Thursday, February 27, 2014 9:30 am

9:30 am
EST (GMT 05:00)
MC 6486
Speaker
David Shirokoff, Department of Mathematics and Statistics, McGill University
Title
High order penalty methods: a Fourier approach to solving PDE's on domains with curved boundaries
Abstract
Penalty
methods
offer
an
attractive
approach
for
solving
partial
differential
equations
(PDEs)
on
domains
with
curved
or
moving
boundaries.
In
this
approach,
one
does
not
enforce
the
PDE
boundary
conditions
directly,
but
rather
solves
the
PDE
in
a
larger
domain
with
a
suitable
source
or
penalty
term.
The
new
penalized
PDE
is
then
attractive
to
solve
since
one
no
longer
needs
to
actively
enforce
the
boundary
conditions.
Despite
the
simplicity,
these
methods
have
suffered
from
poor
convergence
rates
which
limit
the
accuracy
of
any
numerical
scheme
(usually
to
first
order
at
best).
In
this
talk
I
will
show
how
to
systematically
construct
a
new
class
of
penalization
terms
which
improve
the
convergence
rates
of
the
penalized
PDE,
thereby
allowing
for
higher
order
numerical
schemes.
I
will
also
show
that
the
new
penalized
PDE
has
the
added
advantage
of
being
solved
in
a
straightforward
manner
using
Fourier
spectral
methods.
Finally,
I
demonstrate
that
the
method
is
very
general
and
works
for
elliptic
(Poisson),
parabolic
(heat),
and
hyperbolic
(wave)
equations
and
can
be
applied
to
practical
problems
involving
the
incompressible
NavierStokes
equations
and
Maxwell’s
equations.