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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Variational discretizations of gauge field theorie
s using group-equivariant interpolation spaces - M
elvin Leok (University of California\, San Diego)
DTSTART;TZID=Europe/London:20191001T110000
DTEND;TZID=Europe/London:20191001T120000
UID:TALK130564AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/130564
DESCRIPTION:Variational integrators are geometric structure-pr
eserving numerical methods that preserve the sympl
ectic structure\, satisfy a discrete Noether'\;
s theorem\, and exhibit exhibit excellent long-tim
e energy stability properties. An exact discrete L
agrangian arises from Jacobi'\;s solution of th
e Hamilton-Jacobi equation\, and it generates the
exact flow of a Lagrangian system. By approximatin
g the exact discrete Lagrangian using an appropria
te choice of interpolation space and quadrature ru
le\, we obtain a systematic approach for construct
ing variational integrators. The convergence rates
of such variational integrators are related to th
e best approximation properties of the interpolati
on space.
Many gauge field theories can b
e formulated variationally using a multisymplectic
Lagrangian formulation\, and we will present a ch
aracterization of the exact generating functionals
that generate the multisymplectic relation. By di
scretizing these using group-equivariant spacetime
finite element spaces\, we obtain methods that ex
hibit a discrete multimomentum conservation law. W
e will then briefly describe an approach for const
ructing group-equivariant interpolation spaces tha
t take values in the space of Lorentzian metrics t
hat can be efficiently computed using a generalize
d polar decomposition. The goal is to eventually a
pply this to the construction of variational discr
etizations of general relativity\, which is a seco
nd-order gauge field theory whose configuration ma
nifold is the space of Lorentzian metrics.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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