Finite element method in geophysics - NGEO107
Title: Metoda konečných prvků v geofyzice
Guaranteed by: Department of Geophysics (32-KG)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:0/2, C [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
Guarantor: RNDr. Klára Kalousová, Ph.D.
Teacher(s): RNDr. Klára Kalousová, Ph.D.
Opinion survey results   Examination dates   SS schedule   Noticeboard   
Annotation -
Computer modeling is an essential tool for studying solar system bodies. The partial differential equations of continuum mechanics and thermodynamics that describe their internal evolution are solved by different methods (finite element/difference/volume, spectral, etc.). The possibility to solve problems on complex and time evolving domains and straightforward implementation of boundary conditions are the main advantages of finite element method.
Last update: Gallovič František, prof. RNDr., Ph.D. (09.01.2019)
Aim of the course -

The goal of this class is to introduce the finite element method and apply it to solve the problems related to thermal and deformational evolution of the solar system planets and moons.

Last update: Gallovič František, prof. RNDr., Ph.D. (09.01.2019)
Course completion requirements -

Active participation in the class, development and debugging of six homework problems.

Last update: Gallovič František, prof. RNDr., Ph.D. (09.01.2019)
Literature -
  • Logg, A., K. A. Mardal, and G. N. Wells (editors), Automated Solution of Differential Equations by the Finite Element Method, The FEniCS Book, Lecture Notes in Computational Science and Engineering, 84, Springer-Verlag, Berlin Heidelberg, 2012.

  • Blankenbach, B., F. Busse, U. Christensen, L. Cserepes, D. Gunkel, U. Hansen, H. Harder, G. Jarvis, M. Koch, G. Marquart, D. Moore, P. Olson, H. Schmeling, and T. Schnaubelt (1989), A benchmark comparison for mantle convection codes, Geophys. J. Int., 98(1), 23-38.

Additional literature recommended by the lecturer (dependent on the nature of solved problems).

Last update: Gallovič František, prof. RNDr., Ph.D. (09.01.2019)
Teaching methods -

Introduction into the finite element method and the basics of work with the FEniCS software. Independent work on given problems, regular discussion on progress.

Last update: Gallovič František, prof. RNDr., Ph.D. (09.01.2019)
Syllabus -

1. Introduction into the finite element method (weak solution, weak formulation, essential and natural boundary conditions, the Galerkin method, finite element, discrete solution)

2. Short introduction into the Python programming language (variables, operators, conditions, cycles, functions, units, I/O operations)

3. The basics of FEniCS software (computational mesh, spaces of basis function, boundary conditions, linear problem)

4. Time discretization

5. Nonlinear problems

6. Visualization in ParaView

7. Complex computational meshes (Gmsh)

8. Selected problems: Stokes flow of incompressible fluid, heat transfer equation, thermal convection, plasticity, viscoelastic deformation, free surface, thermo-chemical convection, ...

Last update: Gallovič František, prof. RNDr., Ph.D. (09.01.2019)