# Courses

The courses are particularly suitable for bachelor and master students of Computational Engineering (majoring in Electrical Engineering), Electrical Engineering and Information Technology (majoring in Computational Electrodynamics), and Mathematics (e.g. with minor subject Electrical Engineering).

# Fast Boundary Element Methods for Engineers

 How do we solve field problems numerically on the computer? The Boundary Element Method (BEM) has developed into an important alternative to domain-oriented approaches (like Finite Elements), ever since fast implementations of BEM became available. BEM reduces the dimensionality of the problem and can easily take into account unbounded domains.Starting from the representation formulas of Kirchhoff and Stratton-Chu, boundary integral equations are derived. Next, their discretization by collocation and Galerkin methods is discussed.The resulting fully populated matrices have to be compressed for practical applications, by either Fast Multipole or Adaptive Cross Approximation methods.Industrial applications of BEM are considered, for instance acoustic and electromagnetic scattering problems, and thermal analysis.Programming homework will be assigned, to deepen the students’ understanding. Number: 18-dg-2160-vl Lecturer: Prof. Dr.-Ing. Stefan Kurz Semester: Winter Language: English

# Electromagnetics and Differential Forms

 In recent years, the literature dealing with physical models in terms of differential forms (DF) has grown rapidly. For instance, DF allow a clear and elegant representation of electromagnetics. The operators grad, curl, and div of vector analysis are replaced by a single operator of the exterior derivative. Similarly, the integral theorems of Gauss and Stokes are replaced by a single integral theorem. Vector analysis is limited to three dimensions, while DF can be applied to any dimensions. This is useful for relativistic formulations in four dimensions.Because DF can be canonically integrated over appropriate domains, the forms lend themselves naturally to discretizations of the finite integration type.This lecture series provides an introduction to DF calculus, and its relation to vector analysis. Maxwell‘s equations and the constitutive relations are expressed in terms of DF, and the main steps into discretization are outlined briefly. Number: 18-dg-2030-vl Lecturer: Prof. Dr.-Ing. Stefan Kurz Semester: Summer Language: English