Quantitative imaging technique using an adaptive finite element method

Date(s) : 17/06/2015   iCal
14 h 00 min - 15 h 00 min

We will discuss solution of coefficient inverse problems (CIPs) where the goal is to reconstruct the spatially distributed coefficients in different hyperbolic PDE (acoustic, elastodynamic and electromagnetic) using Lagrangian approach and an adaptive finite element method (AFEM).  We will present theoretical results which justify why we can
improve solution of our CIPs using AFEM.  We also will present general approach for derivation of a posteriori error estimates for the error in the Tikhonov functional, Lagrangian and the coefficient to be reconstructed.

At the end of the talk we will present numerical examples which will demonstrate efficiency of application of an adaptive FEM for solution of different hyperbolic CIPs: in the reconstruction of coefficients in Maxwell’s equations and in the computational design of approximate cloaking.



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