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CATEGORIES:Colloquium/Seminar
DESCRIPTION:Jeremy Hoskins\, Department of Mathematics\, Yale University\
n\nElliptic PDEs on regions with corners\n\nMany of the boundary value prob
lems frequently encountered in the simulation of physical problems (electro
statics\, wave propagation\, fluid dynamics in small devices\, etc.) can be
solved by reformulating them as boundary integral equations. This approach
reduces the dimensionality of the problem\, and enables high-order accurac
y in complicated geometries. Unfortunately\, in domains with sharp corners
the solution to both the original governing equations as well as the corres
ponding boundary integral equations develop singularities at the corners. T
his poses significant challenges to many existing integral equation methods
\, typically requiring the introduction of many additional degrees of freed
om. In this talk I show that the solutions to the Laplace\, Helmholtz\, and
biharmonic equations in the vicinity of corners can be represented by a se
ries of elementary functions. Knowledge of these representations can be lev
eraged to construct accurate and efficient NystrÃ¶m discretizations for solv
ing the resulting integral equations. I illustrate the performance of this
method with several numerical examples.
DTEND:20200124T230000Z
DTSTAMP:20201026T164205Z
DTSTART:20200124T220000Z
GEO:40.006791;-105.262818
LOCATION:Engineering Center\, ECCR 265
SEQUENCE:0
SUMMARY:Applied Math Colloquium - Jeremy Hoskins
UID:tag:localist.com\,2008:EventInstance_32298915524852
URL:https://calendar.colorado.edu/event/applied_math_colloquium_-_jeremy_ho
skins
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