Maxwell Obstacle Problems in Electromagnetic Shielding: Numerical Analysis, Shape Design and Nonlinear Permeability

• Applicant: Professor Dr. Irwin Yousept
• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 455353159

Maxwell obstacle problems describe the physical processes of electromagnetic shielding to redirect or block electromagnetic waves through barriers made of magnetic or conductive materials. In the case of magnetic shielding by ferromagnetic materials, the PDE-model considers a nonlinear magnetic permeability posing a particular challenge due to the resulting quasilinear structure in the governing differential operator. Such a nonlinear phenomenon is confirmed through physical experiments and measurements of the B-H-curve. This project aims therefore at developing mathematical foundations for hyperbolic Maxwell obstacle problems motivated by electromagnetic shielding applications. Our first goal is to establish and analyze efficient numerical solutions based on the leapfrog time-stepping method. The second focus is set on the theoretical and numerical studies of shape design in electromagnetic shielding through a rigorous shape sensitivity analysis. The final and ultimate goal is the mathematical analysis for the hyperbolic Maxwell obstacle problem in the quasilinear case. We examine the existence and uniqueness of solutions under a suitable magnetic vector potential formulation based on the underlying mathematical properties of the nonlinear magnetic permeability.

• DFG Programme: Research Grants
• International Connection: Brazil
• Cooperation Partner: Professor Antoine Laurain, Ph.D.