Gurantor department | Department of Applied Mathematics | Credits | 6 |

Subject guarantor | doc. Ing. Dalibor Lukáš, Ph.D. | Subject version guarantor | doc. Ing. Dalibor Lukáš, Ph.D. |

Study level | undergraduate or graduate | Requirement | Optional |

Year | 2 | Semester | winter |

Study language | Czech | ||

Year of introduction | 2010/2011 | Year of cancellation | |

Intended for the faculties | FEI | Intended for study types | Follow-up Master |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

LUK76 | doc. Ing. Dalibor Lukáš, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

Part-time | Credit and Examination | 10+10 |

The course aims at teaching of mathematical models of electromagnetic fields and their solution using state-of-the-art
numerical methods. At benchmarks we will demonstrate solution to electrostatics, magnetostatics, and electromagnetic
scattering. In particular, we emphasize the principles of the finite element method (FEM) as well as the boundary
element method (BEM), their efficient usage and a coupling of both.

Lectures

Tutorials

Project work

Topics covered:
1. Electrostatics - physics, a 2d benchmark, nodal FEM, BEM.
2. Magnetostatics - physics, a 3d benchmark, edge FEM, FEM-BEM coupling.
3. Electromagnetic scattering - physics, a 3d benchmark, FEM with an absorption layer, BEM.

M. Křížek - Mathematical and Numerical Modelling in Electrical Engineering. Kluwer Academic Publishers 1996.
J. Schoeberl - Numerical Methods for Maxwell's Equations. Lecture Notes of Kepler University in Linz, 2005.

P. Monk - Finite Element Methods for Maxwell's Equations. Oxford University Press, 2003.
O. Steinbach, S. Rjasanow - The Fast Solution of Boundary Integral Equations. Springer 2007.

Credit: 30 points (a project), min. 15
Exam: 70 points

No additional requirements are imposed on the student.

Subject has no prerequisities.

Subject has no co-requisities.

Lectures:
1. Principles of electromagnetism - charge interations.
2. Principles of electromagnetism - electric current, conductor interactions, magnetism.
3. Principles of electromagnetism - Maxwell's equations.
4. Analytical solutions to simple problems.
5. Electrostatics - electrostatic field of a capacitor.
6. Electrostatics - variational formulations, numerical solutions by a finite element method (FEM).
7. Electrostatics - boundary integral equations.
8. Electrostatics - boundary element method (BEM).
9. Magnetostatics - magnetostatic field of an electromagnet.
10. Magnetostatics - numerical solutions by FEM.
11. Magnetostatics - numerical solutions by BEM.
12. Magnetostatics - FEM-BEM coupling.
13. Electromagnetic scattering - a polarized light scattered from a slot.
14. Electromagnetic scattering - BEM for the 3D Helmholtz equation.
Exercises:
1. Principles of electromagnetism - charge interations.
2. Principles of electromagnetism - electric current, conductor interactions, magnetism.
3. Principles of electromagnetism - Maxwell's equations.
4. Analytical solutions to simple problems.
5. Electrostatics - electrostatic field of a capacitor.
6. Electrostatics - variational formulations, numerical solutions by a finite element method (FEM).
7. Electrostatics - boundary integral equations.
8. Electrostatics - boundary element method (BEM).
9. Magnetostatics - magnetostatic field of an electromagnet.
10. Magnetostatics - numerical solutions by FEM.
11. Magnetostatics - numerical solutions by BEM.
12. Magnetostatics - FEM-BEM coupling.
13. Electromagnetic scattering - a polarized light scattered from a slot.
14. Electromagnetic scattering - BEM for the 3D Helmholtz equation.
Projects:
BEM for 2d electrostatics.
FEM for 3d magnetostatics.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points | Max. počet pokusů |
---|---|---|---|---|

Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 | |

Exercises evaluation | Credit | 30 | 15 | |

Examination | Examination | 70 | 21 | 3 |

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Conditions for subject completion and attendance at the exercises within ISP: Completion of all mandatory tasks within individually agreed deadlines.

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Academic year | Programme | Branch/spec. | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2020/2021 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2020/2021 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2019/2020 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2019/2020 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2018/2019 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2018/2019 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2017/2018 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2017/2018 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2016/2017 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2016/2017 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2015/2016 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2015/2016 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2014/2015 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2014/2015 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2013/2014 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2013/2014 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2012/2013 | (N3942) Nanotechnology | (3942T001) Nanotechnology | P | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2012/2013 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2012/2013 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2011/2012 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2011/2012 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2011/2012 | (N3942) Nanotechnology | (3942T001) Nanotechnology | P | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2010/2011 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2010/2011 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2010/2011 | (N3942) Nanotechnology | (3942T001) Nanotechnology | P | Czech | Ostrava | 1 | Choice-compulsory | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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2013/2014 Winter |