English

Not applicable.

Student acquires theoretical knowledge as well as skills in practical application of the FEM and FDM, processing the input of the numerical models and their application together with the ability to solve forward, inverse, macroscopic, microscopic, stochastic tasks independently.

Mathematical calculus, Physics, Electromagnetism on the level of MSc, numerical modeling.

Not applicable.

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations. Teaching methods include lectures combined with seminars. Course is taking advantage of e-learning.

Total number of points 100. Discussion on the topic of the study.

Introduction to Functional Analysis, Differential Operators, Overview of Partial Differential Equations, Boundary and Initial Conditions.
Finite Difference Method (MKD). Finite Element Method (FEM) - Introduction. Discretization of the area to the finite elements. Approximation of fields from
the nodal or edge values.
Forward problem. Setup of equations for nodal and edge values by the Galerkin method.
Application of Galerkin's method to static and quasi-static fields (Poisson and Helmholtz equations).
The coupling of MKP and MKD for time-domain variables (diffusion and wave equations). Coupling field equations with circuits described with concentrated parameters, non-stationary time and frequency domains.
Coupled problems, models with respect the theory of relativity, stochastic models.
Field optimization tasks. Overview of deterministic methods. Local and global optimum.
Unconstrained problems – gradient method, method of the steepest descent, Newton’s methods, stochastic models, magnetohydrodynamics, and relativistic approach to model description.
Stochastic modeling in conjunction with FEM, microscopic approach to FEM application, NANO-geometry, models, effects, phenomena.
Inverse tasks for elliptical equations. The smallest square method. Deterministic regularization methods, Survey of Layer Set Methods for inverse tasks and
optimal design.
Using inverse tasks in tomography.
Methods and models of modeling of atomic and subatomic levels, nanoelectronics, periodic structures, structural modeling, photonics, biophotonics.
Note: Practical examples using the ANSYS, HFSS and MATLAB environment will be a part of each point of the curriculum.

Not applicable.

To understand the fundamentals of the PDE numerical solution for application in electrical engineering.
Get acquainted with new applications using FEM and FDM in optimization and inverse tasks.

The content and forms of instruction in the evaluated course are specified by the lecturer responsible for the course. It is advisable for the student to have a written assignment processed.

Numerical modeling courses using ANSYS Classic, ANSYS Maxwell, ANSYS HFSS.

Not applicable.

Bossavit Alain.: Computational Electromagnetism – Variational formulations, complementarity, edge elements. Academic Press, 1998 (EN)
Dědek, L., Dědková J.: Elektromagnetismus. Skripta VUTIUM Brno, 2000 (CS)
Chari, M, V. K., Salon S. J.: Numerical Methods in Electromagnetism. Academic Press, 2000 (EN)
Rektorys Karel: Přehled užité matematiky I, II. Prometheus, 1995 (CS)
Sadiku Mathew: Electromagnetics (second edition), CRC Press, 2001 (EN)

IEEE Transactions on Magnetics, ročník 1996 a výše (EN)
SIAM Journal on Control and Optimization, ročník 1996 a výše (EN)