Seminar in Numerical Analysis: Larisa Beilina (University of Göteborg)
An adaptive finite element/finite difference domain decomposition method for solution of time-dependent Maxwell's equations for electric field in conductive media will be presented. This method is applied for reconstruction of dielectric permittivity and conductivity functions using time-dependent scattered data of electric field at the boundary of the domain.
All reconstruction algorithms are based on optimization approach for finding of stationary point of the Lagrangian. Derivation of a posteriori error estimates for the regularized solution and Tikhonov functional will be presented. Based on these estimates adaptive reconstruction algorithms are developed. Computational tests will show robustness of proposed algorithms in 3D.
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