Integration on sparse grids - Smolyak's construction
Solving partial differential equations
Sparse grid methods
Representation of functions and interpolation
Finite difference discretization on sparse grids
Finite elemen discretization on sparse grids
Quasi Monte Carlo Methods
Particle approximations
Solving the advection equation
Solving the heat equation
Advection diffusion problems
Brownian motion
lecture:
The lecture parts follow the usual style. Hand written notes are available
in the mathematics library (in the shelf Vorlesungsskripte - update 28.01.2001).
seminar:
In contrast to the lectures, the students read and try to understand the
material before the meeting. Questions arising during the preparation
are discussed in the meeting (in practice, the questions should be noted
anonymously on a piece of paper which can be collected in the beginning).
The aim is to practice asking because formulating questions is a
very important aspect of research and science!
tutorial:
Some of the courses will be held in the computer room. Algorithms are implemented
(for example, using Matlab) and tested on several examples. Seeing (quasi-)
random points is much more fun than just talking about them!
