Electromagnetic shielding is a physical process of redirecting or blocking electromagnetic fields by means of obstacles made of  magnetic or conducting materials. In the context of electrostatic shielding, it was first discovered by Faraday in 1836, who experimentally verified that a conductive enclosure is able to eliminate the effect of an electrostatic field by cancelling it out and leaving the zero field in the interior. 

Our research project focuses on a Maxwell obstacle model for electromagnetic shielding phenomena as follows: In the free region, the electromagnetic fields satisfy the fundamental Maxwell equations, whereas in the shielded area obstacle constraints are applied to the electromagnetic fields. The aim of this project includes the analysis, numerics, and optimal shape design in Maxwell obstacle problems.

This project is supported by the DFG research grant YO 159/4-1.

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

Maurice Hensel and Irwin Yousept: Numerical Analysis for Maxwell Obstacle Problems in Electric Shielding [PDF] SIAM Journal on Numerical Analysis 60(3), 1083-1110, 2022

Maurice Hensel and Irwin Yousept: Eddy Current Approximation in Maxwell Obstacle Problems [PDF] Interfaces and Free Boundaries, 25, no. 1, 1–36, 2023

Gabrielle Caselli, Maurice Hensel, Irwin Yousept: Quasilinear Variational Inequalities in Ferromagnetic Shielding: Well-Posedness, Regularity, and Optimal Control [PDF] SIAM Journal on Control and Optimization 61:4, 2043-2068, 2023