Numerical Simulations in Physics (FSI-TFS)

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.

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

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.

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

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

Compulsory participation at tutorials, report with solution of project.

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. Magnetization curve, magnetization, magnetic dipole moment.


4. Fundamentals of numerical solution of ordinary differential equations. Euler's method, Runge-Kutta's method.


5. Eigenvalues and eigenfunctions.


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


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


8. Scattering of light at a structured interface. Near and far field.


9. Time evolution of the field - time domain, frequency domain. Dispersion relations.


10. Implementation of custom physics equations in COMSOL Multiphysics.


11. Project consultation.


12. Project consultation.


13. Presentation of projects.

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


4. Magnetic field of two conductors with current. Force acting on conductors. Ampere's law.


5. Oscillation of the beam - own frequency and own function.


6. Heat conduction and radiation. Joule heat. Multiphysics simulation.


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


8. Scattering of light at a structured interface. Plasmon polaritons, near and far field.


9. Electromagnetic wave propagation. Time evolution. Dispersive environment - calculation in the frequency domain.


10. Implementation of the solver of differential equations.


11. Work on the chosen project.


12. Work on the chosen project


13. Presentation of projects.

ZIMMERMAN, William B. J. Multiphysics Modeling with Finite Element Methods. New Jersey: WORLD SCIENTIFIC, 2006. Series on Stability, Vibration and Control of Systems, Series A. ISBN 978-981-256-843-4.