Numerical Reconstruction of a Discontinuous Diffusive Coefficient in Variable-Order Time-Fractional Subdiffusion

Authors：Fan, Wei; Hu, Xindi; Zhu, Shengfeng^*

Source：JOURNAL OF SCIENTIFIC COMPUTING, 2023, 96(1): 13.

DOI：10.1007/s10915-023-02237-y

• Coefficient identification
• Variable-order
• Time-fractional
• Phase-field method
• Shape optimization

We consider a discontinuous coefficient reconstruction problem associated with a variable-order time-fractional subdiffusion equation. Both interface identification and reconstruction of piecewise constant coefficient values are considered. We show existence of a minimizer of the regularized inverse problem. Shape sensitivity analysis is performed to propose a shape gradient optimization algorithm allowing deformations. Moreover, an algorithm allowing shape and topological changes is proposed by a phase-field method with sensitivity analysis. Numerical examples are presented to demonstrate effectiveness of the two algorithms for recovering both subdiffusion interface and the two subdiffusion constants.