Optimal Control of Variational Inequalities of the Second Kind with Application to Yield Stress Fluids

Description

The project is concerned with the optimal control of variational inequalities of the second kind involving a non-differentiable norm of first derivatives as characteristic non-smooth feature. Such kind of variational inequalities arise in the modeling of yield stress fluids as for instance Bingham fluids. Within this project we focus on Bingham fluids in their stationary form. The simulation of such non-smooth fluid flows is frequently based on regularization techniques and the same holds for their optimization. In order to avoid an associated regularization error, the aim of our project is to optimally control yield stress fluid flows with minimal, respectively, without any regularization. The project addresses theoretical and numerical aspects. First we investigate the limited differentiability properties of the solution operator associated with the variational inequality. Based on these findings, necessary and sufficient optimality conditions are derived in the analytical part of the project. Concerning the numerical component of the project, the differentiability results are used to design a mesh-independent trust-region algorithm in function space for the solution of the optimal control problem. This algorithm will be realized with the in-house flow simulation package FEATFLOW in order to solve application-driven benchmark problems.

Publications

No publications from this project yet.

Preprints

Constantin Christof: Sensitivity Analysis and Optimal Control of Obstacle-type Evolution Variational Inequalities (SPP1962-055, 04/2018, [bib])

Constantin Christof, Juan Carlos de los Reyes, Christian Meyer: A Non-smooth Trust-region Method for Locally Lipschitz Functions with Application to Optimization Problems Constrained by Variational Inequalities (SPP1962-051, 02/2018, [bib])

Constantin Christof, Gerd Wachsmuth: Differential Sensitivity Analysis of Variational Inequalities with Locally Lipschitz Continuous Solution Operators (SPP1962-039, 11/2017, [bib])

Constantin Christof, Gerd Wachsmuth: On the Non-Polyhedricity of Sets with Upper and Lower Bounds in Dual Spaces (SPP1962-031, 08/2017, [bib])

Constantin Christof, Gerd Wachsmuth: No-Gap Second-Order Conditions via a Directional Curvature Functional (SPP1962-026, 07/2017, [bib])

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

Constantin Christof, Christian Meyer: Sensitivity Analysis for a Class of $H^1_0$-Elliptic Variational Inequalities of the Second Kind (SPP1962-012, 03/2017, [bib])

Research Area

Members

  • member's portrait

    Prof. Christian Meyer

    Technische Universität Dortmund
    Principal Investigator
  • member's portrait

    Prof. Ben Schweizer

    Technische Universität Dortmund
    Principal Investigator
  • member's portrait

    Prof. Stefan Turek

    Technische Universität Dortmund
    Principal Investigator
  • member's portrait

    Constantin Christof

    Technische Universität Dortmund
    Research Assistant
  • member's portrait

    Arooj Fatima

    Technische Universität Dortmund
    Research Assistant

Project Related News

  • Oct 10, 2016 : Welcome to our new project member

    Constantin Christof joins project 16.

  • Oct 10, 2016 : Welcome to our new project member

    Arooj Fatima joins project 16.

  • Feb 15, 2018 : New preprint submitted

    Christian Meyer submitted the Preprint SPP1962-051, A Non-smooth Trust-region Method for Locally Lipschitz Functions with Application to Optimization Problems Constrained by Variational Inequalities