Department
of Mathematical and Statistical Sciences
University of Colorado Denver
Time: Tuesday 11:00-12:00
Office hours: TBD
Place: TBD
Prerequisites: Math 7760 or a working
knowledge of some linear algebra, functional analysis and finite element theory
1
credit, see department office about registration – cannot be registered for
online
Book: none required but these might be
handy: Sue Brenner, Theory of finite element methods, 3rd ed; Tosseli,
Widlund, Domain decomposition methods
The
class will deal with a family of iterative methods for large system of
equations from FE and FD for elliptic problems. The class will consist of some
lectures but mostly student presentations on assigned topics. Students will be
graded based on the presentations, which must be also turned in electronically.
We will read original journal articles, tech reports, and monographs.
Topics
·
Schwarz
method and P.L. Lions lemma: how it all started
·
Abstract
Schwarz methods: just some smart linear algebra
·
Overlapping
Schwarz methods: powerful but expensive
·
Non-overlapping
methods: eliminate what you can, iterate on the rest
·
BPS-I:
nice and simple if put right but need a coarse triangulation
·
BDD:
what if I have only the matrices?
·
FETI:
the dual way
·
BDDC
and FETI-DP: currently the best, the primal and the dual meet at last
Links
ddm.org – the official domain
decomposition, proceeding of DD conferences online