Topological Sensitivity Analysis Method in Identifying of Point Sources via Time-Fractional Diffusion Equation

A direct sampling method for time-fractional diffusion equation

“…The sampling method was introduced by Colton and Kirsch [8], where they used far-field observation data to determine the position of a scatterer under the Helmholtz equation. The sampling method consists a variety of sub-methods, including the factorization method [18], the linear sampling method [16,19,32], reverse time migration [5], direct (orthogonality) sampling method [3,6,7,36] and the topological sensitivity method [40,41]. In the direct sampling method, or the orthogonality sampling method, the index function is constructed by pairing the boundary observations with some probing function under an inner product.…”

Combination of Multigrid with Constraint Data for Inverse Problem of Nonlinear Diffusion Equation

“…In general, the inverse problems of diffusion equations are ill-posed, that is, their solution does not fulfill the requirement of the aforementioned conditions in the presence of a tiny disturbance to the input data. To overcome such difficulties, a variety of methods have been proposed [6][7][8][9][10][11][12]. To date, considerable efforts have been devoted to formulating accurate and efficient methods of inverse diffusion problems.…”