Parameter Identification in Models With Sharp Phase Transitions

Description

The aim of this project is the analysis of and development of algorithms for parameter identification problems where the solution of the forward problem exhibits multiple structurally different phases. Such problems occur in climatology (cloud nucleation, glacial melting), material science (crystal growth, steel annealing) and mechanics (contact, defect mechanics) and can be modeled as variational inequalities or partial differential equations involving non-smooth nonlinearities. A common feature of such models is that the solution operator is nonlinear and non-differentiable, making classical analytical and numerical approaches that rely on local linearization inapplicable. Our goal is therefore to derive error estimates and to develop new iterative algorithms for parameter estimation problems for a class of partial differential equations involving non-smooth but Lipschitz continuous and directionally differentiable nonlinearities such as those appearing in the two-phase Stefan problem.

Publications

Constantin Christof, Christian Clason, Christian Meyer, Stephan Walther: Optimal Control of a Non-smooth Semilinear Elliptic Equation, Mathematical Control and Related Fields, 8(1), pp. 247-276, 2018 (SPP1962-020).

Preprints

Christian Clason, Vu Huu Nhu, Arnd Rösch: Optimal Control of a Non-smooth Quasilinear Elliptic Equation (SPP1962-101, 12/2018, [bib])

Christian Clason, Yu Deng, Patrick Mehlitz, Uwe Prüfert: Optimal Control Problems with Control Complementarity Constraints (SPP1962-081, 10/2018, [bib])

Constantin Christof, Christian Clason, Christian Meyer, Stephan Walther: Optimal Control of a Non-smooth Semilinear Elliptic Equation (SPP1962-020, 05/2017, [bib])

Research Area

Modeling, problem analysis, algorithm design and convergence analysis

The focus of this area is on the development and analysis of genuinely non-smooth models in the sciences in order to properly capture real-world effects and to avoid comprising smoothing approaches. In simulation and optimization this requires to advance set-valued analysis and the design of robust algorithms for non-smooth problems.

Incorporation of parameter dependencies and robustness

In many applications the robustness of solutions with respect to a given parameter range (uncertainty set) is highly relevant. Correspondingly, in this research area of the SPP, bi- or multilevel optimization approaches will be studied in order to robustify problem solutions against uncertain parameters.

Members

  • member's portrait

    Prof. Christian Clason

    Universität Duisburg-Essen
    Principal Investigator
  • member's portrait

    Prof. Arnd Rösch

    Universität Duisburg-Essen
    Principal Investigator
  • member's portrait

    Dr. Hữu Nhự Vũ

    Universität Duisburg-Essen
    Research Assistant

Project Related News

  • Dec 11, 2018 : New preprint submitted

    Christian Clason submitted the preprint SPP1962-101, Optimal Control of a Non-smooth Quasilinear Elliptic Equation

  • Oct 09, 2018 : New preprint submitted

    Patrick Mehlitz submitted the preprint SPP1962-081, Optimal Control Problems with Control Complementarity Constraints