F8370 Present-day methods in physical modelling

Faculty of Science
Spring 2011 - only for the accreditation
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: k (colloquium).
Teacher(s)
Mgr. Dušan Hemzal, Ph.D. (lecturer)
Mgr. Filip Münz, PhD. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: Mgr. Dušan Hemzal, Ph.D.
Prerequisites
the knowledge of the basic numerical methods (e.g. at the level up to and including F6150)
basics of MATLAB (possibly to gain during the semester)
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
there are 6 fields of study the course is directly associated with, display
Course objectives
The course is primarily intended for those students of the Master degree and/or doctoral degree programmes who consider future involvement in modelling in physics, both in academic and commercial domain.
The course introduces students into the methods presently used in modelling; the knowledge on the physical and mathematical background of these methods is inevitable for their succesfull implementation both individually as well as when using a third-party software.
Particularly, basics of selected topics from modern methods of numerical solution of the direct differential equation problem with initial/border conditions are taught as well as a selection from advanced topics in experimental data processing.
The necessary theory is lectured simultaneously with application to basic type of examples (including hydrodynamics, Laplace equation, heat transfer equation and equation of diffusion, wave equation and its harmonic subcase (Helmholtz equation); the equilibrium lattice parameters, phonons; eikonal equation).

The main objective of the course is to provide the students with the ability to
- list and describe principles of up-to-date methods used in physical modelling
- analyse the selected problem and suggest suitable method for its solution
- apply both of the previous steps to formulate the problem within a chosen model and to obtain its solution.
Syllabus
  • Finite differences: discretisation ofthe problem, approximation of the differential operator, border condition of the mixed type.
  • Finite elements method: weak formulation of the variational problem, discretisation of the problem and approximation of the sought for function, n-dimensional generic element, approximation and shape function over the element, isoparametrical elements, momentum integrals of the element; mesh generators, border conditions and the damping zone method.
  • Beyond FEM: boundary element method and its combination with FEM using outer radial discretisation, finite differences in the time domain; basics of level set methods for Hamilton-Jacobi type equations: Fast Marching Algorithms.
  • Advanced data manipulation: wavelet transformation and noise reduction, 2D Fourrier transformation in NMR, cosine transformation.
  • Specialised minimalisation: function of many variables, problem of many extremes, Ritz variation.
  • Genetic algorithms: chromozome and genotype, crossover (single-point, multiple-point, cyclic), mutation, star schemes, effectifisation (Grey coding).
  • Forward neural networks with backpropagation learning and mutually connected NN: function of several variables and the notion of neuron (configuration space splitting), perceptron and its activation, neural network (forward, Hopfield), learning (backpropagation), network optimalisation (initial guesses, GA and simmulated annealing).
Literature
  • MITCHELL, A.R. and D.F. GRIFFITS. The Finite Difference Method in Partial Differential Equations. 1980: Jonh Willey & Sons Ltd., 1980. info
  • KOLÁŘ, V. FEM: principy a praxe metody konečných prvků. Computer Press, 1997. info
  • DĚDEK, L. and J. DĚDKOVÁ. Elektromagnetismus. VUTIUM, 1998. info
  • Číslicová filtrace, analýza a restaurace signálů. Edited by Jiří Jan. 2. uprav. a rozš. vyd. Brno: VUTIUM, 2002, 427 s. ISBN 8021415584. info
  • ZELINKA, Ivan. Umělá inteligence, aneb, Úvod do neuronových sítí, evolučních algoritmů--. Vyd. 2. Ve Zlíně: Univerzita Tomáše Bati, 2005, 127 s. ISBN 8073182777. info
Teaching methods
lecture, seminars. individually appointed tasks within solution of selected problem.
Assessment methods
Active participation during the class exercises (at most three absences are allowed without letter of apology).
During a group discussion on the particular programming tasks appointed the colloquium will be granted to those students who by showing the relevant knowledge on the course topics prove their projects functional.
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 Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2024, Spring 2025.