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

被引：1

作者：

Fan, Wei ^{[1
]}

Hu, Xindi ^{[1
]}

Zhu, Shengfeng ^{[1
,2
]}

机构：

[1] East China Normal Univ, Dept Math, Shanghai 200241, Peoples R China

[2] East China Normal Univ, Shanghai Key Lab Pure Math & Math Practice, Shanghai 200241, Peoples R China

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2023年 / 96卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Coefficient identification; Variable-order; Time-fractional; Phase-field method; Shape optimization; FINITE-ELEMENT APPROXIMATIONS; INVERSE SOURCE PROBLEM; LEVEL SET METHOD; SHAPE OPTIMIZATION; EQUATION; ACCURACY;

D O I：

10.1007/s10915-023-02237-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：33

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