Structure-preserving Finite Elements for Computational Electromagnetism

What it is about

In this module you will learn finite-element methods that preserve the underlying geometric and functional structure of electromagnetic problems. By the end you will be able to analyse the well-posedness of typical Maxwell model problems and apply stable, structure-preserving FEM approximations on geometrically non-trivial domains.

What you will be able to do

• Understanding of the de-Rham complexes and Hodge-Helmholtz decompositions
• Analysis of the well-posedness of Poisson, magnetostatic, and time-harmonic Maxwell problems
• Construction and properties of structure-preserving Finite-Element discretisations
• Assessment of discrete well-posedness and convergence of FEM approximations
• Application of spline-based, structure-preserving Finite Elements (including multipatch and non-smooth spaces)
• Reading and presenting research literature on structure-preserving methods
• Practical application with a Python-FEM library

What the module consists of

• VorlesungDelivery of theoretical foundations (de Rham complexes, Hodge-Helmholtz, Hodge-Laplace, Maxwell)
• Übung/KlassenCalculation examples, FEM implementation and application with Python
• Gruppenarbeit/Reading GroupsFrom the 7th session, student groups work on research articles and present them

Teaching method

• VorlesungenIntroduction and systematic presentation of the theory
• Übungs- und ProgrammierklassenPractice of FEM techniques and practical implementation in Python
• Kleingruppen-Lektüre mit PräsentationenDeepening through reading and presenting current research results