Due to their high sensitivity, magnetoelectric (ME) sensors consisting of multiferroic composite materials have wide application areas, mainly focusing on the medical field, e.g. for measuring biomagnetic signals in the diagnostics of human brain or heart functions. These ME are based on composites with magnetostrictive and piezoelectric layers that are usually accompanied by a layer of substrate, made of e.g. silicon or steel. The modeling and simulation of such ME composite structures is particularly challenging as it involves partial differential equations that couple the electric, magnetic and mechanical fields.
The master thesis aims at extending already existing mathematical models to include the piezoelectric effect and simulating the resulting PDEs with the open-source solver GEOPDEs, which uses Isogeometric Analysis (IGA), a generalization of the Finite Element Method (FEM) based on splines that enables exact geometry description.