Optimization of gradient algorithm for solving the nonlinear inverse potential problem

Article type: Research Article

Authors: Akimova, Elena N.^{a; b; *} | Misilov, Vladimir E.^{a; b}

Affiliations: [a] Krasovskii Institute of Mathematics and Mechanics, Ural Branch of RAS, Ekaterinburg, Russia | [b] Yeltsin Ural Federal University, Ekaterinburg, Russia

Correspondence: [*] Corresponding author: Elena N. Akimova, Krasovskii Institute of Mathematics and Mechanics, Ural Branch of RAS, Ekaterinburg, Russia. E-mail: aen15@yandex.ru.

Abstract: The paper is devoted to developing the new and memory-efficient parallel algorithms based on the nonlinear conjugate gradient method. The algorithms are aimed to solving the nonlinear inverse potential problem of finding a boundary surface between two layers with constant densities. The algorithms utilize the structure of the Jacobian matrix of integral operator by excluding the less significant elements. The efficient implementation for multicore CPU was developed. Investigation of efficiency and speedup of the parallel algorithm was performed. A model problem with synthetic gravitational data was solved. It was shown that the new algorithms reduce the computation time in comparison with the unmodified one.

Keywords: Potential theory, inverse problem, nonlinear conjugate gradient method, band matrix, parallel algorithmPACS: 02.60.Nm 93.85.Hj 07.05.Tp 89.20.Ff

DOI: 10.3233/JCM-190025

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 19, no. 2, pp. 417-424, 2019