"More on subspace correction methods"
||Wed, February 20, 2013|
||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:
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.
- In the combination step, how to choose the weights (relaxation
- (Time permitting) Can we guarantee something if we compute
in a large network of computers, where a certain percentage of
subproblem solves is lost?