Calculation of the gradient of Tikhonov’s functional in solving coefficient inverse problems for linear partial differential equations

Autor:	Anatoly G. Yagola, Alexander S. Leonov, Alexander N. Sharov
Rok vydání:	2021
Předmět:	010101 applied mathematics Tikhonov regularization Applied Mathematics Applied mathematics 010103 numerical & computational mathematics Linear partial differential equations 0101 mathematics Inverse problem 01 natural sciences Mathematics
Zdroj:	Journal of Inverse and Ill-posed Problems. 30:23-34
ISSN:	1569-3945 0928-0219
Popis:	A fast algorithm for calculating the gradient of the Tikhonov functional is proposed for solving inverse coefficient problems for linear partial differential equations of a general form by the regularization method. The algorithm is designed for problems with discretized differential operators that linearly depend on the desired coefficients. When discretizing the problem and calculating the gradient, it is possible to use the finite element method. As an illustration, we consider the solution of two inverse problems of elastography using the finite element method: finding the distribution of Young’s modulus in biological tissue from data on its compression and a similar problem of determining the characteristics of local oncological inclusions, which have a special parametric form.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::ab207b03c45c5dc76cc4d90bfacebd2f https://doi.org/10.1515/jiip-2020-0109 Zobrazit plný text záznamu