Inhalt
| Kommentar |
The advent and rapid development of computing devices since the 1940s have led to an enormous progress in numerical analysis. The simulation of complex scientific processes requires many different aspects of numerical analysis, starting with modeling the key for being able to produce computational approximations is the discretization of the problem. This leads to large, sparse linear systems of equations. Typically over 50% of the simulation's time is spent solving these linear systems of equations so that an improvement of solution techniques pays off.
Driven by the demand for fast solvers, iterative techniques have become more and more popular over the last decades and huge progress has been made both regarding efficiency and robustness of these methods. In this course we will give a broad overview of iterative methods, starting with splitting methods that were already known in the early 19th century (e.g., Jacobi, Gauss-Seidel). We will introduce and analyze Krylov subspace methods as the go-to-guys of today's scientific computing arsenal and we will close with a discussion of domain decomposition and the powerful idea of multi-grid methods, which promise the solution of some linear systems in linear complexity!
|
| Literatur |
Iterative Methods for Sparse Linear Systems (2nd ed.),
Y. Saad, Society for Industrial and Applied Mathematics, 2003
Iterative Solution of Large Sparse Systems of Equations,
W. Hackbusch, Springer-Verlag, 1994
Krylov Subspace Methods
J. Liesen and Z. Strakos, Oxford Science Publications, 2013
(to be updated) |
| Bemerkung |
By default this course is taught in english, but if wanted can be taught in german as well.
|
| Voraussetzungen |
Mandatory requirements
- Linear Algebra
- Analysis
- Numerical Analysis
Optional requirements
- Complex Analysis
- Numerical Analysis of PDEs
|
| Leistungsnachweis |
There will be an oral exam at the end of the lecture and some special assignments during lecture time (e.g., programming assignments, protocol duty or preparation of lecture material). The special assignments are going to be discussed at the beginning of the lecture time. |
| Zielgruppe |
Master Mathematik
|
Anmelden