Optimization of Non-smooth Hyperbolic Maxwell's Equations in Type-II Superconductivity Based on the Bean Critical State Model

Description

The goal of the project is to develop theoretical foundations and efficient finite element methods for the optimization of electromagnetic processes in type-II superconductivity. The optimization problem is to find an optimal applied current density, which steers the electromagnetic fields to the desired ones in the presence of a type-II superconductor. The governing PDE system for the electromagnetic fields consists of full time-dependent Maxwell's equations with a non-smooth constitutive law between the electric field and the current density. This non-smooth relation goes back to the Bean critical state model, which describes the irreversible magnetization process in type-II superconductivity. Altogether, it leads to an optimization problem governed by non-smooth hyperbolic evolution Maxwell's equation: The project addresses the mathematical and numerical analysis of the non-smooth PDE-constrained optimization problem, including the derivation of first-order necessary optimality conditions and the development of efficient finite element methods with a priori error estimates.

Publications

Irwin Yousept: Optimal Control of Non-Smooth Hyperbolic Evolution Maxwell Equations in Type-II Superconductivity, SIAM Journal on Control and Optimization 55(4), 2305 - 2332, 2017

Irwin Yousept: Hyperbolic Maxwell Variational Inequalities for Bean's Critical-State Model in Type-II Superconductivity, SIAM Journal on Numerical Analysis 55(5), 2444 - 2464, 2017

Irwin Yousept, Jun Zou: Edge Element Method for Optimal Control of Stationary Maxwell System with Gauss law , SIAM J. Numer. Anal., 55(6), 2787 - 2810, 2017

Livia Susu: Optimal Control of a Viscous Two-Field Gradient Damage Model, GAMM-Mitt. 40, 2018

Preprints

Livia Betz: Strong Stationarity for Optimal Control of a Non-smooth Coupled System: Application to a Viscous Evolutionary VI Coupled with an Elliptic PDE (SPP1962-083, 10/2018, [bib])

Irwin Yousept: Hyperbolic Maxwell Variational Inequalities of the Second Kind (SPP1962-069, 08/2018, [bib])

Livia Betz, Irwin Yousept: Optimal Control of Elliptic Variational Inequalities with Bounded and Unbounded Operators (SPP1962-068, 08/2018, [bib])

Livia Susu: Optimal Control of a Viscous Two-Field Gradient Damage Model (SPP1962-067, 07/2018, [bib])

De-Han Chen, Irwin Yousept: Variational Source Condition for Ill-Posed Backward Nonlinear Maxwell's Equations (SPP1962-064, 07/2018, [bib])

Malte Winckler, Irwin Yousept: Fully Discrete Scheme for Bean's Critical-State Model with Temperature Effects in Superconductivity (SPP1962-065, 07/2018, [bib])

Livia Betz: Second-Order Sufficient Optimality Conditions for Optimal Control of Non-Smooth, Semilinear Parabolic Equations (SPP1962-062, 06/2018, [bib])

Irwin Yousept, Jun Zou: Edge Element Method for Optimal Control of Stationary Maxwell System With Gauss' Law (SPP1962-042, 11/2017, [bib])

Irwin Yousept: Optimal Control of Non-smooth Hyperbolic Evolution Maxwell Equations in Type-II Superconductivity (SPP1962-021, 06/2017, [bib])

Irwin Yousept: Hyperbolic Maxwell Variational Inequalities for Bean’s Critical-state Model in Type-II Superconductivity (SPP1962-022, 06/2017, [bib])

Members

  • member's portrait

    Prof. Irwin Yousept

    Universität Duisburg-Essen
    Principal Investigator
  • member's portrait

    Dr. Livia Betz

    Universität Duisburg-Essen
    Research Assistant

Project Related News

  • Aug 22, 2018 : New preprint submitted

    Irwin Yousept submitted the preprint SPP1962-069, Hyperbolic Maxwell Variational Inequalities of the Second Kind

  • Oct 11, 2018 : New preprint submitted

    Livia Betz submitted the preprint SPP1962-083, Strong Stationarity for Optimal Control of a Non-smooth Coupled System: Application to a Viscous Evolutionary VI Coupled with an Elliptic PDE