Numerical analysis of the Maxwell–Landau–Lifshitz–Gilbert system

In the Maxwell–Landau–Lifshitz–Gilbert system, the Maxwell equations in the three-dimensional unbounded space are coupled with the Landau–Lifshitz–Gilbert equation on a bounded domain. The resulting numerical challenges were solved using a coupling of the finite element method (FEM) with the boundary element method (BEM) via convolution quadrature. The implementation was done during the doctoral thesis The Maxwell–Landau–Lifshitz–Gilbert System: Mathematical Theory and Numerical Approximation of Jan Bohn and realized using the softwares Fenics and Bempp in Python.

Further details are provided in the paper FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation.

Code on Github

used together with Python3, Fenics 2019.1.0, and Bempp-cl 0.2.0

• https://github.com/janbohn/MLLGfirstorder
• https://github.com/janbohn/MLLGsecondorder
• https://github.com/janbohn/Maxwellfirstorder
• https://github.com/janbohn/AdaptiveLLG