---
_id: '30861'
abstract:
- lang: eng
text: AbstractWe consider the problem of maximization
of metabolite production in bacterial cells formulated as a dynamical optimal
control problem (DOCP). According to Pontryagin’s maximum principle, optimal solutions
are concatenations of singular and bang arcs and exhibit the chattering or Fuller
phenomenon, which is problematic for applications. To avoid chattering, we introduce
a reduced model which is still biologically relevant and retains the important
structural features of the original problem. Using a combination of analytical
and numerical methods, we show that the singular arc is dominant in the studied
DOCPs and exhibits the turnpike property. This property
is further used in order to design simple and realistic suboptimal control strategies.
author:
- first_name: Jean-Baptiste
full_name: Caillau, Jean-Baptiste
last_name: Caillau
- first_name: Walid
full_name: Djema, Walid
last_name: Djema
- first_name: Jean-Luc
full_name: Gouzé, Jean-Luc
last_name: Gouzé
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Jean-Baptiste
full_name: Pomet, Jean-Baptiste
last_name: Pomet
citation:
ama: Caillau J-B, Djema W, Gouzé J-L, Maslovskaya S, Pomet J-B. Turnpike Property
in Optimal Microbial Metabolite Production. Journal of Optimization Theory
and Applications. Published online 2022. doi:10.1007/s10957-022-02023-0
apa: Caillau, J.-B., Djema, W., Gouzé, J.-L., Maslovskaya, S., & Pomet, J.-B.
(2022). Turnpike Property in Optimal Microbial Metabolite Production. Journal
of Optimization Theory and Applications. https://doi.org/10.1007/s10957-022-02023-0
bibtex: '@article{Caillau_Djema_Gouzé_Maslovskaya_Pomet_2022, title={Turnpike Property
in Optimal Microbial Metabolite Production}, DOI={10.1007/s10957-022-02023-0},
journal={Journal of Optimization Theory and Applications}, publisher={Springer
Science and Business Media LLC}, author={Caillau, Jean-Baptiste and Djema, Walid
and Gouzé, Jean-Luc and Maslovskaya, Sofya and Pomet, Jean-Baptiste}, year={2022}
}'
chicago: Caillau, Jean-Baptiste, Walid Djema, Jean-Luc Gouzé, Sofya Maslovskaya,
and Jean-Baptiste Pomet. “Turnpike Property in Optimal Microbial Metabolite Production.”
Journal of Optimization Theory and Applications, 2022. https://doi.org/10.1007/s10957-022-02023-0.
ieee: 'J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, and J.-B. Pomet, “Turnpike
Property in Optimal Microbial Metabolite Production,” Journal of Optimization
Theory and Applications, 2022, doi: 10.1007/s10957-022-02023-0.'
mla: Caillau, Jean-Baptiste, et al. “Turnpike Property in Optimal Microbial Metabolite
Production.” Journal of Optimization Theory and Applications, Springer
Science and Business Media LLC, 2022, doi:10.1007/s10957-022-02023-0.
short: J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, J.-B. Pomet, Journal
of Optimization Theory and Applications (2022).
date_created: 2022-04-08T17:23:13Z
date_updated: 2022-04-08T18:23:02Z
department:
- _id: '636'
doi: 10.1007/s10957-022-02023-0
keyword:
- Applied Mathematics
- Management Science and Operations Research
- Control and Optimization
language:
- iso: eng
publication: Journal of Optimization Theory and Applications
publication_identifier:
issn:
- 0022-3239
- 1573-2878
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Turnpike Property in Optimal Microbial Metabolite Production
type: journal_article
user_id: '87909'
year: '2022'
...
---
_id: '29673'
abstract:
- lang: eng
text: Koopman operator theory has been successfully applied to problems from various
research areas such as fluid dynamics, molecular dynamics, climate science, engineering,
and biology. Applications include detecting metastable or coherent sets, coarse-graining,
system identification, and control. There is an intricate connection between dynamical
systems driven by stochastic differential equations and quantum mechanics. In
this paper, we compare the ground-state transformation and Nelson's stochastic
mechanics and demonstrate how data-driven methods developed for the approximation
of the Koopman operator can be used to analyze quantum physics problems. Moreover,
we exploit the relationship between Schrödinger operators and stochastic control
problems to show that modern data-driven methods for stochastic control can be
used to solve the stationary or imaginary-time Schrödinger equation. Our findings
open up a new avenue towards solving Schrödinger's equation using recently developed
tools from data science.
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: 'Klus S, Nüske F, Peitz S. Koopman analysis of quantum systems. Journal
of Physics A: Mathematical and Theoretical. 2022;55(31):314002. doi:10.1088/1751-8121/ac7d22'
apa: 'Klus, S., Nüske, F., & Peitz, S. (2022). Koopman analysis of quantum systems.
Journal of Physics A: Mathematical and Theoretical, 55(31), 314002.
https://doi.org/10.1088/1751-8121/ac7d22'
bibtex: '@article{Klus_Nüske_Peitz_2022, title={Koopman analysis of quantum systems},
volume={55}, DOI={10.1088/1751-8121/ac7d22},
number={31}, journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP
Publishing Ltd.}, author={Klus, Stefan and Nüske, Feliks and Peitz, Sebastian},
year={2022}, pages={314002} }'
chicago: 'Klus, Stefan, Feliks Nüske, and Sebastian Peitz. “Koopman Analysis of
Quantum Systems.” Journal of Physics A: Mathematical and Theoretical 55,
no. 31 (2022): 314002. https://doi.org/10.1088/1751-8121/ac7d22.'
ieee: 'S. Klus, F. Nüske, and S. Peitz, “Koopman analysis of quantum systems,” Journal
of Physics A: Mathematical and Theoretical, vol. 55, no. 31, p. 314002, 2022,
doi: 10.1088/1751-8121/ac7d22.'
mla: 'Klus, Stefan, et al. “Koopman Analysis of Quantum Systems.” Journal of
Physics A: Mathematical and Theoretical, vol. 55, no. 31, IOP Publishing Ltd.,
2022, p. 314002, doi:10.1088/1751-8121/ac7d22.'
short: 'S. Klus, F. Nüske, S. Peitz, Journal of Physics A: Mathematical and Theoretical
55 (2022) 314002.'
date_created: 2022-01-31T09:49:40Z
date_updated: 2022-07-18T14:26:41Z
department:
- _id: '655'
- _id: '101'
doi: 10.1088/1751-8121/ac7d22
external_id:
arxiv:
- '2201.12062'
intvolume: ' 55'
issue: '31'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://iopscience.iop.org/article/10.1088/1751-8121/ac7d22/pdf
oa: '1'
page: '314002'
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_status: published
publisher: IOP Publishing Ltd.
status: public
title: Koopman analysis of quantum systems
type: journal_article
user_id: '47427'
volume: 55
year: '2022'
...
---
_id: '34618'
abstract:
- lang: eng
text: "In this article, we show how second-order derivative information can be\r\nincorporated
into gradient sampling methods for nonsmooth optimization. The\r\nsecond-order
information we consider is essentially the set of coefficients of\r\nall second-order
Taylor expansions of the objective in a closed ball around a\r\ngiven point. Based
on this concept, we define a model of the objective as the\r\nmaximum of these
Taylor expansions. Iteratively minimizing this model\r\n(constrained to the closed
ball) results in a simple descent method, for which\r\nwe prove convergence to
minimal points in case the objective is convex. To\r\nobtain an implementable
method, we construct an approximation scheme for the\r\nsecond-order information
based on sampling objective values, gradients and\r\nHessian matrices at finitely
many points. Using a set of test problems, we\r\ncompare the resulting method
to five other available solvers. Considering the\r\nnumber of function evaluations,
the results suggest that the method we propose\r\nis superior to the standard
gradient sampling method, and competitive compared\r\nto other methods."
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
citation:
ama: Gebken B. Using second-order information in gradient sampling methods for
nonsmooth optimization. arXiv:221004579. Published online 2022.
apa: Gebken, B. (2022). Using second-order information in gradient sampling methods
for nonsmooth optimization. In arXiv:2210.04579.
bibtex: '@article{Gebken_2022, title={Using second-order information in gradient
sampling methods for nonsmooth optimization}, journal={arXiv:2210.04579}, author={Gebken,
Bennet}, year={2022} }'
chicago: Gebken, Bennet. “Using Second-Order Information in Gradient Sampling Methods
for Nonsmooth Optimization.” ArXiv:2210.04579, 2022.
ieee: B. Gebken, “Using second-order information in gradient sampling methods for
nonsmooth optimization,” arXiv:2210.04579. 2022.
mla: Gebken, Bennet. “Using Second-Order Information in Gradient Sampling Methods
for Nonsmooth Optimization.” ArXiv:2210.04579, 2022.
short: B. Gebken, ArXiv:2210.04579 (2022).
date_created: 2022-12-20T15:25:17Z
date_updated: 2022-12-20T15:28:54Z
department:
- _id: '101'
external_id:
arxiv:
- '2210.04579'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2210.04579
oa: '1'
publication: arXiv:2210.04579
status: public
title: Using second-order information in gradient sampling methods for nonsmooth
optimization
type: preprint
user_id: '32643'
year: '2022'
...
---
_id: '31556'
abstract:
- lang: ger
text: Mehrzieloptimierung behandelt Probleme, bei denen mehrere skalare Zielfunktionen
simultan optimiert werden sollen. Ein Punkt ist in diesem Fall optimal, wenn es
keinen anderen Punkt gibt, der mindestens genauso gut ist in allen Zielfunktionen
und besser in mindestens einer Zielfunktion. Ein notwendiges Optimalitätskriterium
lässt sich über Ableitungsinformationen erster Ordnung der Zielfunktionen herleiten.
Die Menge der Punkte, die dieses notwendige Kriterium erfüllen, wird als Pareto-kritische
Menge bezeichnet. Diese Arbeit enthält neue Resultate über Pareto-kritische Mengen
für glatte und nicht-glatte Mehrzieloptimierungsprobleme, sowohl was deren Berechnung
betrifft als auch deren Struktur. Im glatten Fall erfolgt die Berechnung über
ein Fortsetzungsverfahren, im nichtglatten Fall über ein Abstiegsverfahren. Anschließend
wird die Struktur des Randes der Pareto-kritischen Menge analysiert, welcher aus
Pareto-kritischen Mengen kleinerer Subprobleme besteht. Schlussendlich werden
inverse Probleme betrachtet, bei denen zu einer gegebenen Datenmenge ein Zielfunktionsvektor
gefunden werden soll, für den die Datenpunkte kritisch sind.
- lang: eng
text: Multiobjective optimization is concerned with the simultaneous optimization
of multiple scalar-valued functions. In this case, a point is optimal if there
is no other point that is at least as good in all objectives and better in at
least one objective. A necessary condition for optimality can be derived based
on first-order information of the objectives. The set of points that satisfy this
necessary condition is called the Pareto critical set. This thesis presents new
results about Pareto critical sets for smooth and nonsmooth multiobjective optimization
problems, both in terms of their efficient computation and structural properties.
In the smooth case they are computed via a continuation method and in the nonsmooth
case via a descent method. Afterwards, the structure of the boundary of the Pareto
critical set is analyzed, which consists of Pareto critical sets of smaller subproblems.
Finally, inverse problems are considered, where a data set is given and an objective
vector is sought for which the data points are critical.
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
citation:
ama: Gebken B. Computation and Analysis of Pareto Critical Sets in Smooth and
Nonsmooth Multiobjective Optimization.; 2022. doi:10.17619/UNIPB/1-1327
apa: Gebken, B. (2022). Computation and analysis of Pareto critical sets in smooth
and nonsmooth multiobjective optimization. https://doi.org/10.17619/UNIPB/1-1327
bibtex: '@book{Gebken_2022, title={Computation and analysis of Pareto critical sets
in smooth and nonsmooth multiobjective optimization}, DOI={10.17619/UNIPB/1-1327},
author={Gebken, Bennet}, year={2022} }'
chicago: Gebken, Bennet. Computation and Analysis of Pareto Critical Sets in
Smooth and Nonsmooth Multiobjective Optimization, 2022. https://doi.org/10.17619/UNIPB/1-1327.
ieee: B. Gebken, Computation and analysis of Pareto critical sets in smooth and
nonsmooth multiobjective optimization. 2022.
mla: Gebken, Bennet. Computation and Analysis of Pareto Critical Sets in Smooth
and Nonsmooth Multiobjective Optimization. 2022, doi:10.17619/UNIPB/1-1327.
short: B. Gebken, Computation and Analysis of Pareto Critical Sets in Smooth and
Nonsmooth Multiobjective Optimization, 2022.
date_created: 2022-06-01T06:48:08Z
date_updated: 2022-06-01T07:13:09Z
department:
- _id: '101'
doi: 10.17619/UNIPB/1-1327
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://digital.ub.uni-paderborn.de/hs/download/pdf/6531779
oa: '1'
status: public
supervisor:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
title: Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective
optimization
type: dissertation
user_id: '32643'
year: '2022'
...
---
_id: '33150'
abstract:
- lang: eng
text: In this article, we build on previous work to present an optimization algorithm
for nonlinearly constrained multi-objective optimization problems. The algorithm
combines a surrogate-assisted derivative-free trust-region approach with the filter
method known from single-objective optimization. Instead of the true objective
and constraint functions, so-called fully linear models are employed and we show
how to deal with the gradient inexactness in the composite step setting, adapted
from single-objective optimization as well. Under standard assumptions, we prove
convergence of a subset of iterates to a quasi-stationary point and if constraint
qualifications hold, then the limit point is also a KKT-point of the multi-objective
problem.
author:
- first_name: Manuel Bastian
full_name: Berkemeier, Manuel Bastian
id: '51701'
last_name: Berkemeier
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Berkemeier MB, Peitz S. Multi-Objective Trust-Region Filter Method for Nonlinear
Constraints using Inexact Gradients. arXiv:220812094. Published online
2022.
apa: Berkemeier, M. B., & Peitz, S. (2022). Multi-Objective Trust-Region Filter
Method for Nonlinear Constraints using Inexact Gradients. In arXiv:2208.12094.
bibtex: '@article{Berkemeier_Peitz_2022, title={Multi-Objective Trust-Region Filter
Method for Nonlinear Constraints using Inexact Gradients}, journal={arXiv:2208.12094},
author={Berkemeier, Manuel Bastian and Peitz, Sebastian}, year={2022} }'
chicago: Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region
Filter Method for Nonlinear Constraints Using Inexact Gradients.” ArXiv:2208.12094,
2022.
ieee: M. B. Berkemeier and S. Peitz, “Multi-Objective Trust-Region Filter Method
for Nonlinear Constraints using Inexact Gradients,” arXiv:2208.12094. 2022.
mla: Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region
Filter Method for Nonlinear Constraints Using Inexact Gradients.” ArXiv:2208.12094,
2022.
short: M.B. Berkemeier, S. Peitz, ArXiv:2208.12094 (2022).
date_created: 2022-08-26T06:08:06Z
date_updated: 2022-08-26T06:12:10Z
department:
- _id: '101'
- _id: '655'
external_id:
arxiv:
- '2208.12094'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2208.12094
oa: '1'
publication: arXiv:2208.12094
status: public
title: Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using
Inexact Gradients
type: preprint
user_id: '47427'
year: '2022'
...
---
_id: '20731'
abstract:
- lang: eng
text: We present a novel algorithm that allows us to gain detailed insight into
the effects of sparsity in linear and nonlinear optimization, which is of great
importance in many scientific areas such as image and signal processing, medical
imaging, compressed sensing, and machine learning (e.g., for the training of neural
networks). Sparsity is an important feature to ensure robustness against noisy
data, but also to find models that are interpretable and easy to analyze due to
the small number of relevant terms. It is common practice to enforce sparsity
by adding the ℓ1-norm as a weighted penalty term. In order to gain a better understanding
and to allow for an informed model selection, we directly solve the corresponding
multiobjective optimization problem (MOP) that arises when we minimize the main
objective and the ℓ1-norm simultaneously. As this MOP is in general non-convex
for nonlinear objectives, the weighting method will fail to provide all optimal
compromises. To avoid this issue, we present a continuation method which is specifically
tailored to MOPs with two objective functions one of which is the ℓ1-norm. Our
method can be seen as a generalization of well-known homotopy methods for linear
regression problems to the nonlinear case. Several numerical examples - including
neural network training - demonstrate our theoretical findings and the additional
insight that can be gained by this multiobjective approach.
article_type: original
author:
- first_name: Katharina
full_name: Bieker, Katharina
id: '32829'
last_name: Bieker
- 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: 0000-0002-3389-793X
citation:
ama: Bieker K, Gebken B, Peitz S. On the Treatment of Optimization Problems with
L1 Penalty Terms via Multiobjective Continuation. IEEE Transactions on Pattern
Analysis and Machine Intelligence. 2022;44(11):7797-7808. doi:10.1109/TPAMI.2021.3114962
apa: Bieker, K., Gebken, B., & Peitz, S. (2022). On the Treatment of Optimization
Problems with L1 Penalty Terms via Multiobjective Continuation. IEEE Transactions
on Pattern Analysis and Machine Intelligence, 44(11), 7797–7808. https://doi.org/10.1109/TPAMI.2021.3114962
bibtex: '@article{Bieker_Gebken_Peitz_2022, title={On the Treatment of Optimization
Problems with L1 Penalty Terms via Multiobjective Continuation}, volume={44},
DOI={10.1109/TPAMI.2021.3114962},
number={11}, journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
publisher={IEEE}, author={Bieker, Katharina and Gebken, Bennet and Peitz, Sebastian},
year={2022}, pages={7797–7808} }'
chicago: 'Bieker, Katharina, Bennet Gebken, and Sebastian Peitz. “On the Treatment
of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation.”
IEEE Transactions on Pattern Analysis and Machine Intelligence 44, no.
11 (2022): 7797–7808. https://doi.org/10.1109/TPAMI.2021.3114962.'
ieee: 'K. Bieker, B. Gebken, and S. Peitz, “On the Treatment of Optimization Problems
with L1 Penalty Terms via Multiobjective Continuation,” IEEE Transactions on
Pattern Analysis and Machine Intelligence, vol. 44, no. 11, pp. 7797–7808,
2022, doi: 10.1109/TPAMI.2021.3114962.'
mla: Bieker, Katharina, et al. “On the Treatment of Optimization Problems with L1
Penalty Terms via Multiobjective Continuation.” IEEE Transactions on Pattern
Analysis and Machine Intelligence, vol. 44, no. 11, IEEE, 2022, pp. 7797–808,
doi:10.1109/TPAMI.2021.3114962.
short: K. Bieker, B. Gebken, S. Peitz, IEEE Transactions on Pattern Analysis and
Machine Intelligence 44 (2022) 7797–7808.
date_created: 2020-12-15T07:46:36Z
date_updated: 2022-10-21T12:27:16Z
ddc:
- '510'
department:
- _id: '101'
- _id: '530'
- _id: '655'
doi: 10.1109/TPAMI.2021.3114962
file:
- access_level: closed
content_type: application/pdf
creator: speitz
date_created: 2021-09-25T11:59:15Z
date_updated: 2021-09-25T11:59:15Z
file_id: '25040'
file_name: On_the_Treatment_of_Optimization_Problems_with_L1_Penalty_Terms_via_Multiobjective_Continuation.pdf
file_size: 7990831
relation: main_file
success: 1
file_date_updated: 2021-09-25T11:59:15Z
has_accepted_license: '1'
intvolume: ' 44'
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9547772
oa: '1'
page: 7797-7808
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
publication_status: epub_ahead
publisher: IEEE
status: public
title: On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective
Continuation
type: journal_article
user_id: '47427'
volume: 44
year: '2022'
...
---
_id: '30733'
abstract:
- lang: eng
text: Hamilton-Jacobi reachability methods for safety-critical control have been
well studied, but the safety guarantees derived rely on the accuracy of the numerical
computation. Thus, it is crucial to understand and account for any inaccuracies
that occur due to uncertainty in the underlying dynamics and environment as well
as the induced numerical errors. To this end, we propose a framework for modeling
the error of the value function inherent in Hamilton-Jacobi reachability using
a Gaussian process. The derived safety controller can be used in conjuncture with
arbitrary controllers to provide a safe hybrid control law. The marginal likelihood
of the Gaussian process then provides a confidence metric used to determine switches
between a least restrictive controller and a safety controller. We test both the
prediction as well as the correction capabilities of the presented method in a
classical pursuit-evasion example.
author:
- first_name: Nikolaus
full_name: Vertovec, Nikolaus
id: '93930'
last_name: Vertovec
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Kostas
full_name: Margellos, Kostas
last_name: Margellos
citation:
ama: 'Vertovec N, Ober-Blöbaum S, Margellos K. Verification of safety critical control
policies using kernel methods. In: ; 2022:1870-1875.'
apa: Vertovec, N., Ober-Blöbaum, S., & Margellos, K. (2022). Verification
of safety critical control policies using kernel methods. 1870–1875.
bibtex: '@inproceedings{Vertovec_Ober-Blöbaum_Margellos_2022, title={Verification
of safety critical control policies using kernel methods}, author={Vertovec, Nikolaus
and Ober-Blöbaum, Sina and Margellos, Kostas}, year={2022}, pages={1870–1875}
}'
chicago: Vertovec, Nikolaus, Sina Ober-Blöbaum, and Kostas Margellos. “Verification
of Safety Critical Control Policies Using Kernel Methods,” 1870–75, 2022.
ieee: N. Vertovec, S. Ober-Blöbaum, and K. Margellos, “Verification of safety critical
control policies using kernel methods,” London, 2022, pp. 1870–1875.
mla: Vertovec, Nikolaus, et al. Verification of Safety Critical Control Policies
Using Kernel Methods. 2022, pp. 1870–75.
short: 'N. Vertovec, S. Ober-Blöbaum, K. Margellos, in: 2022, pp. 1870–1875.'
conference:
end_date: 2022-07-15
location: London
name: 2022 European Control Conference (ECC)
start_date: 2022-07-12
date_created: 2022-03-31T11:14:13Z
date_updated: 2023-11-29T10:00:18Z
ddc:
- '510'
department:
- _id: '636'
has_accepted_license: '1'
language:
- iso: eng
page: 1870-1875
status: public
title: Verification of safety critical control policies using kernel methods
type: conference
user_id: '15694'
year: '2022'
...
---
_id: '45970'
abstract:
- lang: eng
text: ' We introduce a new phase field model for tumor growth where viscoelastic
effects are taken into account. The model is derived from basic thermodynamical
principles and consists of a convected Cahn–Hilliard equation with source terms
for the tumor cells and a convected reaction–diffusion equation with boundary
supply for the nutrient. Chemotactic terms, which are essential for the invasive
behavior of tumors, are taken into account. The model is completed by a viscoelastic
system consisting of the Navier–Stokes equation for the hydrodynamic quantities,
and a general constitutive equation with stress relaxation for the left Cauchy–Green
tensor associated with the elastic part of the total mechanical response of the
viscoelastic material. For a specific choice of the elastic energy density and
with an additional dissipative term accounting for stress diffusion, we prove
existence of global-in-time weak solutions of the viscoelastic model for tumor
growth in two space dimensions [Formula: see text] by the passage to the limit
in a fully-discrete finite element scheme where a CFL condition, i.e. [Formula:
see text], is required. Moreover, in arbitrary dimensions [Formula:
see text], we show stability and existence of solutions for the fully-discrete
finite element scheme, where positive definiteness of the discrete Cauchy–Green
tensor is proved with a regularization technique that was first introduced by
Barrett and Boyaval [Existence and approximation of a (regularized) Oldroyd-B
model, Math. Models Methods Appl. Sci. 21 (2011) 1783–1837]. After that, we improve
the regularity results in arbitrary dimensions [Formula: see text] and in two
dimensions [Formula: see text], where a CFL condition is required. Then, in two
dimensions [Formula: see text], we pass to the limit in the discretization parameters
and show that subsequences of discrete solutions converge to a global-in-time
weak solution. Finally, we present numerical results in two dimensions [Formula:
see text]. '
author:
- first_name: Harald
full_name: Garcke, Harald
last_name: Garcke
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Dennis
full_name: Trautwein, Dennis
last_name: Trautwein
citation:
ama: Garcke H, Kovács B, Trautwein D. Viscoelastic Cahn–Hilliard models for tumor
growth. Mathematical Models and Methods in Applied Sciences. 2022;32(13):2673-2758.
doi:10.1142/s0218202522500634
apa: Garcke, H., Kovács, B., & Trautwein, D. (2022). Viscoelastic Cahn–Hilliard
models for tumor growth. Mathematical Models and Methods in Applied Sciences,
32(13), 2673–2758. https://doi.org/10.1142/s0218202522500634
bibtex: '@article{Garcke_Kovács_Trautwein_2022, title={Viscoelastic Cahn–Hilliard
models for tumor growth}, volume={32}, DOI={10.1142/s0218202522500634},
number={13}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World
Scientific Pub Co Pte Ltd}, author={Garcke, Harald and Kovács, Balázs and Trautwein,
Dennis}, year={2022}, pages={2673–2758} }'
chicago: 'Garcke, Harald, Balázs Kovács, and Dennis Trautwein. “Viscoelastic Cahn–Hilliard
Models for Tumor Growth.” Mathematical Models and Methods in Applied Sciences
32, no. 13 (2022): 2673–2758. https://doi.org/10.1142/s0218202522500634.'
ieee: 'H. Garcke, B. Kovács, and D. Trautwein, “Viscoelastic Cahn–Hilliard models
for tumor growth,” Mathematical Models and Methods in Applied Sciences,
vol. 32, no. 13, pp. 2673–2758, 2022, doi: 10.1142/s0218202522500634.'
mla: Garcke, Harald, et al. “Viscoelastic Cahn–Hilliard Models for Tumor Growth.”
Mathematical Models and Methods in Applied Sciences, vol. 32, no. 13, World
Scientific Pub Co Pte Ltd, 2022, pp. 2673–758, doi:10.1142/s0218202522500634.
short: H. Garcke, B. Kovács, D. Trautwein, Mathematical Models and Methods in Applied
Sciences 32 (2022) 2673–2758.
date_created: 2023-07-10T11:47:27Z
date_updated: 2024-04-03T09:15:35Z
department:
- _id: '841'
doi: 10.1142/s0218202522500634
intvolume: ' 32'
issue: '13'
keyword:
- Applied Mathematics
- Modeling and Simulation
language:
- iso: eng
page: 2673-2758
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
issn:
- 0218-2025
- 1793-6314
publication_status: published
publisher: World Scientific Pub Co Pte Ltd
status: public
title: Viscoelastic Cahn–Hilliard models for tumor growth
type: journal_article
user_id: '100441'
volume: 32
year: '2022'
...
---
_id: '45969'
abstract:
- lang: eng
text: 'AbstractAn evolving surface finite element
discretisation is analysed for the evolution of a closed two-dimensional surface
governed by a system coupling a generalised forced mean curvature flow and a reaction–diffusion
process on the surface, inspired by a gradient flow of a coupled energy. Two algorithms
are proposed, both based on a system coupling the diffusion equation to evolution
equations for geometric quantities in the velocity law for the surface. One of
the numerical methods is proved to be convergent in the$$H^1$$H1norm
with optimal-order for finite elements of degree at least two. We present numerical
experiments illustrating the convergence behaviour and demonstrating the qualitative
properties of the flow: preservation of mean convexity, loss of convexity, weak
maximum principles, and the occurrence of self-intersections.'
author:
- first_name: Charles M.
full_name: Elliott, Charles M.
last_name: Elliott
- first_name: Harald
full_name: Garcke, Harald
last_name: Garcke
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Elliott CM, Garcke H, Kovács B. Numerical analysis for the interaction of mean
curvature flow and diffusion on closed surfaces. Numerische Mathematik.
2022;151(4):873-925. doi:10.1007/s00211-022-01301-3
apa: Elliott, C. M., Garcke, H., & Kovács, B. (2022). Numerical analysis for
the interaction of mean curvature flow and diffusion on closed surfaces. Numerische
Mathematik, 151(4), 873–925. https://doi.org/10.1007/s00211-022-01301-3
bibtex: '@article{Elliott_Garcke_Kovács_2022, title={Numerical analysis for the
interaction of mean curvature flow and diffusion on closed surfaces}, volume={151},
DOI={10.1007/s00211-022-01301-3},
number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business
Media LLC}, author={Elliott, Charles M. and Garcke, Harald and Kovács, Balázs},
year={2022}, pages={873–925} }'
chicago: 'Elliott, Charles M., Harald Garcke, and Balázs Kovács. “Numerical Analysis
for the Interaction of Mean Curvature Flow and Diffusion on Closed Surfaces.”
Numerische Mathematik 151, no. 4 (2022): 873–925. https://doi.org/10.1007/s00211-022-01301-3.'
ieee: 'C. M. Elliott, H. Garcke, and B. Kovács, “Numerical analysis for the interaction
of mean curvature flow and diffusion on closed surfaces,” Numerische Mathematik,
vol. 151, no. 4, pp. 873–925, 2022, doi: 10.1007/s00211-022-01301-3.'
mla: Elliott, Charles M., et al. “Numerical Analysis for the Interaction of Mean
Curvature Flow and Diffusion on Closed Surfaces.” Numerische Mathematik,
vol. 151, no. 4, Springer Science and Business Media LLC, 2022, pp. 873–925, doi:10.1007/s00211-022-01301-3.
short: C.M. Elliott, H. Garcke, B. Kovács, Numerische Mathematik 151 (2022) 873–925.
date_created: 2023-07-10T11:47:11Z
date_updated: 2024-04-03T09:15:44Z
department:
- _id: '841'
doi: 10.1007/s00211-022-01301-3
intvolume: ' 151'
issue: '4'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 873-925
publication: Numerische Mathematik
publication_identifier:
issn:
- 0029-599X
- 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Numerical analysis for the interaction of mean curvature flow and diffusion
on closed surfaces
type: journal_article
user_id: '100441'
volume: 151
year: '2022'
...
---
_id: '45963'
abstract:
- lang: eng
text: AbstractThe scattering of electromagnetic
waves from obstacles with wave-material interaction in thin layers on the surface
is described by generalized impedance boundary conditions, which provide effective
approximate models. In particular, this includes a thin coating around a perfect
conductor and the skin effect of a highly conducting material. The approach taken
in this work is to derive, analyse and discretize a system of time-dependent boundary
integral equations that determines the tangential traces of the scattered electric
and magnetic fields. In a familiar second step, the fields are evaluated in the
exterior domain by a representation formula, which uses the time-dependent potential
operators of Maxwell’s equations. The time-dependent boundary integral equation
is discretized with Runge–Kutta based convolution quadrature in time and Raviart–Thomas
boundary elements in space. Using the frequency-explicit bounds from the well-posedness
analysis given here together with known approximation properties of the numerical
methods, the full discretization is proved to be stable and convergent, with explicitly
given rates in the case of sufficient regularity. Taking the same Runge–Kutta
based convolution quadrature for discretizing the time-dependent representation
formulas, the optimal order of convergence is obtained away from the scattering
boundary, whereas an order reduction occurs close to the boundary. The theoretical
results are illustrated by numerical experiments.
author:
- first_name: Jörg
full_name: Nick, Jörg
last_name: Nick
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Christian
full_name: Lubich, Christian
last_name: Lubich
citation:
ama: Nick J, Kovács B, Lubich C. Time-dependent electromagnetic scattering from
thin layers. Numerische Mathematik. 2022;150(4):1123-1164. doi:10.1007/s00211-022-01277-0
apa: Nick, J., Kovács, B., & Lubich, C. (2022). Time-dependent electromagnetic
scattering from thin layers. Numerische Mathematik, 150(4), 1123–1164.
https://doi.org/10.1007/s00211-022-01277-0
bibtex: '@article{Nick_Kovács_Lubich_2022, title={Time-dependent electromagnetic
scattering from thin layers}, volume={150}, DOI={10.1007/s00211-022-01277-0},
number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business
Media LLC}, author={Nick, Jörg and Kovács, Balázs and Lubich, Christian}, year={2022},
pages={1123–1164} }'
chicago: 'Nick, Jörg, Balázs Kovács, and Christian Lubich. “Time-Dependent Electromagnetic
Scattering from Thin Layers.” Numerische Mathematik 150, no. 4 (2022):
1123–64. https://doi.org/10.1007/s00211-022-01277-0.'
ieee: 'J. Nick, B. Kovács, and C. Lubich, “Time-dependent electromagnetic scattering
from thin layers,” Numerische Mathematik, vol. 150, no. 4, pp. 1123–1164,
2022, doi: 10.1007/s00211-022-01277-0.'
mla: Nick, Jörg, et al. “Time-Dependent Electromagnetic Scattering from Thin Layers.”
Numerische Mathematik, vol. 150, no. 4, Springer Science and Business Media
LLC, 2022, pp. 1123–64, doi:10.1007/s00211-022-01277-0.
short: J. Nick, B. Kovács, C. Lubich, Numerische Mathematik 150 (2022) 1123–1164.
date_created: 2023-07-10T11:44:57Z
date_updated: 2024-04-03T09:18:23Z
department:
- _id: '841'
doi: 10.1007/s00211-022-01277-0
intvolume: ' 150'
issue: '4'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 1123-1164
publication: Numerische Mathematik
publication_identifier:
issn:
- 0029-599X
- 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Time-dependent electromagnetic scattering from thin layers
type: journal_article
user_id: '100441'
volume: 150
year: '2022'
...
---
_id: '45964'
abstract:
- lang: eng
text: "Abstract\r\n Maximal parabolic
$L^p$-regularity of linear parabolic equations on an evolving surface is shown
by pulling back the problem to the initial surface and studying the maximal $L^p$-regularity
on a fixed surface. By freezing the coefficients in the parabolic equations at
a fixed time and utilizing a perturbation argument around the freezed time, it
is shown that backward difference time discretizations of linear parabolic equations
on an evolving surface along characteristic trajectories can preserve maximal
$L^p$-regularity in the discrete setting. The result is applied to prove the stability
and convergence of time discretizations of nonlinear parabolic equations on an
evolving surface, with linearly implicit backward differentiation formulae characteristic
trajectories of the surface, for general locally Lipschitz nonlinearities. The
discrete maximal $L^p$-regularity is used to prove the boundedness and stability
of numerical solutions in the $L^\\infty (0,T;W^{1,\\infty })$ norm, which is
used to bound the nonlinear terms in the stability analysis. Optimal-order error
estimates of time discretizations in the $L^\\infty (0,T;W^{1,\\infty })$ norm
is obtained by combining the stability analysis with the consistency estimates."
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
citation:
ama: Kovács B, Li B. Maximal regularity of backward difference time discretization
for evolving surface PDEs and its application to nonlinear problems. IMA Journal
of Numerical Analysis. Published online 2022. doi:10.1093/imanum/drac033
apa: Kovács, B., & Li, B. (2022). Maximal regularity of backward difference
time discretization for evolving surface PDEs and its application to nonlinear
problems. IMA Journal of Numerical Analysis. https://doi.org/10.1093/imanum/drac033
bibtex: '@article{Kovács_Li_2022, title={Maximal regularity of backward difference
time discretization for evolving surface PDEs and its application to nonlinear
problems}, DOI={10.1093/imanum/drac033},
journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
(OUP)}, author={Kovács, Balázs and Li, Buyang}, year={2022} }'
chicago: Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference
Time Discretization for Evolving Surface PDEs and Its Application to Nonlinear
Problems.” IMA Journal of Numerical Analysis, 2022. https://doi.org/10.1093/imanum/drac033.
ieee: 'B. Kovács and B. Li, “Maximal regularity of backward difference time discretization
for evolving surface PDEs and its application to nonlinear problems,” IMA Journal
of Numerical Analysis, 2022, doi: 10.1093/imanum/drac033.'
mla: Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference Time
Discretization for Evolving Surface PDEs and Its Application to Nonlinear Problems.”
IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2022,
doi:10.1093/imanum/drac033.
short: B. Kovács, B. Li, IMA Journal of Numerical Analysis (2022).
date_created: 2023-07-10T11:45:14Z
date_updated: 2024-04-03T09:17:59Z
department:
- _id: '841'
doi: 10.1093/imanum/drac033
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
publication_identifier:
issn:
- 0272-4979
- 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Maximal regularity of backward difference time discretization for evolving
surface PDEs and its application to nonlinear problems
type: journal_article
user_id: '100441'
year: '2022'
...
---
_id: '45966'
abstract:
- lang: eng
text: "Abstract\r\n This paper studies
bulk–surface splitting methods of first order for (semilinear) parabolic partial
differential equations with dynamic boundary conditions. The proposed Lie splitting
scheme is based on a reformulation of the problem as a coupled partial differential–algebraic
equation system, i.e., the boundary conditions are considered as a second dynamic
equation that is coupled to the bulk problem. The splitting approach is combined
with bulk–surface finite elements and an implicit Euler discretization of the
two subsystems. We prove first-order convergence of the resulting fully discrete
scheme in the presence of a weak CFL condition of the form $\\tau \\leqslant c
h$ for some constant $c>0$. The convergence is also illustrated numerically
using dynamic boundary conditions of Allen–Cahn type."
author:
- first_name: Robert
full_name: Altmann, Robert
last_name: Altmann
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Christoph
full_name: Zimmer, Christoph
last_name: Zimmer
citation:
ama: Altmann R, Kovács B, Zimmer C. Bulk–surface Lie splitting for parabolic problems
with dynamic boundary conditions. IMA Journal of Numerical Analysis. 2022;43(2):950-975.
doi:10.1093/imanum/drac002
apa: Altmann, R., Kovács, B., & Zimmer, C. (2022). Bulk–surface Lie splitting
for parabolic problems with dynamic boundary conditions. IMA Journal of Numerical
Analysis, 43(2), 950–975. https://doi.org/10.1093/imanum/drac002
bibtex: '@article{Altmann_Kovács_Zimmer_2022, title={Bulk–surface Lie splitting
for parabolic problems with dynamic boundary conditions}, volume={43}, DOI={10.1093/imanum/drac002}, number={2},
journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
(OUP)}, author={Altmann, Robert and Kovács, Balázs and Zimmer, Christoph}, year={2022},
pages={950–975} }'
chicago: 'Altmann, Robert, Balázs Kovács, and Christoph Zimmer. “Bulk–Surface Lie
Splitting for Parabolic Problems with Dynamic Boundary Conditions.” IMA Journal
of Numerical Analysis 43, no. 2 (2022): 950–75. https://doi.org/10.1093/imanum/drac002.'
ieee: 'R. Altmann, B. Kovács, and C. Zimmer, “Bulk–surface Lie splitting for parabolic
problems with dynamic boundary conditions,” IMA Journal of Numerical Analysis,
vol. 43, no. 2, pp. 950–975, 2022, doi: 10.1093/imanum/drac002.'
mla: Altmann, Robert, et al. “Bulk–Surface Lie Splitting for Parabolic Problems
with Dynamic Boundary Conditions.” IMA Journal of Numerical Analysis, vol.
43, no. 2, Oxford University Press (OUP), 2022, pp. 950–75, doi:10.1093/imanum/drac002.
short: R. Altmann, B. Kovács, C. Zimmer, IMA Journal of Numerical Analysis 43 (2022)
950–975.
date_created: 2023-07-10T11:45:49Z
date_updated: 2024-04-03T09:16:47Z
department:
- _id: '841'
doi: 10.1093/imanum/drac002
intvolume: ' 43'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
page: 950-975
publication: IMA Journal of Numerical Analysis
publication_identifier:
issn:
- 0272-4979
- 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions
type: journal_article
user_id: '100441'
volume: 43
year: '2022'
...
---
_id: '45968'
abstract:
- lang: eng
text: "Abstract\r\n We derive a numerical
method, based on operator splitting, to abstract parabolic semilinear boundary
coupled systems. The method decouples the linear components that describe the
coupling and the dynamics in the abstract bulk- and surface-spaces, and treats
the nonlinear terms similarly to an exponential integrator. The convergence proof
is based on estimates for a recursive formulation of the error, using the parabolic
smoothing property of analytic semigroups, and a careful comparison of the exact
and approximate flows. This analysis also requires a deep understanding of the
effects of the Dirichlet operator (the abstract version of the harmonic extension
operator), which is essential for the stable coupling in our method. Numerical
experiments, including problems with dynamic boundary conditions, reporting on
convergence rates are presented."
author:
- first_name: Petra
full_name: Csomós, Petra
last_name: Csomós
- first_name: Bálint
full_name: Farkas, Bálint
last_name: Farkas
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Csomós P, Farkas B, Kovács B. Error estimates for a splitting integrator for
abstract semilinear boundary coupled systems. IMA Journal of Numerical Analysis.
Published online 2022. doi:10.1093/imanum/drac079
apa: Csomós, P., Farkas, B., & Kovács, B. (2022). Error estimates for a splitting
integrator for abstract semilinear boundary coupled systems. IMA Journal of
Numerical Analysis. https://doi.org/10.1093/imanum/drac079
bibtex: '@article{Csomós_Farkas_Kovács_2022, title={Error estimates for a splitting
integrator for abstract semilinear boundary coupled systems}, DOI={10.1093/imanum/drac079},
journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
(OUP)}, author={Csomós, Petra and Farkas, Bálint and Kovács, Balázs}, year={2022}
}'
chicago: Csomós, Petra, Bálint Farkas, and Balázs Kovács. “Error Estimates for a
Splitting Integrator for Abstract Semilinear Boundary Coupled Systems.” IMA
Journal of Numerical Analysis, 2022. https://doi.org/10.1093/imanum/drac079.
ieee: 'P. Csomós, B. Farkas, and B. Kovács, “Error estimates for a splitting integrator
for abstract semilinear boundary coupled systems,” IMA Journal of Numerical
Analysis, 2022, doi: 10.1093/imanum/drac079.'
mla: Csomós, Petra, et al. “Error Estimates for a Splitting Integrator for Abstract
Semilinear Boundary Coupled Systems.” IMA Journal of Numerical Analysis,
Oxford University Press (OUP), 2022, doi:10.1093/imanum/drac079.
short: P. Csomós, B. Farkas, B. Kovács, IMA Journal of Numerical Analysis (2022).
date_created: 2023-07-10T11:46:54Z
date_updated: 2024-04-03T09:15:52Z
department:
- _id: '841'
doi: 10.1093/imanum/drac079
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
publication_identifier:
issn:
- 0272-4979
- 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Error estimates for a splitting integrator for abstract semilinear boundary
coupled systems
type: journal_article
user_id: '100441'
year: '2022'
...
---
_id: '45958'
abstract:
- lang: eng
text: AbstractIn this paper, we consider a non-linear
fourth-order evolution equation of Cahn–Hilliard-type on evolving surfaces with
prescribed velocity, where the non-linear terms are only assumed to have locally
Lipschitz derivatives. High-order evolving surface finite elements are used to
discretise the weak equation system in space, and a modified matrix–vector formulation
for the semi-discrete problem is derived. The anti-symmetric structure of the
equation system is preserved by the spatial discretisation. A new stability proof,
based on this structure, combined with consistency bounds proves optimal-order
and uniform-in-time error estimates. The paper is concluded by a variety of numerical
experiments.
author:
- first_name: Cedric Aaron
full_name: Beschle, Cedric Aaron
last_name: Beschle
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Beschle CA, Kovács B. Stability and error estimates for non-linear Cahn–Hilliard-type
equations on evolving surfaces. Numerische Mathematik. 2022;151(1):1-48.
doi:10.1007/s00211-022-01280-5
apa: Beschle, C. A., & Kovács, B. (2022). Stability and error estimates for
non-linear Cahn–Hilliard-type equations on evolving surfaces. Numerische Mathematik,
151(1), 1–48. https://doi.org/10.1007/s00211-022-01280-5
bibtex: '@article{Beschle_Kovács_2022, title={Stability and error estimates for
non-linear Cahn–Hilliard-type equations on evolving surfaces}, volume={151}, DOI={10.1007/s00211-022-01280-5},
number={1}, journal={Numerische Mathematik}, publisher={Springer Science and Business
Media LLC}, author={Beschle, Cedric Aaron and Kovács, Balázs}, year={2022}, pages={1–48}
}'
chicago: 'Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates
for Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” Numerische
Mathematik 151, no. 1 (2022): 1–48. https://doi.org/10.1007/s00211-022-01280-5.'
ieee: 'C. A. Beschle and B. Kovács, “Stability and error estimates for non-linear
Cahn–Hilliard-type equations on evolving surfaces,” Numerische Mathematik,
vol. 151, no. 1, pp. 1–48, 2022, doi: 10.1007/s00211-022-01280-5.'
mla: Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates for
Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” Numerische Mathematik,
vol. 151, no. 1, Springer Science and Business Media LLC, 2022, pp. 1–48, doi:10.1007/s00211-022-01280-5.
short: C.A. Beschle, B. Kovács, Numerische Mathematik 151 (2022) 1–48.
date_created: 2023-07-10T11:43:44Z
date_updated: 2024-04-03T09:19:34Z
department:
- _id: '841'
doi: 10.1007/s00211-022-01280-5
intvolume: ' 151'
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 1-48
publication: Numerische Mathematik
publication_identifier:
issn:
- 0029-599X
- 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Stability and error estimates for non-linear Cahn–Hilliard-type equations on
evolving surfaces
type: journal_article
user_id: '100441'
volume: 151
year: '2022'
...
---
_id: '45956'
abstract:
- lang: eng
text: "Abstract\r\n The full Maxwell
equations in the unbounded three-dimensional space coupled to the Landau–Lifshitz–Gilbert
equation serve as a well-tested model for ferromagnetic materials.\r\nWe propose
a weak formulation of the coupled system based on the boundary integral formulation
of the exterior Maxwell equations.\r\nWe show existence and partial uniqueness
of a weak solution and propose a new numerical algorithm based on finite elements
and boundary elements as spatial discretization with backward Euler and convolution
quadrature for the time domain.\r\nThis is the first numerical algorithm which
is able to deal with the coupled system of Landau–Lifshitz–Gilbert equation and
full Maxwell’s equations without any simplifications like quasi-static approximations
(e.g. eddy current model) and without restrictions on the shape of the domain
(e.g. convexity).\r\nWe show well-posedness and convergence of the numerical algorithm
under minimal assumptions on the regularity of the solution.\r\nThis is particularly
important as there are few regularity results available and one generally expects
the solution to be non-smooth.\r\nNumerical experiments illustrate and expand
on the theoretical results."
author:
- first_name: Jan
full_name: Bohn, Jan
last_name: Bohn
- first_name: Michael
full_name: Feischl, Michael
last_name: Feischl
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: 'Bohn J, Feischl M, Kovács B. FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
Equations via Convolution Quadrature: Weak Form and Numerical Approximation. Computational
Methods in Applied Mathematics. 2022;23(1):19-48. doi:10.1515/cmam-2022-0145'
apa: 'Bohn, J., Feischl, M., & Kovács, B. (2022). FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
Equations via Convolution Quadrature: Weak Form and Numerical Approximation. Computational
Methods in Applied Mathematics, 23(1), 19–48. https://doi.org/10.1515/cmam-2022-0145'
bibtex: '@article{Bohn_Feischl_Kovács_2022, title={FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
Equations via Convolution Quadrature: Weak Form and Numerical Approximation},
volume={23}, DOI={10.1515/cmam-2022-0145},
number={1}, journal={Computational Methods in Applied Mathematics}, publisher={Walter
de Gruyter GmbH}, author={Bohn, Jan and Feischl, Michael and Kovács, Balázs},
year={2022}, pages={19–48} }'
chicago: 'Bohn, Jan, Michael Feischl, and Balázs Kovács. “FEM-BEM Coupling for the
Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form
and Numerical Approximation.” Computational Methods in Applied Mathematics
23, no. 1 (2022): 19–48. https://doi.org/10.1515/cmam-2022-0145.'
ieee: 'J. Bohn, M. Feischl, and B. Kovács, “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
Equations via Convolution Quadrature: Weak Form and Numerical Approximation,”
Computational Methods in Applied Mathematics, vol. 23, no. 1, pp. 19–48,
2022, doi: 10.1515/cmam-2022-0145.'
mla: 'Bohn, Jan, et al. “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
Equations via Convolution Quadrature: Weak Form and Numerical Approximation.”
Computational Methods in Applied Mathematics, vol. 23, no. 1, Walter de
Gruyter GmbH, 2022, pp. 19–48, doi:10.1515/cmam-2022-0145.'
short: J. Bohn, M. Feischl, B. Kovács, Computational Methods in Applied Mathematics
23 (2022) 19–48.
date_created: 2023-07-10T11:43:13Z
date_updated: 2024-04-03T09:20:30Z
department:
- _id: '841'
doi: 10.1515/cmam-2022-0145
intvolume: ' 23'
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
- Numerical Analysis
language:
- iso: eng
page: 19-48
publication: Computational Methods in Applied Mathematics
publication_identifier:
issn:
- 1609-4840
- 1609-9389
publication_status: published
publisher: Walter de Gruyter GmbH
status: public
title: 'FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution
Quadrature: Weak Form and Numerical Approximation'
type: journal_article
user_id: '100441'
volume: 23
year: '2022'
...
---
_id: '55280'
author:
- first_name: Ch.
full_name: Elsholtz, Ch.
last_name: Elsholtz
- first_name: B.
full_name: Klahn, B.
last_name: Klahn
- first_name: Marc
full_name: Technau, Marc
id: '106108'
last_name: Technau
orcid: 0000-0001-9650-2459
citation:
ama: Elsholtz Ch, Klahn B, Technau M. On polynomials with roots modulo almost all
primes. Acta Arith. 2022;205:3(3):251–263. doi:10.4064/aa220407-9-7
apa: Elsholtz, Ch., Klahn, B., & Technau, M. (2022). On polynomials with roots
modulo almost all primes. Acta Arith., 205:3(3), 251–263. https://doi.org/10.4064/aa220407-9-7
bibtex: '@article{Elsholtz_Klahn_Technau_2022, title={On polynomials with roots
modulo almost all primes}, volume={205:3}, DOI={10.4064/aa220407-9-7},
number={3}, journal={Acta Arith.}, author={Elsholtz, Ch. and Klahn, B. and Technau,
Marc}, year={2022}, pages={251–263} }'
chicago: 'Elsholtz, Ch., B. Klahn, and Marc Technau. “On Polynomials with Roots
modulo Almost All Primes.” Acta Arith. 205:3, no. 3 (2022): 251–263. https://doi.org/10.4064/aa220407-9-7.'
ieee: 'Ch. Elsholtz, B. Klahn, and M. Technau, “On polynomials with roots modulo
almost all primes,” Acta Arith., vol. 205:3, no. 3, pp. 251–263, 2022,
doi: 10.4064/aa220407-9-7.'
mla: Elsholtz, Ch., et al. “On Polynomials with Roots modulo Almost All Primes.”
Acta Arith., vol. 205:3, no. 3, 2022, pp. 251–263, doi:10.4064/aa220407-9-7.
short: Ch. Elsholtz, B. Klahn, M. Technau, Acta Arith. 205:3 (2022) 251–263.
date_created: 2024-07-16T11:09:01Z
date_updated: 2024-07-24T07:26:22Z
department:
- _id: '102'
doi: 10.4064/aa220407-9-7
extern: '1'
issue: '3'
language:
- iso: eng
page: 251–263
publication: Acta Arith.
status: public
title: On polynomials with roots modulo almost all primes
type: journal_article
user_id: '106108'
volume: 205:3
year: '2022'
...
---
_id: '34839'
abstract:
- lang: eng
text: We describe the relations among the ℓ-torsion conjecture, a conjecture of
Malle giving an upper bound for the number of extensions, and the discriminant
multiplicity conjecture. We prove that the latter two conjectures are equivalent
in some sense. Altogether, the three conjectures are equivalent for the class
of solvable groups. We then prove the ℓ-torsion conjecture for ℓ-groups and the
other two conjectures for nilpotent groups.
author:
- first_name: Jürgen
full_name: Klüners, Jürgen
id: '21202'
last_name: Klüners
- first_name: Jiuya
full_name: Wang, Jiuya
last_name: Wang
citation:
ama: Klüners J, Wang J. ℓ-torsion bounds for the class group of number fields with
an ℓ-group as Galois group. Proceedings of the American Mathematical Society.
2022;150(7):2793-2805. doi:10.1090/proc/15882
apa: Klüners, J., & Wang, J. (2022). ℓ-torsion bounds for the class group of
number fields with an ℓ-group as Galois group. Proceedings of the American
Mathematical Society, 150(7), 2793–2805. https://doi.org/10.1090/proc/15882
bibtex: '@article{Klüners_Wang_2022, title={ℓ-torsion bounds for the class group
of number fields with an ℓ-group as Galois group}, volume={150}, DOI={10.1090/proc/15882},
number={7}, journal={Proceedings of the American Mathematical Society}, publisher={American
Mathematical Society (AMS)}, author={Klüners, Jürgen and Wang, Jiuya}, year={2022},
pages={2793–2805} }'
chicago: 'Klüners, Jürgen, and Jiuya Wang. “ℓ-Torsion Bounds for the Class Group
of Number Fields with an ℓ-Group as Galois Group.” Proceedings of the American
Mathematical Society 150, no. 7 (2022): 2793–2805. https://doi.org/10.1090/proc/15882.'
ieee: 'J. Klüners and J. Wang, “ℓ-torsion bounds for the class group of number fields
with an ℓ-group as Galois group,” Proceedings of the American Mathematical
Society, vol. 150, no. 7, pp. 2793–2805, 2022, doi: 10.1090/proc/15882.'
mla: Klüners, Jürgen, and Jiuya Wang. “ℓ-Torsion Bounds for the Class Group of Number
Fields with an ℓ-Group as Galois Group.” Proceedings of the American Mathematical
Society, vol. 150, no. 7, American Mathematical Society (AMS), 2022, pp. 2793–805,
doi:10.1090/proc/15882.
short: J. Klüners, J. Wang, Proceedings of the American Mathematical Society 150
(2022) 2793–2805.
date_created: 2022-12-22T10:47:01Z
date_updated: 2023-03-06T08:47:42Z
department:
- _id: '102'
doi: 10.1090/proc/15882
external_id:
arxiv:
- '2003.12161 '
intvolume: ' 150'
issue: '7'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
page: 2793-2805
publication: Proceedings of the American Mathematical Society
publication_identifier:
issn:
- 0002-9939
- 1088-6826
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois
group
type: journal_article
user_id: '93826'
volume: 150
year: '2022'
...
---
_id: '34835'
abstract:
- lang: eng
text: 'We prove an upper bound for the asymptotics of counting functions of number
fields with nilpotent Galois groups. '
author:
- first_name: Jürgen
full_name: Klüners, Jürgen
id: '21202'
last_name: Klüners
citation:
ama: Klüners J. The asymptotics of nilpotent Galois groups. Acta Arithmetica.
2022;204(2):165-184. doi:10.4064/aa211207-16-5
apa: Klüners, J. (2022). The asymptotics of nilpotent Galois groups. Acta Arithmetica,
204(2), 165–184. https://doi.org/10.4064/aa211207-16-5
bibtex: '@article{Klüners_2022, title={The asymptotics of nilpotent Galois groups},
volume={204}, DOI={10.4064/aa211207-16-5},
number={2}, journal={Acta Arithmetica}, publisher={Institute of Mathematics, Polish
Academy of Sciences}, author={Klüners, Jürgen}, year={2022}, pages={165–184} }'
chicago: 'Klüners, Jürgen. “The Asymptotics of Nilpotent Galois Groups.” Acta
Arithmetica 204, no. 2 (2022): 165–84. https://doi.org/10.4064/aa211207-16-5.'
ieee: 'J. Klüners, “The asymptotics of nilpotent Galois groups,” Acta Arithmetica,
vol. 204, no. 2, pp. 165–184, 2022, doi: 10.4064/aa211207-16-5.'
mla: Klüners, Jürgen. “The Asymptotics of Nilpotent Galois Groups.” Acta Arithmetica,
vol. 204, no. 2, Institute of Mathematics, Polish Academy of Sciences, 2022, pp.
165–84, doi:10.4064/aa211207-16-5.
short: J. Klüners, Acta Arithmetica 204 (2022) 165–184.
date_created: 2022-12-22T10:08:23Z
date_updated: 2023-03-06T08:48:33Z
department:
- _id: '102'
doi: 10.4064/aa211207-16-5
external_id:
arxiv:
- '2011.04325 '
intvolume: ' 204'
issue: '2'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 165-184
publication: Acta Arithmetica
publication_identifier:
issn:
- 0065-1036
- 1730-6264
publication_status: published
publisher: Institute of Mathematics, Polish Academy of Sciences
status: public
title: The asymptotics of nilpotent Galois groups
type: journal_article
user_id: '93826'
volume: 204
year: '2022'
...
---
_id: '44624'
author:
- first_name: Timm
full_name: Faulwasser, Timm
last_name: Faulwasser
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Manuel
full_name: Schaller, Manuel
last_name: Schaller
- first_name: Karl
full_name: Worthmann, Karl
last_name: Worthmann
citation:
ama: Faulwasser T, Flaßkamp K, Ober-Blöbaum S, Schaller M, Worthmann K. Manifold
turnpikes, trims, and symmetries. Mathematics of Control, Signals, and Systems.
2022;34:759-788.
apa: Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., Schaller, M., & Worthmann,
K. (2022). Manifold turnpikes, trims, and symmetries. Mathematics of Control,
Signals, and Systems, 34, 759–788.
bibtex: '@article{Faulwasser_Flaßkamp_Ober-Blöbaum_Schaller_Worthmann_2022, title={Manifold
turnpikes, trims, and symmetries}, volume={34}, journal={Mathematics of Control,
Signals, and Systems}, publisher={Springer}, author={Faulwasser, Timm and Flaßkamp,
Kathrin and Ober-Blöbaum, Sina and Schaller, Manuel and Worthmann, Karl}, year={2022},
pages={759–788} }'
chicago: 'Faulwasser, Timm, Kathrin Flaßkamp, Sina Ober-Blöbaum, Manuel Schaller,
and Karl Worthmann. “Manifold Turnpikes, Trims, and Symmetries.” Mathematics
of Control, Signals, and Systems 34 (2022): 759–88.'
ieee: T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, M. Schaller, and K. Worthmann,
“Manifold turnpikes, trims, and symmetries,” Mathematics of Control, Signals,
and Systems, vol. 34, pp. 759–788, 2022.
mla: Faulwasser, Timm, et al. “Manifold Turnpikes, Trims, and Symmetries.” Mathematics
of Control, Signals, and Systems, vol. 34, Springer, 2022, pp. 759–88.
short: T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, M. Schaller, K. Worthmann, Mathematics
of Control, Signals, and Systems 34 (2022) 759–788.
date_created: 2023-05-08T09:04:06Z
date_updated: 2023-05-08T09:04:26Z
department:
- _id: '636'
intvolume: ' 34'
language:
- iso: eng
page: 759-788
publication: Mathematics of Control, Signals, and Systems
publisher: Springer
status: public
title: Manifold turnpikes, trims, and symmetries
type: journal_article
user_id: '15694'
volume: 34
year: '2022'
...
---
_id: '33741'
abstract:
- lang: eng
text: There are many concepts of signed graph coloring which are defined by assigning
colors to the vertices of the graphs. These concepts usually differ in the number
of self-inverse colors used. We introduce a unifying concept for this kind of
coloring by assigning elements from symmetric sets to the vertices of the signed
graphs. In the first part of the paper, we study colorings with elements from
symmetric sets where the number of self-inverse elements is fixed. We prove a
Brooks’-type theorem and upper bounds for the corresponding chromatic numbers
in terms of the chromatic number of the underlying graph. These results are used
in the second part where we introduce the symset-chromatic number χsym(G,σ) of
a signed graph (G,σ). We show that the symset-chromatic number gives the minimum
partition of a signed graph into independent sets and non-bipartite antibalanced
subgraphs. In particular, χsym(G,σ)≤χ(G). In the final section we show that these
colorings can also be formalized as DP-colorings.
author:
- first_name: Chiara
full_name: Cappello, Chiara
id: '72874'
last_name: Cappello
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
citation:
ama: Cappello C, Steffen E. Symmetric Set Coloring of Signed Graphs. Annals of
Combinatorics. Published online 2022. doi:10.1007/s00026-022-00593-4
apa: Cappello, C., & Steffen, E. (2022). Symmetric Set Coloring of Signed Graphs.
Annals of Combinatorics. https://doi.org/10.1007/s00026-022-00593-4
bibtex: '@article{Cappello_Steffen_2022, title={Symmetric Set Coloring of Signed
Graphs}, DOI={10.1007/s00026-022-00593-4},
journal={Annals of Combinatorics}, publisher={Springer Science and Business Media
LLC}, author={Cappello, Chiara and Steffen, Eckhard}, year={2022} }'
chicago: Cappello, Chiara, and Eckhard Steffen. “Symmetric Set Coloring of Signed
Graphs.” Annals of Combinatorics, 2022. https://doi.org/10.1007/s00026-022-00593-4.
ieee: 'C. Cappello and E. Steffen, “Symmetric Set Coloring of Signed Graphs,” Annals
of Combinatorics, 2022, doi: 10.1007/s00026-022-00593-4.'
mla: Cappello, Chiara, and Eckhard Steffen. “Symmetric Set Coloring of Signed Graphs.”
Annals of Combinatorics, Springer Science and Business Media LLC, 2022,
doi:10.1007/s00026-022-00593-4.
short: C. Cappello, E. Steffen, Annals of Combinatorics (2022).
date_created: 2022-10-17T07:54:41Z
date_updated: 2023-05-16T10:37:58Z
department:
- _id: '542'
doi: 10.1007/s00026-022-00593-4
external_id:
arxiv:
- '2106.05928'
keyword:
- Discrete Mathematics and Combinatorics
language:
- iso: eng
publication: Annals of Combinatorics
publication_identifier:
issn:
- 0218-0006
- 0219-3094
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Symmetric Set Coloring of Signed Graphs
type: journal_article
user_id: '15540'
year: '2022'
...