Information for the course NMNV571 - Multilevel Methods

Lectures take place on Thursday, from 12:20 at K4.

Literature and sources

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

Planned outline (subject to change)

the numbers in brackets refer to the pages in lecture notes

• 20.2. - the lecture in the first week of the semester is cancelled
• 27.2. (pp.3-8), 6.3. (pp.8-12), 13.3. (pp.12-18) - introduction to geometric multigrid (Poisson problem and finite differences)
• 20.3. (pp.19-23), 27.3. (pp.23-25), 3.4. (pp.25-26) - convergence of a multigrid (including an abstract formulation of MG)
• 10.4. - no lecture; replaced by project assigned to students
• 17.4. - presentations of the projects
• 24.4., 15.5. - stable splitting
• 1.5., 8.5 - no lectures (holidays)
• 15.5. - stable splitting in error estimation
• 22.5. - BPX preconditioner

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%).