BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Local analysis of the inverse problem associated w
ith the Helmholtz equation -- Lipschitz stability
and iterative reconstruction - de Hoop\, M (Purdue
University)
DTSTART;TZID=Europe/London:20111213T100000
DTEND;TZID=Europe/London:20111213T103000
UID:TALK34963AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/34963
DESCRIPTION:We consider the Helmholtz equation on a bounded do
main\, and the Dirichlet-to-Neumann map as the dat
a. Following the work of Alessandrini and Vessalla
\, we establish conditions under which the inverse
problem defined by the Dirichlet-to-Neumann map i
s Lipschitz stable. Recent advances in developing
structured massively parallel multifrontal direct
solvers of the Helmholtz equation have motivated t
he further study of iterative approaches to solvin
g this inverse problem. We incorporate structure t
hrough conormal singularities in the coefficients
and consider partial boundary data. Essentially\,
the coefficients are finite linear combinations of
piecewise constant functions. We then establish c
onvergence (radius and rate) of the Landweber iter
ation in appropriately chosen Banach spaces\, avoi
ding the fact the coefficients originally can be $
L^{infty}$\, to obtain a reconstruction. Here\, Li
pschitz (or possibly H"{o}lder) stability replaces
the so-called source condition. We accommodate th
e exponential growth of the Lipschitz constant usi
ng approximations by finite linear combinations of
piecewise constant functions and the frequency de
pendencies to obtain a convergent projected steepe
st descent method containing elements of a nonline
ar conjugate gradient method. We point out some co
rrespondences with discretization\, compression\,
and multigrid techniques.\n \nJoint work with E. B
eretta\, L. Qiu and O. Scherzer.\n\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
END:VEVENT
END:VCALENDAR