PDE-based Parameter Reconstruction through Schur and Schwarz Decompositions

where Ω ⊂ R, with n = 2 for the results in section 4. Q and ∂Q are defined as Q ≡ Ω× (0, T ) and ∂Q ≡ ∂Ω× (0, T ), respectively. See [8] for details on system parameters. The objective of the parameter identification is to reconstruct the reactive coefficient α(x) in the first equation from boundary measurements of the electrical potential u. Our aim here is to present a numerical algorithm that can solve the reconstruction problem in large-scale (parallel) environments. The algorithm is of NewtonKrylov-Schur-Schwarz type; it combines Newton’s method for numerical optimization with Krylov subspace solvers for the resulting reduced Karush-Kuhn-Tucker (KKT) systems. Schwarz preconditioning is used to solve the partial differential equations that are involved in the inversion procedure.