Harbir Antil - Research

PDE Constrained Optimization and Model Reduction with Localized Nonlinearities

For a description of PDE constrained optimization problems we refer to: link

For a description of model reduction techniques we refer to: link

A real time solution to river pollution, let say two factories are discharging waste in the river and we want to control the discharge and want to attain a desired concentration of pollutants in the river. We solve the minimization problem using the model reduction techniques, the reduced problem takes 1 sec as compared to 10 min for full problem. link


The goal of this project is to develop optimization algorithm to solve the time dependent linear and nonlinear PDE constrained optimization problems with localized nonlinearities, using balanced truncation model reduction (BTMR) and domain decomposition.



Related Publications

  • H. Antil, M. Heinkenschloss, and R.H.W. Hoppe.
    Domain decomposition and balanced truncation model reduction for shape optimization of the Stokes system (2010).
    Optimization Methods and Software (2011), 26(4-5):643--669. preprint
    Most cited article in this journal. Years 2012-13.
  • H. Antil, M. Heinkenschloss, R.H.W. Hoppe, and D.C. Sorensen.
    Domain decomposition and model reduction for the numerical solution of PDE constrained optimization problems with localized optimization variables .
    Computing and Visualization in Science (2010), 13(6):249--264. link