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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Lie-Poisson methods for isospectral flows and thei
r application to long-time simulation of spherical
ideal hydrodynamics - Milo Viviani (Chalmers Univ
ersity of Technology)
DTSTART;TZID=Europe/London:20190828T150000
DTEND;TZID=Europe/London:20190828T160000
UID:TALK129175AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/129175
DESCRIPTION:The theory of isospectral flows comprises a large
class of continuous dynamical systems\, particular
ly \;integrable systems and Lie&ndash\;Poisson
 \;systems. Their discretization is a classica
l problem in numerical \;analysis. Preserving
the spectra in the discrete flow requires the cons
ervation of \;high order polynomials\, \;w
hich is hard to come by. Existing methods achievin
g this are complicated and usually fail to preserv
e \;the underlying Lie-Poisson structure. Here
we present a class of numerical methods of arbitr
ary order \;for Hamiltonian and non-Hamiltonia
n isospectral flows\, which \;preserve both th
e spectra and the Lie-Poisson structure. The metho
ds are surprisingly simple\, and avoid the use of
constraints or exponential \;maps. Furthermore
\, due to preservation of \;the Lie&ndash\;Poi
sson structure\, they exhibit near conservation&nb
sp\;of the Hamiltonian function. As an illustratio
n\, we apply the methods to long-time \;simula
tion of the \;Euler equations on a sphere. Our
findings suggest that our structure-preserving al
gorithms\, on the \;one hand\, perform at leas
t as \;well as other popular methods (i.e. CLA
M) without adding spurious \;hyperviscosity te
rms\, on the other hand\, show that the conservati
on of the \;Casimir functions can be \;act
ually used to predict the final state of the fluid
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:INI IT
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