## Computational and Analytical Methods in Electromagnetics

Lecturer (assistant) 0000001890 5 SWS Wintersemester 2019/20 English See TUMonline See TUMonline

### Objectives

At the end of the module students understand advanced computational and analytical methods for the solution of electromagnetic field problems. They are able to apply these methods to develop field solutions for modified geometrical and material configurations within the scope of the methods. They understand the relationship and the mutual utilization of mathematical and physical considerations in order to develop field solutions of practical relevance. They understand the importance of analytical concepts for the development of advanced numerical methods in electromagnetics.

### Description

1) Mathematical and physical basics - Maxwells Equations - Boundary conditions - Vector spaces - Distributions and complex analysis - Uniqueness of field solutions - Green's functions - Radiation of electromagnetic sources - Huygens' principle 2) Numerical solvers - Finite-difference method - Finite-difference time-domain method - Finite element method - Integral equation method - Method of moments 3) Field solutions by Green's functions - Orthogonal series representations of Green's functions - Solution of the Laplace-/Helmholtz equation in Cartesian cylindrical and spherical coordinates - Surface and volume integral equation formulations of radiation and scattering problems 4) Vector wave solutions in Cartesian and spherical coordinates - Mie series solutions - Dyadic Green's functions in planar multilayered media - Spectral domain immitance approach - Transmission line representation - Sommerfeld integral representation - Michalski's mixed potential representation - Dipole over a halfspace (earth) 5) Basics of Variational Calculus - Functional formulation of field solutions - First variation of functionals - Stationary field representations - Direct solution of variational problems - Rayleigh-Ritz procedure - Finite element method

### Prerequisites

- Mathematics - Electrodynamics The successful participation in the following modules is recommended: - Technische Felder und Wellen

### Teaching and learning methods

Teaching method: During the lectures students are instructed in a teacher-centered style. The tutorials are held in a student-centered style. The students are expected to give tutorials themselves. Learning method: In addition to the individual methods of the students, consolidated knowledge is aspired by repeated lessons in excercises and tutorials. The following types os media will be used: - PowerPoint Presentations - Printed lecture notes - Tutorial problems with sample solutions - Project tasks with presentations