Numerical Algorithms for Diffusion Coefficient Identification in Problems of Tissue Engineering
Alexey V. Penenko, Sergey V. Nikolaev, Sergey K. Golushko, Alexander V. Romashenko, Irina A. Kirilova
Institute of computational mathematics and mathematical Geophysics of Siberian branch of Russian Academy of Sciences (ICM&MG SB RAS)
Abstract. Identification algorithms of diffusion coefficients in a specimen with tomographic images of the solution penetration dynamics are considered. With the sensitivity operator, built on the basis of adjoint equations for diffusion process model, the corresponding coefficient inverse problem is reduced to the quasilinear operator equation which is then solved by the Newton-type method with successive evaluation of r-pseudo inverse operators of increasing dimensionality. The efficiency of the constructed algorithm is tested in numerical experiments. For comparison, a gradient-based algorithm for the inverse problem solution is considered.
Key words: inverse coefficient problem, sensitivity operator, Newton-type algorithm, r-pseudoinverse operator, magnetic resonance imaging, diffusion coefficient.