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UID:calendar.341216.field_date.0@www.wpi.edu
DTSTAMP:20210726T191734Z
CREATED:20210414T200621Z
DESCRIPTION:Description of Event: \n\n\n\nPhD Candidate: Yi Yu\nTitle: 'Non
-Overlapping Spectral Additive Schwarz Methods'\n\nAbstract: Domain decomp
osition methods is one of the most important techniques commonly used in p
arallel computation for solving algebraic system of equations arising from
the approximation of the partial differential equations. The basic idea i
s that instead of solving one huge problem in a global domain\, it may be
more convenient to solve smaller problems in subdomains simultaneously and
combine their solutions to obtain an approximation for the global solutio
n. This process is called 'preconditioning the system' and is used as an i
terative method and can be accelerated by Krylov space methods. Additive A
verage Schwarz methods--AAS were designed as domain decomposition precondi
tioners for solving 2D and 3D elliptic problems with discontinuous diffusi
ve coefficients across subdomains. These problems are then discretized usi
ng finite element methods and denote the element diameter by h and subdoma
in diameter by H. The Non-Overlapping Spectral Additive Schwarz Methods--N
OSAS are the enhancement of AAS\, which are robust for any type of coeffic
ients.NOSAS are two-level domain decomposition preconditioners that use no
n-overlapping subdomains\, and the subdomain interaction is via the coarse
space. The methods do not require a coarse triangulation\, and the coarse
problem can be seen as inverting a low-rank discrete harmonic extension o
n the subdomain interfaces. This rank is related to the lowest modes of a
local generalized eigenvalue problem. Moreover\, these methods can be modi
fied to have a better localization and\, therefore\, better scalability. W
e prove that the condition number of NOSAS for heterogeneous elliptic prob
lems does not depend on the coefficients\, and with a specific choice of t
he threshold of the eigenvalues\, the condition number is O(H/h). In this
dissertation\, we also consider NOSAS for Hybrid Discontinuous Galerkin di
scretizations of elliptic problems with heterogeneous coefficients and dev
elop three-level domain decomposition preconditioners based on NOSAS. Fina
lly\, we show that NOSAS also works for Multiscale discretizations.\n\n\n
\nThis event will be held via Zoom\, please contact Rhonda Podell at rpode
ll@wpi.edu for Zoom meeting information.
DTSTART;TZID=America/New_York:20210526T110000
DTEND;TZID=America/New_York:20210526T130000
LAST-MODIFIED:20210414T200621Z
SUMMARY:Mathematical Sciences-PhD Defense- Yi Yu 'Non-Overlapping Spectral
Additive Schwarz Methods'
URL;TYPE=URI:https://www.wpi.edu/news/calendar/events/mathematical-sciences
-phd-defense-yi-yu-non-overlapping-spectral-additive
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