On Some Classes of Inverse Problems on Determining the Source Function

DOI

10.2991/aisr.k.201029.047How to use a DOI?

Keywords

parabolic equation, inverse problem, finite element method, source function

Abstract

The inverse problem of determining the solution, the location, and intensity of a point source in the multidimensional advection-dispersion-reaction equation is considered. The equation is supplemented with the initial and boundary conditions of the Neumann or Dirichlet type. Methods for a numerical solution of similar inverse problems in the multidimensional case are considered in many articles. However, most of them are based on reducing the problem to an optimal control problem and minimizing the corresponding functional, which as a rule requires large computational capabilities and does not always lead to the desired result. Our numerical algorithm for determining the location of the source is justified using an explicit asymptotic formula for the Green function of the corresponding elliptic problem with a parameter. The intensity is determined by the Duhamel formula and the Tikhonov regularization. The numerical implementation is based on the finite element method and the finite difference method for the corresponding system of ordinary differential equations. The results of numerical experiments of recovering the location and intensity of a source are presented. Numerical experiments demonstrate good convergence. The corresponding software packages of recovering pollution sources were created which can be included into intelligent decision support system for sustainable regional development.

Copyright

© 2020, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Safonov Egor
AU  - Pyatkov Sergei
PY  - 2020
DA  - 2020/11/10
TI  - On Some Classes of Inverse Problems on Determining the Source Function
BT  - Proceedings of the 8th Scientific Conference on Information Technologies for Intelligent Decision Making Support (ITIDS 2020)
PB  - Atlantis Press
SP  - 242
EP  - 248
SN  - 1951-6851
UR  - https://doi.org/10.2991/aisr.k.201029.047
DO  - 10.2991/aisr.k.201029.047
ID  - Egor2020
ER  -