F6150 Advanced numerical methods

Faculty of Science
Spring 2023
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: k (colloquium).
Teacher(s)
doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
doc. Mgr. Jiří Chaloupka, Ph.D.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. Mgr. Jiří Chaloupka, Ph.D.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Timetable
Tue 10:00–11:50 Fcom,01034
  • Timetable of Seminar Groups:
F6150/01: Tue 12:00–12:50 Fcom,01034
Prerequisites (in Czech)
F5330 Basic numerical methods
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
An introduction of advanced numerical methods, with a particular emphasis on spectral analysis and multidimensional optimalization. An emphasis is put on the applications of these methods when solving physical problems.
Learning outcomes
The main objective of the course is to provide the students with the ability to:
- list and explain the details of the lectured numerical methods;
- apply these methods in particular modelling tasks;
- learn to utilize suitable software to perform numerical simulations of physical systems.
Syllabus
  • 1. Discrete Fourier transform (FFT algorithm, DFT of real data, DFT variants with symmetry - cosine and sine transforms, multidimensional DFT, applications: spectral analysis, filtering, convolution and deconvolution, jpeg and mp3)
  • 2. Multidimensional minimization (simplex method, Powell's method, conjugate-gradient methods, variable metric method, Marquardt-Levenberg algorithm for the sum of squares, simulated annealing, particle swarm method)
  • 3. Lanczos diagonalization of sparse matrices
  • 4. Numerical quadrature (Gaussian quadrature, Gauss-Kronrod rules, adaptive quadrature)
  • 5. Interpolation and approximation (polynomial interpolation - classical formulas and Neville's algorithm, cubic splines, rational interpolation, multidimensional case)
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for graded credit: successful presentation of the solution of the assigned semestral project.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.physics.muni.cz/~chaloupka/F6150/
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, 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 2020, Spring 2021, Spring 2022, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2023, recent)
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