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Optimal solution of a diffusion equation with a discrete source term
Author(s) -
Araújo A.,
Patrício F.,
Santos José L.
Publication year - 2010
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1204
Subject(s) - discretization , term (time) , generalization , context (archaeology) , diffusion equation , mathematics , optimal control , diffusion , mathematical optimization , mathematical analysis , engineering , physics , thermodynamics , paleontology , metric (unit) , operations management , quantum mechanics , biology
In this paper we study the numerical behavior of a diffusion equation with a discrete control source term. The equation is discretized in space by finite differences and in time by an implicit scheme. The control variables are calculated in order to minimize an objective function, taking into account some restrictions. We define two strategies to obtain the optimal solution, with and without time dependence. For the time‐independent case we present a theoretical result that characterizes the optimal solution. Some numerical results are presented in a context of a model that describes the oxygen concentration in a single chamber microbial fuel cell. A generalization of these results for the two‐dimensional model is also considered. Copyright © 2008 John Wiley & Sons, Ltd.