinsic geometry of finite dimensional invariant sets of infinite
dimensional dynamical systems
type: preprint
user_id: '32655'
year: '2019'
...
---
_id: '8482'
author:
- first_name: Benjamin
full_name: Jurgelucks, Benjamin
last_name: Jurgelucks
- first_name: Veronika
full_name: Schulze, Veronika
last_name: Schulze
- first_name: Nadine
full_name: Feldmann, Nadine
id: '23082'
last_name: Feldmann
- first_name: Leander
full_name: Claes, Leander
id: '11829'
last_name: Claes
orcid: 0000-0002-4393-268X
citation:
ama: Jurgelucks B, Schulze V, Feldmann N, Claes L. Arbitrary Sensitivity for
Inverse Problems in Piezoelectricity.; 2019.
apa: Jurgelucks, B., Schulze, V., Feldmann, N., & Claes, L. (2019). Arbitrary
sensitivity for inverse problems in piezoelectricity.
bibtex: '@book{Jurgelucks_Schulze_Feldmann_Claes_2019, place={GAMM Annual Meeting,
Wien}, title={Arbitrary sensitivity for inverse problems in piezoelectricity},
author={Jurgelucks, Benjamin and Schulze, Veronika and Feldmann, Nadine and Claes,
Leander}, year={2019} }'
chicago: Jurgelucks, Benjamin, Veronika Schulze, Nadine Feldmann, and Leander Claes.
Arbitrary Sensitivity for Inverse Problems in Piezoelectricity. GAMM Annual
Meeting, Wien, 2019.
ieee: B. Jurgelucks, V. Schulze, N. Feldmann, and L. Claes, Arbitrary sensitivity
for inverse problems in piezoelectricity. GAMM Annual Meeting, Wien, 2019.
mla: Jurgelucks, Benjamin, et al. Arbitrary Sensitivity for Inverse Problems
in Piezoelectricity. 2019.
short: B. Jurgelucks, V. Schulze, N. Feldmann, L. Claes, Arbitrary Sensitivity for
Inverse Problems in Piezoelectricity, GAMM Annual Meeting, Wien, 2019.
date_created: 2019-03-08T13:20:14Z
date_updated: 2026-01-05T07:53:43Z
department:
- _id: '104'
- _id: '49'
language:
- iso: eng
place: GAMM Annual Meeting, Wien
project:
- _id: '90'
name: Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen
Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums
- _id: '245'
name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
für Leistungsschallanwendungen (NEPTUN)'
status: public
title: Arbitrary sensitivity for inverse problems in piezoelectricity
type: misc
user_id: '11829'
year: '2019'
...
---
_id: '19935'
abstract:
- lang: eng
text: 'A bifurcation is a qualitative change in a family of solutions to an equation
produced by varying parameters. In contrast to the local bifurcations of dynamical
systems that are often related to a change in the number or stability of equilibria,
bifurcations of boundary value problems are global in nature and may not be related
to any obvious change in dynamical behaviour. Catastrophe theory is a well-developed
framework which studies the bifurcations of critical points of functions. In this
paper we study the bifurcations of solutions of boundary-value problems for symplectic
maps, using the language of (finite-dimensional) singularity theory. We associate
certain such problems with a geometric picture involving the intersection of Lagrangian
submanifolds, and hence with the critical points of a suitable generating function.
Within this framework, we then study the effect of three special cases: (i) some
common boundary conditions, such as Dirichlet boundary conditions for second-order
systems, restrict the possible types of bifurcations (for example, in generic
planar systems only the A-series beginning with folds and cusps can occur); (ii)
integrable systems, such as planar Hamiltonian systems, can exhibit a novel periodic
pitchfork bifurcation; and (iii) systems with Hamiltonian symmetries or reversing
symmetries can exhibit restricted bifurcations associated with the symmetry. This
approach offers an alternative to the analysis of critical points in function
spaces, typically used in the study of bifurcation of variational problems, and
opens the way to the detection of more exotic bifurcations than the simple folds
and cusps that are often found in examples. '
article_type: original
author:
- first_name: Robert I
full_name: McLachlan, Robert I
last_name: McLachlan
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: https://orcid.org/0000-0002-5940-8057
citation:
ama: McLachlan RI, Offen C. Bifurcation of solutions to Hamiltonian boundary value
problems. Nonlinearity. 2018:2895-2927. doi:10.1088/1361-6544/aab630
apa: McLachlan, R. I., & Offen, C. (2018). Bifurcation of solutions to Hamiltonian
boundary value problems. Nonlinearity, 2895–2927. https://doi.org/10.1088/1361-6544/aab630
bibtex: '@article{McLachlan_Offen_2018, title={Bifurcation of solutions to Hamiltonian
boundary value problems}, DOI={10.1088/1361-6544/aab630},
journal={Nonlinearity}, author={McLachlan, Robert I and Offen, Christian}, year={2018},
pages={2895–2927} }'
chicago: McLachlan, Robert I, and Christian Offen. “Bifurcation of Solutions to
Hamiltonian Boundary Value Problems.” Nonlinearity, 2018, 2895–2927. https://doi.org/10.1088/1361-6544/aab630.
ieee: R. I. McLachlan and C. Offen, “Bifurcation of solutions to Hamiltonian boundary
value problems,” Nonlinearity, pp. 2895–2927, 2018.
mla: McLachlan, Robert I., and Christian Offen. “Bifurcation of Solutions to Hamiltonian
Boundary Value Problems.” Nonlinearity, 2018, pp. 2895–927, doi:10.1088/1361-6544/aab630.
short: R.I. McLachlan, C. Offen, Nonlinearity (2018) 2895–2927.
date_created: 2020-10-06T16:28:36Z
date_updated: 2022-01-06T06:54:14Z
department:
- _id: '636'
doi: 10.1088/1361-6544/aab630
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://doi.org/10.1088/1361-6544/aab630
page: 2895-2927
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
status: public
title: Bifurcation of solutions to Hamiltonian boundary value problems
type: journal_article
user_id: '85279'
year: '2018'
...
---
_id: '19937'
abstract:
- lang: eng
text: Symplectic integrators can be excellent for Hamiltonian initial value problems.
Reasons for this include their preservation of invariant sets like tori, good
energy behaviour, nonexistence of attractors, and good behaviour of statistical
properties. These all refer to {\em long-time} behaviour. They are directly connected
to the dynamical behaviour of symplectic maps φ:M→M' on the phase space under
iteration. Boundary value problems, in contrast, are posed for fixed (and often
quite short) times. Symplecticity manifests as a symplectic map φ:M→M' which is
not iterated. Is there any point, therefore, for a symplectic integrator to be
used on a Hamiltonian boundary value problem? In this paper we announce results
that symplectic integrators preserve bifurcations of Hamiltonian boundary value
problems and that nonsymplectic integrators do not.
article_type: original
author:
- first_name: Robert I
full_name: McLachlan, Robert I
last_name: McLachlan
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: https://orcid.org/0000-0002-5940-8057
citation:
ama: McLachlan RI, Offen C. Symplectic integration of boundary value problems. Numerical
Algorithms. 2018:1219-1233. doi:10.1007/s11075-018-0599-7
apa: McLachlan, R. I., & Offen, C. (2018). Symplectic integration of boundary
value problems. Numerical Algorithms, 1219–1233. https://doi.org/10.1007/s11075-018-0599-7
bibtex: '@article{McLachlan_Offen_2018, title={Symplectic integration of boundary
value problems}, DOI={10.1007/s11075-018-0599-7},
journal={Numerical Algorithms}, author={McLachlan, Robert I and Offen, Christian},
year={2018}, pages={1219–1233} }'
chicago: McLachlan, Robert I, and Christian Offen. “Symplectic Integration of Boundary
Value Problems.” Numerical Algorithms, 2018, 1219–33. https://doi.org/10.1007/s11075-018-0599-7.
ieee: R. I. McLachlan and C. Offen, “Symplectic integration of boundary value problems,”
Numerical Algorithms, pp. 1219–1233, 2018.
mla: McLachlan, Robert I., and Christian Offen. “Symplectic Integration of Boundary
Value Problems.” Numerical Algorithms, 2018, pp. 1219–33, doi:10.1007/s11075-018-0599-7.
short: R.I. McLachlan, C. Offen, Numerical Algorithms (2018) 1219–1233.
date_created: 2020-10-06T16:29:14Z
date_updated: 2022-01-06T06:54:14Z
department:
- _id: '636'
doi: 10.1007/s11075-018-0599-7
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://rdcu.be/b79ap
page: 1219-1233
publication: Numerical Algorithms
publication_identifier:
issn:
- 1017-1398
- 1572-9265
publication_status: published
status: public
title: Symplectic integration of boundary value problems
type: journal_article
user_id: '85279'
year: '2018'
...
---
_id: '21634'
abstract:
- lang: eng
text: "Predictive control of power electronic systems always requires a suitable\r\nmodel
of the plant. Using typical physics-based white box models, a trade-off\r\nbetween
model complexity (i.e. accuracy) and computational burden has to be\r\nmade. This
is a challenging task with a lot of constraints, since the model\r\norder is directly
linked to the number of system states. Even though white-box\r\nmodels show suitable
performance in most cases, parasitic real-world effects\r\noften cannot be modeled
satisfactorily with an expedient computational load.\r\nHence, a Koopman operator-based
model reduction technique is presented which\r\ndirectly links the control action
to the system's outputs in a black-box\r\nfashion. The Koopman operator is a linear
but infinite-dimensional operator\r\ndescribing the dynamics of observables of
nonlinear autonomous dynamical\r\nsystems which can be nicely applied to the switching
principle of power\r\nelectronic devices. Following this data-driven approach,
the model order and\r\nthe number of system states are decoupled which allows
us to consider more\r\ncomplex systems. Extensive experimental tests with an automotive-type
permanent\r\nmagnet synchronous motor fed by an IGBT 2-level inverter prove the
feasibility\r\nof the proposed modeling technique in a finite-set model predictive
control\r\napplication."
author:
- first_name: Sören
full_name: Hanke, Sören
last_name: Hanke
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Oliver
full_name: Wallscheid, Oliver
last_name: Wallscheid
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Joachim
full_name: Böcker, Joachim
last_name: Böcker
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Hanke S, Peitz S, Wallscheid O, Klus S, Böcker J, Dellnitz M. Koopman Operator-Based
Finite-Control-Set Model Predictive Control for Electrical Drives. arXiv:180400854.
2018.
apa: Hanke, S., Peitz, S., Wallscheid, O., Klus, S., Böcker, J., & Dellnitz,
M. (2018). Koopman Operator-Based Finite-Control-Set Model Predictive Control
for Electrical Drives. ArXiv:1804.00854.
bibtex: '@article{Hanke_Peitz_Wallscheid_Klus_Böcker_Dellnitz_2018, title={Koopman
Operator-Based Finite-Control-Set Model Predictive Control for Electrical Drives},
journal={arXiv:1804.00854}, author={Hanke, Sören and Peitz, Sebastian and Wallscheid,
Oliver and Klus, Stefan and Böcker, Joachim and Dellnitz, Michael}, year={2018}
}'
chicago: Hanke, Sören, Sebastian Peitz, Oliver Wallscheid, Stefan Klus, Joachim
Böcker, and Michael Dellnitz. “Koopman Operator-Based Finite-Control-Set Model
Predictive Control for Electrical Drives.” ArXiv:1804.00854, 2018.
ieee: S. Hanke, S. Peitz, O. Wallscheid, S. Klus, J. Böcker, and M. Dellnitz, “Koopman
Operator-Based Finite-Control-Set Model Predictive Control for Electrical Drives,”
arXiv:1804.00854. 2018.
mla: Hanke, Sören, et al. “Koopman Operator-Based Finite-Control-Set Model Predictive
Control for Electrical Drives.” ArXiv:1804.00854, 2018.
short: S. Hanke, S. Peitz, O. Wallscheid, S. Klus, J. Böcker, M. Dellnitz, ArXiv:1804.00854
(2018).
date_created: 2021-04-19T16:17:30Z
date_updated: 2022-01-06T06:55:08Z
department:
- _id: '101'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/1804.00854.pdf
oa: '1'
publication: arXiv:1804.00854
status: public
title: Koopman Operator-Based Finite-Control-Set Model Predictive Control for Electrical
Drives
type: preprint
user_id: '47427'
year: '2018'
...