Course detail

Numerical Simulations in Physics

FSI-TFS Acad. year: 2025/2026 Summer semester

The course deals with the modeling of physical problems on the computer. It is focused on field calculations using the COMSOL Multiphysics program. Emphasised is the implementation of the physical problem the choice of boundary conditions, the determination of the accuracy of the achieved results and the visualization of the simulation.

Language of instruction

Czech

Number of ECTS credits

4

Supervisor

Ing. Jakub Zlámal, Ph.D.

Department

Institute of Physical Engineering

Entry knowledge

Knowledge of physics on the level defined by the textbook HALLIDAY, D. – RESNICK, R. – WALKER, J.: Fundamentals of Physics. J. Wiley and Sons.

Rules for evaluation and completion of the course

The report on the solution of the selected physical problem is evaluated.


Compulsory participation at tutorials, report with solution of project.

Aims

The goal of the course is to teach students to use modern software to calculate physical problems, to understand what simplifications (geometry, physics) can be made in the calculation. Emphasis is placed on the verification of the obtained results and their interpretation.


Gaining practice in solving physics problems on the computer. Familiarization with the method of entering the problem, verifying the correctness of the results and their further use.

The study programmes with the given course

Programme N-FIN-P: Physical Engineering and Nanotechnology, Master's, compulsory

Programme B-FIN-P: Physical Engineering and Nanotechnology, Bachelor's, compulsory

Type of course unit

 

Lecture

13 hours, optionally

Syllabus


  1. Fundamentals of numerical solution of partial differential equations. Finite elements method, finite differences method, boundary elements method. Software overview.

  2. Verification of the accuracy of calculations – use of Gauss's, Ampere's integral laws. Effect of geometric tolerances on the result – estimation of uncertainty during experimental verification of calculations.

  3. Static electric and magnetic fields. Scalar and vector potential.

  4. Magnetization curve, magnetization, magnetic dipole moment.

  5. Elasticity.

  6. Eigenvalues and eigenfunctions. Q-factor, resonance

  7. Heat transfer. Conduction, radiation. Solving multiphysics problems.

  8. Implementation of custom physics equations in COMSOL Multiphysics.

  9. Solving Maxwell's equations. Electromagnetic wave at the interface of materials.

  10. Scattering of light at a structured interface.

  11. Project consultation.

  12. Project consultation.

  13. Presentation of projects.

Computer-assisted exercise

26 hours, compulsory

Syllabus


  1. Introduction to the COMSOL Multiphysics program. Solution of plate capacitor – 1D, 2D and 3D. Determining the capacitance of a capacitor. Point charge field. Electric induction vector flux, Gauss's law of electrostatics. Electric field shielding.

  2. Child-Langmuir law – space charge field. Discretization order, mesh density, solution convergence. Comparison of the results with the analytical solution

  3. Boundary conditions and their effect on the solution. Use of symmetry. Magnetic field of coil, inductance.

  4. Permanent magnet field. Comparison with the analytical solution of the magnetic dipole field. Magnetic flux.

  5. Permanent nonlinear magnet. Demagnetization

  6. Electric currents, Joule heat. Multiphysics simulation. Hall effect.

  7. Oscillation of the beam – own frequency and own function.

  8. Tuning fork as detector in AFM. Q factor, external force, linearization of Lenard-Jones potential.

  9. Implementation of the solver of differential equations. PN junction, IV curve.

  10. Reflection and refraction of a plane wave at an interface. Fresnel coefficients, polarization of light.

  11. Scattering of light at a structured interface.ns.

  12. Work on the chosen project.

  13. Presentation of projects.