Topological sensitivity method for reconstruction of the spatial component in the source term of a time-fractional diffusion equation

Abstract

In the paper, an inverse source problem for a time-fractional diffusion equation is formulated and proved. The topological sensitivity analysis method is presented. The considered problem is formulated as a topology optimization one. The proposed process leads to a non-iterative reconstruction algorithm can be applied for large class of cost functional. The unknown shape of the term source support is reconstructed using a level-set curve of the topological gradient. Several numerical simulations are presented to show the efficiency and the accuracy of the algorithm.