### CAS Seminar

# Peter Oswald

### (Jacobs University)

## "More on subspace correction methods"

** Date: ** |
Wed, February 20, 2013 |

** Time: ** |
14:15 |

** Place: ** |
Research I Seminar Room |

**Abstract:** I will report on some ongoing research with Griebel and
Hullmann (Bonn) on an old favorite of mine, the theory of
additive Schwarz methods (to solve a "large" problem, cut it into
(many) small and easy-to-solve problems, solve them (in parallel),
combine the partial solutions into an update, and iterate).
The new aspects we are interested in are:

- In the combination step, how to choose the weights (relaxation
parameters)?
- (Time permitting) Can we guarantee something if we compute
in a large network of computers, where a certain percentage of
subproblem solves is lost?

I will give an introduction to subspace correction methods in the simplest
situation of solving a linear system with spd matrix, mention the connection
to subspace optimization methods in (convex) optimization, and show some
numerical test results for sparse grid discretizations.