FA045 Selected chapters from modern computational methods

Faculty of Science
Spring 2021
Extent and Intensity
2/1/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. Filip Hroch, Ph.D. (lecturer)
Mgr. Viktor Votruba, Ph.D. (lecturer)
Guaranteed by
prof. Mgr. Jiří Krtička, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Filip Hroch, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Prerequisites (in Czech)
We are assuming some skills in mathematics: a common function handle (derivation, integration), linear algebra. Computer skills includes a basic knowledge of programming, and usual Unix tools.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives (in Czech)
An introduction to modern computation methods of physical problems: non-linear partial diferential equations, massive data processing, etc.
Learning outcomes (in Czech)
Students will be able to applicate of the methods on solution of various numerical problems.
Syllabus (in Czech)
  • Explicit methods for partial diferential equations of hyperbolic and parabolic kinds by the finnite diference methods. Applications in fluid dynamics, Kelvin-Helmholtz unstability simulations.
  • Implicit methods for for partial diferential equations of hyperbolic and parabolic kinds by the finnite diference methods. Applications on difusion, heat propagation. NUmerical limits of applications, stability.
  • Smooth particle hydrodynamics (SPH), Particle Mesh(PM) and Particle in Cell (PIC). Plasma process simulation, two-component unstability.
  • N-particle algorithms, particle in gravitation field, methods for molecular dynamics.
  • Methods for handling of large data sets, data mining.
  • Machine learning, supervised and unsupervised, Support Vector Machines, K-means clustering, neural networks.
  • General classification, regression. Time-series anomaly recognizing.
Literature
  • BODENHEIMER, Peter. Numerical methods in astrophysics : an introduction. New York: Taylor & Francis, 2007, 329 s. ISBN 9780750308830. info
Teaching methods (in Czech)
A common form of teaching will be lectures iterative presenting given topics.
Assessment methods (in Czech)
A final project should be prepared, and referred, for the successful complete. Homeworks may be included.
Language of instruction
English
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught: every week.
General note: L.
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