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Course, academic year 2023/2024
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Computer Solutions of Continuum Physics Problems - NMMO403
Title: Počítačové řešení úloh fyziky kontinua
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English
Teaching methods: full-time
Teaching methods: full-time
Additional information:
Guarantor: RNDr. Jaroslav Hron, Ph.D.
Class: M Mgr. MOD
M Mgr. MOD > Povinné
M Mgr. NVM
M Mgr. NVM > Volitelné
Classification: Mathematics > Mathematical Modeling in Physics, Numerical Analysis
Incompatibility : NMOD041
Interchangeability : NMOD041
Is interchangeable with: NMOD041
Annotation -
Last update: Mgr. Dalibor Šmíd, Ph.D. (11.05.2023)
Introduction to modern methods for numerical solution of systems of partial differential equations obtained by mathematical modeling of continuum mechanics problems (heat transfer, fluid flow, elastic deformation, etc.). The course includes overview of the basic software for numerical computation and its application to solution of PDEs. Major part includes overview and practical use of parallel HPC computational cluster, the basic numerical libraries (Blas, Lapack, Petsc, etc. ), finite element libraries (Fenics) and libraries for parallel computation (MPI, OpenMP)
Aim of the course -
Last update: RNDr. Jaroslav Hron, Ph.D. (12.01.2022)

This course aims to introduce students to numerical solution of problems in continuum mechanics by finite element method. Students will learn how to use modern parallel computers and how to use some suitable academic open source software tools.

Course completion requirements -
Last update: RNDr. Jaroslav Hron, Ph.D. (12.01.2022)

Students will prepare a short report on solving a prototypical problem in continuum mechanics, which will be choose during the semester.

Literature - Czech
Last update: RNDr. Jaroslav Hron, Ph.D. (15.05.2017)

[1] A. Logg, K.-A. Mardal, G. Wells, eds., Automated Solution of Differential Equations by the Finite Element Method, Lecture Notes in Computational Science and Engineering. (2012).

[2] K. Eriksson, D. Estep, P. Hansbo, C. Johnson, Computational Differential Equations, 1996.

[3] D. Goldberg, What every computer scientist should know about floating-point arithmetic, ACM Computing Surveys. 23 (1991) 5-48.

Requirements to the exam -
Last update: RNDr. Jaroslav Hron, Ph.D. (12.01.2022)

Examination will consists of a question in the frame of syllabus or areas covered during the semester.

The main part will be discussion of the problem solved in the credit test.

Syllabus -
Last update: RNDr. Jaroslav Hron, Ph.D. (12.01.2022)

Solving a partial differential equation by finite element method using FEniCS.

  • Introduction to Python language and typical HPC enviroment and tools.

  • Overview of the basic components for finite element solution of partial differential equations:

domain description and discretization, basis function implementation (parametric, non-parametric finite elements),

boundary condition implementation, efficient linear system assembly, solution of large,

sparse linear systems (direct, preconditioned iterative, multigrid methods)

  • Nonlinear problems, fixed point method, Newton method

  • Example applications: the Poisson equation, the convection-diffusion-reaction equation, the heat transfer equation, the Navier--Stokes

equation, the elastic deformation equation, multi-phase flows, the levelset method

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