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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Linear Algebra Methods for Parameter-Dependent Par
tial Differential Equations - Howard Elman (Unive
rsity of Maryland\, College Park)
DTSTART;TZID=Europe/London:20180110T113000
DTEND;TZID=Europe/London:20180110T123000
UID:TALK97504AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/97504
DESCRIPTION:We discuss some recent developments in solution al
gorithms for the linear algebra problems that aris
e from parameter-dependent partial differential eq
uations (PDEs). In this setting\, there is a need
to solve large coupled algebraic systems (which co
me from stochastic Galerkin methods)\, or large nu
mbers of standard spatially discrete systems (from
Monte Carlo or stochastic collocation methods).
The ultimate goal is solutions that represent surr
ogate approximations that can be evaluated cheaply
for multiple values of the parameters\, which can
be used effectively for simulation or uncertainty
quantification.

Our focus is on rep
resenting parameterized solutions in reduced-basis
or low-rank matrix formats. We show that efficie
nt solution algorithms can be built from multigrid
methods designed for the underlying discrete PDE\
, in combination with methods for truncating the r
anks of iterates\, which reduce both cost and stor
age requirements of solution algorithms. These ide
as can be applied to the systems arising from many
ways of treating the parameter spaces\, includin
g stochastic Galerkin and collocation. In additio
n\, we present new approaches for solving the dens
e systems that arise from reduced-order models by
preconditioned iterative methods and we show that
such approaches can also be combined with empirica
l interpolation methods to solve the algebraic sys
tems that arise from nonlinear PDEs. \;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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