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Fundamentals of Computational Physics II - NEVF138

Title:	Základy počítačové fyziky II
Guaranteed by:	Department of Surface and Plasma Science (32-KFPP)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2021
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Štěpán Roučka, Ph.D. doc. RNDr. Radek Plašil, Ph.D.

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

Last update: doc. RNDr. Štěpán Roučka, Ph.D. (28.01.2019)

The lecture deals with the accuracy and stability of numerical algorithms. Theoretical analysis as well as practical examples are demonstrated. Special attention is paid to the solution of partial differential equations.

Aim of the course -

Last update: IBARVIK/MFF.CUNI.CZ (16.05.2008)

Students will learn basic numerical algorithms (see annotation and syllabus).

Course completion requirements - Czech

Last update: doc. RNDr. Jiří Pavlů, Ph.D. (14.06.2019)

Podmínkou zakončení předmětu je úspěšné složení zkoušky, tj. hodnocení zkoušky známkou "výborně", "velmi dobře" nebo "dobře". Zkouška musí být složena v období předepsaném harmonogramem akademického roku, ve kterém student předmět zapsal.

Literature - Czech

Last update: T_KEVF (07.05.2005)

Vicher M.: Numerická matematika, PF UJEP, Ústí nad Labem 2003.

Press W.H. et al.: Numerical Recipes in FORTRAN (Pascal, C) Cambridge University Press, Cambridge 1992.

Hrach R.: Počítačová fyzika I, II, PF UJEP, Ústí nad Labem 2003.

Rapaport D.C.: The Art of Molecular Dynamics Simulation, Cambridge University Press, Cambridge 1995.

Teaching methods -

Last update: IBARVIK/MFF.CUNI.CZ (16.05.2008)

Lectures and practical exercises in computer lab

Requirements to the exam - Czech

Last update: doc. RNDr. Štěpán Roučka, Ph.D. (27.02.2018)

Zkouška sestává pouze z ústní části. Okruhy otázek odpovídají látce který byla prezentován na přednášce a studenti jsou s nimi seznámeni na první přednášce.

Syllabus -

Last update: doc. RNDr. Štěpán Roučka, Ph.D. (28.01.2019)

1. Accuracy and stability of basic numerical algorithms
Numerical mathematics - accuracy of operations, computation errors, algorithm stability. Numerical integration and differentiation - integration with uniform and adaptive steps. Solution of ordinary differential equations - Euler, Runge-Kutta, and predictor-corrector methods.

2. Linear algebra
Second difference matrix, its eigenvalues and eigenvectors. Condition number of a matrix and its importance for numerical methods.

3. Numerical solution of partial differential equations
Finite difference method. Solution of boundary value problems - direct (Gauss elimination, LU decomposition, Fourier transform), indirect (relaxation methods - Jacobi, Gauss-Seidel...). Evolutionary equations, FTCS (forward time, centered space), Lax(-Friedrichs) method, Crank-Nicolson method. Von Neumann stability analysis, Courant Friedrichs Lewy condition. Principles of finite element method, weak formulation, discretization of the space of functions, practical demonstrations.

4. Selected algorithms of computer physics
Integral transforms - fast Fourier transform, deconvolution, Wiener and Lucy-Richardson deconvolution. Tikhonov regularization.