Course detail

Electromagnetic Field Modeling

FEKT-MKC-MEMAcad. year: 2022/2023

Principles of the finite element method and its application to different variants of electromagnetic fields. In the computer-based exercises, the possibilities and perspectives of the method are shown and practiced together with various application examples facilitating the computation of various types of electromagnetic fields (the static to optical frequency forms). In addition to the above mentioned elements, the students carry out the following tasks:
- practice in the ANSYS environment
- solution of more complex tasks by means of working input data
- direct solution of Maxwell’s equations via the method of finite differences in the time domain (FDTD)

Language of instruction


Number of ECTS credits


Mode of study

Not applicable.

Learning outcomes of the course unit

An overview will be provided of the principles characterizing the methods for numerical modelling of electromagnetic fields. On this basis, the students will be able to:
- explain the numerical modelling methods
- perform a numerical analysis of simpler problems related to the electrostatic field, the steady-state electric field in conductive materials, the magnetostatic and stationary magnetic fields, the vf electromagnetic field.
- set up a numerical model for combined coupled problems (electromechanical, electrothermal).


Students wishing to enroll in the course should be able to explain the basic notions and physical principles of electromagnetism, and they ought to have a basic understanding of the mathematical notation of partial differential equations. In the course-based discussions, the participants are expected to assess the consequences of electromagnetic principles and/or effects.


Not applicable.

Planned learning activities and teaching methods

The teaching methods include lectures and computer laboratories. Cource is taking advantage of e-learning system.
Student have to do compulsory ten projects/assignment in computer laboratories during the cource.

Assesment methods and criteria linked to learning outcomes

The students are required to produce 10 computer-based tasks during the semester. A task can be marked with max. 5 pts; thus, 50 pts in total can be won by a student in this portion of course work. Another grading component consists in the semester exam, for which the students can gain 50 pts.
The credits are awarded to students who actively participate in all tutorials (computer-based exercises), submit all assigned tasks, and win at least the minimum of 30 pts for the tasks submitted.
In order to successfully complete the course, a student is required to gain the credits before taking the semester exam, and the exam results must not be below 20 points.

Course curriculum

1) Elementary concepts related to the numerical modelling of fields. The physical, mathematical, and numerical model. Selected problems of vector analysis. Physical quantities describing the properties of the electromagnetic field. Maxwell’s equations.
2) Analysis of the electrostatic field. Properties of materials in the electrostatic field. Poisson’s and Laplace's equations. Elementary, analytical, and numerical methods of solving Poisson’s equation. Principles of superposition and reflection. Computation of induction fluxes, the energy in a system of electrodes, the actual and mutual capacity of the system of electrodes. Computation of electrostatic forces, trajectory of the moving charge.
3) Analysis of the electric field of steady-state currents; the form of Poisson’s equation. Computation of Joule losses; the transfer (ground) resistance of earthed electrodes; step voltage.
4) Formal analogies of physical fields and their significance for practical modelling. Coupled problems: conductor heating as a consequence of current conduction.
5) Application examples and possibilities in the finite element method (FEM). Elements for the two-dimensional or spatial discretization of the geometry of the assigned configuration. Principles and operation of FEM network generators. Shape and approximation functions; approximation examples.
6) Principles of the FEM. Discretization of one- and two-dimensional linear Poisson’s equation. Examples of deriving the coefficients of a system of equations for the numerical solution of the electrostatic problem. Discretization of non-linear, two-dimensional Poisson’s equation.
7) Analysis of the magnetic field by means of the scalar magnetic potential. The reduced, differential, and generalized scalar potential. Computation of magnetic forces in a circuit having a permanent magnet and an air gap. Shielding of magnetostatic fields.
8) Analysis of the magnetic field using a vector potential. Voltage-excited coil field; coil field excited by an electronic circuit. Computation of the actual and mutual inductance of coils.
9) Analysis of harmonically variable fields. Eddy currents. Shielding of alternating magnetic fields. Current conductor located in the stator slot. Conducting cylinder and sphere in a harmonically variable magnetic field. Skineffect.
10) Analysis of high-frequency electromagnetic fields in waveguides and resonators. Computation of the radiation diagram; computation of the near and radiation fields of a dipole antenna. Computation of the peripheral parameters of an hf apparatus. Propagation of waves in free space; radiation and diffraction.
11) Principles of the method of finite differences and conditions for its practical use. Principle and application of the FDTD method.

Work placements

Not applicable.


Introduce the students to elementary numerical methods for the computation of electromagnetic fields. Use various field calculation programs as an instrument enabling the students to design their own simple programs based on the ANSYS system.

Specification of controlled education, way of implementation and compensation for absences

The controlled instruction and methods of its realization are stipulated within the yearly directive issued by the guarantor of the subject.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Basic literature

Dědek L., Dědková, J.: Elektromagnetismus. Skripta, VUTIUM, Brno 2000 (CS)
Haňka, L.: Teorie elektromagnetického pole, Praha, SNTL, 1982. (CS)
Dědková, J., Kříž T.: Modelování elektromagnetických polí. Skripta, VUTIUM, Brno 2012. (CS)

Recommended reading

Hesthaven, J. S., Rozza, G., & Stamm, B. (2015). Certified reduced basis methods for parametrized partial differential equations. Certified reduced basis methods for parametrized partial differential equations (pp. 1-131) doi:10.1007/978-3-319-22470-1 Hesthaven, J. S., Rozza, G., & Stamm, B. (2015). Certified reduced basis methods for parametrized partial differential equations. Certified reduced basis methods for parametrized partial differential equations (pp. 1-131) doi:10.1007/978-3-319-22470-1 (EN)

Classification of course in study plans

  • Programme MKC-SVE Master's, 1. year of study, summer semester, compulsory-optional

Type of course unit



26 hours, compulsory

Teacher / Lecturer


Basic information about the ability and examples of application of the finite element method (FEM).
Elements, shape and approximation functions, examples of approximation.
Principle of the finite element mesh generators and their handling.
Discretization of 1D and 2D linear Poisson equation.
Discretization of 2D non-linear Poisson equation.
Basic equations of the electromagnetic field and different potentials.
Reduced, differential and general scalar potential method for the magnetic field.
Time dependent field solution by FEM.
Principles and reason for the introduction of the edge elements.
Solution of Maxwell equations in the frequency domain. Examples: waveguides, antennas.
Direct solution of the Maxwell equations by the FDTD method

Exercise in computer lab

26 hours, compulsory

Teacher / Lecturer


Program ANSYS - introduction.
Electric field modelling by the ANSYS program
2D magnetic circuit modelling by the ANSYS program
3D transformer magnetic field model by ANSYS.
Waveguide field models by ANSYS.
Model of shielding by ANSYS.
Application of the FEM system in the MATLAB environment.
Field calculation by the FEM system in the MATLAB.
Electric field in the switching station by the charge simulation method.
Wave diffraction on a cylinder by a FDTD program.