Graduate Seminar "Aktuelle Themen der Numerik"
Thursday, Oct 24, 2013, 02:00 pm
A model-data variational formulation: rapid and reliable in-painting for partial differential equations
Masayuki Yano, Ph.D. (MIT)
We present the model-data variational formulation, an integrated variational framework which combines a "model" (partial differential equation) and "data" (M experimental observations) to yield estimates for state and model bias. We first abstract the estimation problem as a variational problem in the presence of unlimited observations. We then consider an approximate solution of the variational problem based on experimentally-realizable limited observations; we provide an associated a priori theory which identifies distinct contributions to reduction in the state error with the number of observations. We then incorporate certified reduced basis method into the model-data variational formulation. We in particular develop an efficient offline-online computational strategy in the reduced basis setting in which we invoke real data in real-time. We finally apply the method to a synthetic two-dimensional Helmholtz problem and real-data associated with a (three-dimensional) acoustic resonator to assess the effectiveness of the proposed method.
(This is work in collaboration with Prof. Anthony Patera and Dr. James Penn.)
Time: 02:00 pm
Location: Room 149, Hauptgebäude, RWTH Aachen, Templergraben 55, 52056 Aachen