Multi-Physics Phenomena in High-Temperature Superconductivity: Analysis, Numerics and Optimization


The physical phenomena of temperature-dependent critical current density and hysteresis losses in high-temperature superconductivity (HTS) lead to a complex multi-physics HTS-system with a two-way nonlinear electromagnetic and thermal coupling. In particular, the coupled problem features a non-smooth character stemming from the governing hyperbolic Maxwell variational inequality for the electromagnetic fields and the governing non-smooth parabolic equation for the temperature distribution. The goal of the reseach project is to develop mathematical and numerical methods for the multi-physics coupled HTS-system with three main aims: First, we shall analyze the existence and uniqueness of solutions by means of the convergence and stability analysis of the implicit Euler method in combination with the Stampacchia method and Fixpoint approaches. Second, we aim at developing and analyzing a semi-smooth Newton algorithm in function spaces and an adaptive mesh refinement strategy on the basis of a residual-type a posteriori error analysis. Finally, based on the achieved mathematical results, we shall investigate the optimal control of the corresponding time-discrete HTS-system with the aim to derive necessary optimality conditions in the form of Pontryagin's maximum principle.


De-Han Chen, Irwin Yousept: Variational Source Conditions in $L^p$-spaces, SIAM J. Math. Anal., 53(3), 2863--2889, 2021.

Yuri F. Albuquerque, Antoine Laurain, Irwin Yousept: Level Set-Based Shape Optimization Approach for Sharp-Interface Reconstructions in Time-Domain Full Waveform Inversion, SIAM J. Appl. Math., 81(3), 939--964, 2021.

Agnes Lamacz-Keymling, Irwin Yousept: High-order homogenization in optimal control by the Bloch wave method , ESAIM: COCV 27 (2021) 100 , 2021.

Irwin Yousept: Maxwell quasi-variational inequalities in superconductivity, ESAIM: M2AN 55 (2021) 1545-1568 , 2021.

De-Han Chen, Bernd Hofmann, Irwin Yousept: Oversmoothing Tikhonov regularization in Banach spaces, Inverse Problems 37 (2021) 085007, 2021.

Antoine Laurain, Malte Winckler, Irwin Yousept: Shape Optimization for Superconductors Governed by H(Curl)-Elliptic Variational Inequalities, SIAM Journal on Control and Optimization Analysis 59(3), pp. 2247--2272, 2021, 2021 (SPP1962-127).

Kei Fong Lam, Irwin Yousept: Consistency of a Phase Field Regularisation for an Inverse Problem Governed by a Quasilinear Maxwell System , Inverse Problems 36 045011, 2020.

Malte Winckler, Irwin Yousept, Jun Zou: Adaptive Edge Element Approximation for H(curl) Elliptic Variational Inequalities of Second Kind, SIAM Journal on Numerical Analysis 58(3): 1941-1964, 2020.

Irwin Yousept: Hyperbolic Maxwell Variational Inequalities of the Second Kind , ESAIM: COCV 26, Paper No. 34, 2020.

Irwin Yousept: Well-posedness theory for electromagnetic obstacle problems. , Journal of Differential Equations 269(10): 8855--8881, 2020.


Antoine Laurain, Malte Winckler, Irwin Yousept: Shape Optimization for Superconductors Governed by H(Curl)-Elliptic Variational Inequalities (SPP1962-127, 11/2019, [bib])


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