KD-Tree based adaptive interpolation algorithm for chemical kinetics problems with interval parameters

 
PIIS023408790001940-8-1
DOI10.31857/S023408790001940-8
Publication type Article
Status Published
Authors
Affiliation: Moscow Aviation Institute, Department of Information Technology and Applied Mathematics
Address: Russian Federation
Affiliation: Dorodnicyn Computing Center of RAS
Address: Russian Federation
Affiliation: Moscow Aviation Institute, Department of Information Technology and Applied Mathematics
Address: Russian Federation
Journal nameMatematicheskoe modelirovanie
EditionVolume 30 Number 12
Pages129-144
Abstract

In this paper, the question of simulating chemical processes with uncertainty in parameters is considered. A new approach is suggested, which consists in building a dynamic structured net based on a kd-tree, over a space formed by the interval parameters. When the algorithm is executed, during each integration step a piecewise constant polynomial function is build, interpolating the connection between the solution and the exact values of interval parameters. The algorithm has been tested on chemical kinetics problems, including combustion processes, demonstrating its efficiency and wide area of application.

Keywordsinterval systems of ODE, dynamic structured grid, Lotka-Volterra model, chemical kinetics
Received10.11.2018
Publication date30.11.2018
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