CRM-McGill Applied Math Seminar
Tuesday Feb 5, 2008, 3:35pm
Burnside Room 1205

-speaker
Andrei Draganescu 
University of Maryland Baltimore County

-title
Multigrid methods for large-scale inverse problems

-abstract
Scenario: An air contamination event takes place in a heavily populated
area.  A chemical agent is being diffused in the air and moved by the wind.
Sensors monitoring air quality detect increased concentrations of the
pollutant. At what location was the pollutant released in the air? What
areas will be affected over the next few minutes, hours, days, and to what
degree?

Fast answers to these questions are critical for hazard containment and
assessment, and for evacuation strategies. An efficient response to the
above scenario requires the backward solution of a time-dependent
advection-reaction-diffusion equation, a problem that is ill-posed. In this
talk I will present a method for efficiently solving the regularized inverse
problem of identifying initial conditions given various measurements in
space and time for an equation of parabolic type. The method is a new
embodiment of the multigrid paradigm, which consists in using several
discretizations of an equation in order to speed up the solution process. I
will discuss mathematical results both for linear and nonlinear models, and
I will present supporting numerical results. The method is applied to the
above scenario, showing that the associated high-resolution inverse problem
can be solved in a reasonable time-frame.