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Author: Lu, Shuai ×

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    Parameter identification in non-isothermal nucleation and growth processes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Hömberg, Dietmar; Lu, Shuai; Sakamoto, Kenichi; Yamamoto, Masahiro
    We study non-isothermal nucleation and growth phase transformations, which are described by a generalized Avrami model for the phase transition coupled with an energy balance to account for recalescence effects. The main novelty of our work is the identification of temperature dependent nucleation rates. We prove that such rates can be uniquely identified from measurements in a subdomain and apply an optimal control approach to develop a numerical strategy for its computation.
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    Heuristic parameter selection based on functional minimization : optimality and model function approach
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Lu, Shuai; Mathé, Karsten
    We analyze some parameter choice strategies in regularization of inverse problems, in particular the (modified) L-curve method and a variant of the Hanke-Raus rule. These are heuristic rules, free of the noise level, and they are based on minimization of some functional. We analyze these functionals, and we prove some optimality results under general smoothness conditions. We also devise some numerical approach for finding the minimizers, which uses model functions. Numerical experiments indicate that this is an efficient numerical procedure.
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    Uniqueness for an inverse problem for a nonlinear parabolic system with an integral term by one-point Dirichlet data
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Hömberg, Dietmar; Lu, Shuai; Yamamoto, Masahiro
    We consider an inverse problem arising in laser-induced thermotherapy, a minimally invasive method for cancer treatment, in which cancer tissues is destroyed by coagulation. For the dosage planning quantitatively reliable numerical simulation are indispensable. To this end the identification of the thermal growth kinetics of the coagulated zone is of crucial importance. Mathematically, this problem is a nonlinear and nonlocal parabolic heat source inverse problem. We show in this paper that the temperature dependent thermal growth parameter can be identified uniquely from a one-point measurement.