Czech

4

doc. Ing. Jakub Zlámal, Ph.D.

Institute of Physical Engineering

Basic knowledge of physics at the bachelor’s level, particularly in mechanics, electricity and magnetism, thermodynamics, and wave phenomena. Basic knowledge of the mathematical methods used in physics, particularly differential and integral calculus and the fundamentals of differential equations.

Students should be able to formulate a physical problem using basic physical laws, work with physical quantities and their units, and interpret the results of physical calculations.

Basic computer literacy. Prior knowledge of COMSOL Multiphysics is not required.

The course is completed with course credit. The requirements for obtaining the credit are regular and active participation in the required practical classes and the successful preparation and submission of a report on the independent solution of a selected physical problem.

The report must include a formulation and physical justification of the problem being solved, a description of the numerical model used, the selected boundary conditions and other relevant parameters of the calculation, the simulation results, an assessment of their accuracy, and verification of the results using an appropriate analytical or physical approach. The report must also include an interpretation of the results obtained.

The report is assessed primarily with regard to the correctness of the physical model, the suitability of the selected boundary conditions and numerical approach, the verification and critical assessment of the results, and the quality of their interpretation and documentation.

If the requirements are not met, the report may be returned for completion or revision.

Upon completion of the course, the student will be able to:

• Explain the basic principles of the numerical solution of physical problems described by partial differential equations and the principles of the finite element method.

• Develop a numerical model of a selected physical problem and appropriately define its geometry, physical model, material parameters, and boundary conditions.

• Apply an appropriate numerical procedure to solve a physical problem using COMSOL Multiphysics.

• Assess the influence of discretization, mesh density, geometry, and boundary conditions on the accuracy of the numerical solution.

• Verify the correctness and accuracy of the obtained results using an analytical solution, integral laws, or another appropriate physical verification method.

• Analyze and interpret the results of a numerical simulation and assess the significance of the simplifications used.

• Create a clear visualization of the results of a numerical calculation.

• Independently design and carry out a numerical simulation of a selected physical problem and professionally document its results.

Study materials and resources for the course are available in the course’s e-learning environment. The materials include, in particular, lecture and practical-class materials, assignments for the problems to be solved, materials for working with COMSOL Multiphysics, and instructions for the independent project.

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

26 hours, compulsory

1. 
   

   Introduction to COMSOL Multiphysics. Modeling the electric field of a parallel-plate capacitor in 1D, 2D, and 3D. Determination of capacitance. Electric displacement flux and Gauss’s law for electrostatics. Electric field shielding.

   
   


2. 
   

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

   
   


3. 
   

   Boundary conditions and their influence on the solution. Use of symmetry. Magnetic field of a coil and determination of inductance.

   
   


4. 
   

   Field of a permanent magnet. Comparison with the analytical solution for a magnetic dipole field. Magnetic flux density.

   
   


5. 
   

   Magnetic field of a nonlinear magnet. Demagnetization.

   
   


6. 
   

   Electric current conduction – Joule heating. Multiphysics simulations. Hall effect.

   
   


7. 
   

   Mechanics of solid bodies. Rod vibrations, damping, natural frequencies, and eigenfunctions.

   
   


8. 
   

   Tuning fork as a detector in atomic force microscopy (AFM). Q factor, influence of force on natural frequency, and linearization of the Lennard–Jones potential.

   
   


9. 
   

   Custom implementation of a differential equation solver. PN junction and current–voltage characteristics of a diode.

   
   


10. 
    

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

    
    


11. 
    

    Light scattering at structured interfaces.

    
    


12. 
    

    Work on an individually selected project.

    
    


13. 
    

    Project presentations.