Information for the course NMNV571 - Multilevel Methods

... winter semester 2025/26 ...

Lectures take place on Wednesday, from 10:40 at KNM seminar room.

Literature and sources

• lecture notes
• scripts for the project
• Link to the book A Multigrid Tutorial, used in the first part of the course.
• [in Czech] Sken mých poznámek z roku 2024- Poznámky I a II, Poznámky III, obrázky ke smoothing property, Poznámky IV, Poznámky V, Poznámky VI.
• hand written notes for the lecture on BPX preconditioner
• part of book of Ulrich Rüde - section 2.1 (abstract description of stable splitting)

Planned outline (subject to change)

• 18.2., 25.2., 4.3. - introduction to geometric multigrid (Poisson problem and finite differences)
• 11.3., 18.3. - no lectures (my holiday)
• 25.3., 1.4., 8.4. - convergence of a multigrid (including an abstract formulation of MG)
• 25.5. - BPX preconditioner
• 22.4., 29.4. - stable splitting
• 6.5. - stable splitting in error estimation
• 13.5. - no lecture (sport day at MFF)
• 20.5. - presentation of projects

The students' project aim at testing various variants (parameters) of geometric multigrid and comparing them.

The final grade is based on the presentation of the project (40%) and on the final exam (60%).