Scientific computing

Dr. Alexander Heinlein

Vorlesung
Di.  09:45 - 11:15 online
Do. 09:45 - 11:15 online
Erste Vorlesung: Dienstag, den 03.11.2020

Übung
Mi. 09:45 - 11:15 online

We discuss modern topics in the numerical approximation of solutions of partial differential equations. This includes in particular aspects of parallelising discretisation and solution schemes: On the one hand, phones are parallel computers nowadays, but on the other hand, "typical" textbooks and lectures are still sequential and thus, do not match the modern hardware. We will see that exciting new theories are necessary for parallelisation, and that many schemes need to be redesigned from scratch.

List of topics:

• Abstract Krylov theory and solvers for nonsymmetric problems
• Crash course OpenMP programming (if requested by participants)
• Parallel preconditioning
• Domain decomposition methods: abstract Schwarz theory, hierarchical Schwarz- and substructuring methods
• Depending on the audience: fault tolerant algorithms, asynchronous algorithms, parallel-in-time schemes

Some knowledge of Numerics for PDEs, e.g. PDEMAS (Bachelor) or Einführung in die Numerik partieller Differentialgleichungen (Master)

will be announced in the lecture

M.Sc. Mathematik, M.Sc. SimTech

9 LP

oral exam