TFNPF0003 Numerical Modeling in Physics II

Institute of physics in Opava
winter 2020
Extent and Intensity
4/2/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Kateřina Klimovičová, Ph.D. (lecturer)
doc. RNDr. Jan Schee, Ph.D. (lecturer)
RNDr. Kateřina Klimovičová, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jan Schee, Ph.D.
Institute of physics in Opava
Prerequisites (in Czech)
(FAKULTA(FU) && TYP_STUDIA(N))
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of the course is to introduce the advanced methods of numerical modelling of physical processes and to illustrate application of those methods on specific physical tasks (i.e. numerical solution for given charge distribution).
Learning outcomes
Passing the course a student will acquire following skills:
-to mathematically formulate physical problem with respect to numerical representation of its solution;
-to apply presented numerical algorithms to physical problems;
-to analyze suitability of an algorithm for given problem;
-to present results in form form of tables and plots of suitably chosen quantities that are characteristic for solution of physical problem;
-to use learned algorithms in other branches of technology and science, where it is necessary to solve mathematically formulated problem numericaly;
Syllabus
  • Outline:
  • -Introduction to numerical methods study. Definition of fundamental concepts: digital representation of floating point numbers, error of representation and truncation, numerical arithmetic and error propagation, algorithm stability.
  • -Electrostatics: electrostatic field of a point charge, Poisson equation, numerical solution of elliptic PDEs using relaxation method.
  • -Diffusion equation and wave equation: heat conduction in thin rod, wave propagation along stretched string and in elastic membrane, numerical solutions of parabolic a hyperbolic PDEs, utilization of Leapfrog and Lax-Wendrof methods.
  • -Self-consistent solutions of Euler and Poisson equations: spherical and toroidal stars.
  • -Timeless Schrödinger equation: bound states, energy spectrum, eigen system of differential equations with boundary conditions.
  • Quasinormal modes of gravitational perturbations of Schwarzchild spacetime : WKB and Leaver metods of finding Regge-Wheeler equation solutions.
  • -Random number generators, uniform and Gauss distributions, Maxwell-Boltzman distribution.
  • -Random walk, optical depth and opacity, Monte Carlo simulation of radiation transfer through material.
  • -Monte Carlo Simulation: isotropic and anizotropic scattering (electron scattering, dust grains scattering).
Literature
    recommended literature
  • Press, W. H., Teukolsky, S. A., Vettering, W. T. Numerical Recipes:The Art of Scientific Computing, Cambridge University Press, 2007
  • Misner, C. W., Thorne, K. S., Wheeler, J. A. Gravitation, Freeman, San Francisco, 1973 (2017)
  • P. Schneider, J. Ehlers and E. E. Falco. Gravitational lenses. Springer, 1999. info
  • RYBICKI G. B., LIGHTMAN A. P. Radiative Processes in Astrophysics. Wiley-VCH, Weinheim, 2004. ISBN 978-0-471-82759-7. info
Teaching methods
Lectures, discussing selected physical problems, solving given physical problems.
Assessment methods
Oral exam and final project. Oral exam corresponds with given final project. Students defend their projects during discussion.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms winter 2021, winter 2022, winter 2023, winter 2024.
  • Enrolment Statistics (winter 2020, recent)
  • Permalink: https://is.slu.cz/course/fu/winter2020/TFNPF0003