Research Group of Prof. Dr. Ira Neitzel
Contact Information
Friedrich-Hirzebruch-Allee 7
53115 Bonn
Teaching
Winter semester 2024/25
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Wissenschaftliches Rechnen I Scientific Computing I
Winter semester 2023/24
See teaching activities of the whole group.
Research Projects
Current
Sparse controls in optimization of quasilinear partial differential equations
Project C10, DFG SFB 1060.
Completed
Optimizing Fracture Propagation Using a Phase-Field Approach
Project SPP 1962, DFG priority program 1962.
Optimizing Fracture Propagation Using a Phase-Field Approach, Part II
Project SPP 1962 Phase 2, DFG priority program 1962, Phase II.
Participants
Institut für Numerische Simulation der Rheinischen Friedrich-Wilhelms-Universität Bonn: Prof. Dr. Ira Neitzel
Institut für angewandte Mathematik der Leibniz Universtität Hannover: Prof. Dr. Thomas Wick
Fachbereich Mathematik der Technischen Universtität Darmstadt: Prof. Dr. Winnifried Wollner
Description
Within this project, we consider the numerical approximation and solution of control problems governed by a quasi-static brittle fracture propagation model. As a central modeling component, a phase-field formulation for the fracture formation and propagation is considered.
The fracture propagation problem itself can be formulated as a minimization problem with inequality constraints, imposed by multiple relevant side conditions, such as irreversibility of the fracture-growth or non-selfpenetration of the material across the fracture surface. These lead to variational inequalities as first order necessary conditions. Consequently, optimization problems for the control of the fracture process give rise to a mathematical program with complementarity constraints (MPCC) in function spaces.
Within this project, we intend to focus on mathematical challenges, that are also motivated by applications, such as control of the coefficients of the variational inequality, or nonsmooth and/or nonconvex cost functionals in the outer optimization, such as, e.g., maximizing the released energy of the fracture. We will develop first and second order optimality conditions for the resulting MPCC as well as other obstacle-like formulations. Additionally, we will consider the discretization by finite elements and show the convergence of the discrete approximations to the continuous limit. These findings will be substantiated with prototype numerical tests.
Cooperation
See all projects of the group.
Publications
Submitted Articles
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Journal Papers
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First-order conditions for the optimal control of the obstacle problem with state constraints.
I. Neitzel and G. Wachsmuth.
PAFA, 2020.
also available as arXive Preprint arXiv:2012.15324.
BibTeX
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Sufficient optimality conditions for the Moreau-Yosida-type regularization concept applied to semilinear elliptic optimal control problems with pointwise state constraints.
K. Krumbiegel, I. Neitzel, and A. Rösch.
Ann. Acad. Rom. Sci. Ser. Math. Appl., 2(2):222–246, 2010.
BibTeX
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On convergence of regularization methods for nonlinear parabolic optimal control problems with control and state constraints.
I. Neitzel and F. Tröltzsch.
Control Cybernet., 37(4):1013–1043, 2008.
BibTeX
Proceedings, Series- and Book Contributions, Technical Reporst
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Optimizing fracture propagation using a phase-field approach.
A. Hehl, M. Mohammadi, I. Neitzel, and W. Wollner.
In to appear.
2020.
BibTeX
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Optimal pde control using comsol multiphysics.
I. Neitzel, U. Prüfert, and T. Slawig.
Proceedings CD of the 2008 European COMSOL Conference, 2008.
BibTeX
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Solving time-dependent optimal control problems in comsol multiphysics.
I. Neitzel, U. Prüfert, and T. Slawig.
Proceedings CD of the 2008 European COMSOL Conference, 2008.
BibTeX
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First-order conditions for the optimal control of the obstacle problem with state constraints. I. Neitzel and G. Wachsmuth. PAFA, 2020. also available as arXive Preprint arXiv:2012.15324. BibTeX
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Sufficient optimality conditions for the Moreau-Yosida-type regularization concept applied to semilinear elliptic optimal control problems with pointwise state constraints. K. Krumbiegel, I. Neitzel, and A. Rösch. Ann. Acad. Rom. Sci. Ser. Math. Appl., 2(2):222–246, 2010. BibTeX
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On convergence of regularization methods for nonlinear parabolic optimal control problems with control and state constraints. I. Neitzel and F. Tröltzsch. Control Cybernet., 37(4):1013–1043, 2008. BibTeX
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Optimizing fracture propagation using a phase-field approach. A. Hehl, M. Mohammadi, I. Neitzel, and W. Wollner. In to appear. 2020. BibTeX
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Optimal pde control using comsol multiphysics. I. Neitzel, U. Prüfert, and T. Slawig. Proceedings CD of the 2008 European COMSOL Conference, 2008. BibTeX
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Solving time-dependent optimal control problems in comsol multiphysics. I. Neitzel, U. Prüfert, and T. Slawig. Proceedings CD of the 2008 European COMSOL Conference, 2008. BibTeX