A numerical method for reconstructing the potential in fractional Calder\'{o}n problem with a single measurement

Autor:	Li, Xinyan
Rok vydání:	2024
Předmět:	Mathematics - Numerical Analysis
Druh dokumentu:	Working Paper
Popis:	In this paper, we develop a numerical method for determining the potential in one and two dimensional fractional Calder\'{o}n problems with a single measurement. Finite difference scheme is employed to discretize the fractional Laplacian, and the parameter reconstruction is formulated into a variational problem based on Tikhonov regularization to obtain a stable and accurate solution. Conjugate gradient method is utilized to solve the variational problem. Moreover, we also provide a suggestion to choose the regularization parameter. Numerical experiments are performed to illustrate the efficiency and effectiveness of the developed method and verify the theoretical results. Comment: 18 pages and 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.16711 Zobrazit plný text záznamu View this record from Arxiv