My research focuses on the mathematical modeling, analysis and simulation of magnetoelastic coupling phenomena, which occur in so-called “magnetostrictive” materials. The main emphasis is on the derivation, analysis and solution of systems of coupled PDEs including the equations of elasticity and Maxwell's equations. Magnetostrictive materials have wide application areas: they are often used as sensors or actuators in mechanical systems or as artificial muscles in robotics. Our current eld of research in which multiphysics is relevant (coupling of electromagnetic, thermal and mechanical fields) is the development of high-temperature superconducting magnets for particle accelerators. Unlike conventional magnets, the high-current coils of superconducting magnets are exposed to massive Lorentz forces, which can lead to significant deformations within the structures. These deformations, on the other hand, can change the structure of the magnets and have a negative effect on the quality of the magnetic eld as well as the homogeneity of the temperature eld. From the modeling point of view, a coupled multi- eld problem arises, whose mathematical formalization, analysis and solution is essential for the study of the functionality, robustness and lifetime of the construction.