Research Group of Prof. Dr. Ira Neitzel

Contact Information

Institut für Numerische Simulation
Endenicher Allee 19b
53115 Bonn
Phone: +49 228 73-69837
Office: EA19b 3.034
E-Mail: ed tod nnob-inu tod sni ta leztiena tod b@foo tod de

Optimizing Fracture Propagation Using a Phase-Field Approach

Project SPP 1962, DFG priority program 1962.

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 analyze the resulting MPCC with respect to it’s necessary and sufficient optimality conditions by means of a regularization of the lower-level problem and passage to the limit with respect to the regularization parameter. Moreover, we will consider SQP-type algorithms for the solution of this MPCC in function space and investigate its properties. Additionally, we will consider the discretization by finite elements and show the convergence of the discrete approximations to the continuous limit.

The simultaneous consideration of the inexactness due to discretization and regularization error will allow us to construct and analyze an efficient inexact SQP-type solver for the MPCC under consideration.

Cooperation

DFG Priority Programme SPP 1962, “Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization”

FWF-Project P29181, “Goal-Oriented Error Control for Phase-Field Fracture Coupled to Multiphysics Problems”

Publications

Journal Papers

1. Second order optimality conditions for optimal control of quasilinear parabolic pdes. L. Bonifacius and I. Neitzel. Mathematical Control and Related Fields, 8(1):1–34, 2018. Preprint version available as INS Preprint No. 1705.
2. An optimal control problem governed by a regularized phase field fracture propagation model. I. Neitzel, T. Wick, and W. Wollner. SIAM J. Control Optim., 55(4):2271–2288, 2017. also available as IGDK 1754 Preprint 2015-12.
3. A priori $l^2$-discretization error estimates for the state in elliptic optimization problems with pointwise inequality state constraints. I. Neitzel and W. Wollner. Numer. Math., 2017. also available as INS Preprint No. 1606.
4. Dirichlet control of elliptic state constrained problems. M. Mateos and I. Neitzel. Comput. Optim. Appl., 2015.
5. An adaptive numerical method for semi-infinite elliptic control problems based on error estimates. P. Merino, I. Neitzel, and F. Tröltzsch. Optim. Methods Softw., 30(3):492–515, 2015.
6. Finite element discretization of state-constrained elliptic optimal control problems with semilinear state equation. I. Neitzel, J. Pfefferer, and A. Rösch. SIAM J. Control Optim., 53(2):874–904, 2015.
7. Regularization for semilinear elliptic optimal control problems with pointwise state and control constraints. K. Krumbiegel, I. Neitzel, and A. Rösch. Comput. Optim. Appl., 52(1):181–207, 2012.
8. A priori error estimates for space-time finite element discretization of semilinear parabolic optimal control problems. I. Neitzel and B. Vexler. Numer. Math., 120(2):345–386, 2012.
9. On linear-quadratic elliptic control problems of semi-infinite type. P. Merino, I. Neitzel, and F. Tröltzsch. Appl. Anal., 90(6):1047–1074, 2011.
10. A smooth regularization of the projection formula for constrained parabolic optimal control problems. I. Neitzel, U. Prüfert, and T. Slawig. Numer. Funct. Anal. Optim., 32(12):1283–1315, 2011.
11. 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.
12. Error estimates for the finite element discretization of semi-infinite elliptic optimal control problems. P. Merino, I. Neitzel, and F. Tröltzsch. Discuss. Math. Differ. Incl. Control Optim., 30(2):221–236, 2010.
13. Strategies for time-dependent PDE control with inequality constraints using an integrated modeling and simulation environment. I. Neitzel, U. Prüfert, and T. Slawig. Numer. Algorithms, 50(3):241–269, 2009.
14. On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints. I. Neitzel and F. Tröltzsch. ESAIM Control Optim. Calc. Var., 15(2):426–453, 2009.
15. 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.

Proceedings, Series- and Book Contributions

1. A-posteriori error estimation of discrete pod models for pde-constrained optimal control. M. Gubisch, I. Neitzel, and S. Volkwein. In Model reduction and approximation: theory and algorithms, volume of Computational Science and Engineering, pages. SIAM.
2. A priori error estimates for nonstationary optimal control problems with gradient constraints. F. Ludovici, I. Neitzel, and W. Wollner. PAMM, 15(1):611–612, 2015.
3. Numerical analysis of state-constrained optimal control problems for PDEs. I. Neitzel and F. Tröltzsch. In Constrained optimization and optimal control for partial differential equations, volume 160 of Internat. Ser. Numer. Math., pages 467–482. Birkhäuser/Springer Basel AG, Basel, 2012.
4. Optimal pde control using comsol multiphysics. I. Neitzel, U. Prüfert, and T. Slawig. Proceedings CD of the 2008 European COMSOL Conference, 2008.
5. 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.

Submitted Articles

1. Multigoal-oriented optimal control problems with nonlinear pde constraints. B. Endthmayer, U. L. I. Neitzel, T. Wick, and W. Wollner. Technical Report SPP1962-108, SPP 1962, 2019.
2. Finite element error estimates for elliptic optimal control by bv functions. D. Hafemeyer, F. Mannel, I. Neitzel, and B. Vexler. Technical Report arXiv:1902.05893, Arxiv, 2019.
3. A lagrange multiplier method for semilinear elliptic state constrained optimal control problems. V. Karl, I. Neitzel, and D. Wachsmuth. Technical Report SPP1962-087, SPP 1962, 2018.
4. A sparse control approach to optimal sensor placement in pde-constrained parameter estimation problems. I. Neitzel, K. Pieper, B. Vexler, and D. Walter. Technical Report IGDK-2018-07, IGDK 1754, 2018.
5. An optimal control problem governed by a regularized phase-field fracture propagation model. Part II the regularization limit. I. Neitzel, T. Wick, and W. Wollner. Technical Report SPP1962-91, SPP 1962, 2018.