no. 8
Numerical Analysis
A dynamic optimization problem related to organic aerosols
[Un problème d'optimization dynamique lié à la modélisation d'aérosols organiques]

Présenté par : Roland Glowinski

Amundson, Neal R.1 ; Caboussat, Alexandre1 ; He, Jiwen1 ; Landry, Chantal2 ; Seinfeld, John H.3
1 Department of Mathematics, University of Houston, Houston, TX 77204, USA
2 Institute of Analysis and Scientific Computing, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
3 Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
Comptes Rendus. Mathématique, Tome 344 (2007) no. 8, pp. 519-522.

Nous proposons un modèle pour le calcul de l'équilibre thermodynamique et la séparation de phases entre une particule et la phase gazeuse. La dynamique des transferts de masse entre particule et phase gazeuse est caractérisée par un système d'équations différentielles couplées avec un problème d'optimisation décrivant l'équilibre interne de la particule. Les conditions de premier ordre et une discrétisation implicite des équations différentielles forment un système d'équations non linéaires qui est traité avec une méthode de point intérieur couplée à une itération de Newton. Des résultats numériques et une comparaison des temps caractéristiques montrent la précision et l'efficacité de notre algorithme.

A model that rigorously computes the gas–particle partitioning and liquid–liquid equilibrium for organic atmospheric aerosol particles is presented. The dynamics of the mass transfers between the particle and the gas phase are modeled with differential equations and are coupled with a constrained optimization problem for the thermodynamic equilibrium inside the particle. The nonlinear system composed by the first order optimality conditions coupled with the discretized differential equations is solved with an interior-point method and a Newton method. The resulting linear system is decoupled with sequential quadratic programming techniques. Numerical results and comparisons of time scales show the accuracy and efficiency of our algorithm.

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DOI : 10.1016/j.crma.2007.03.002
Amundson, Neal R. 1 ; Caboussat, Alexandre 1 ; He, Jiwen 1 ; Landry, Chantal 2 ; Seinfeld, John H. 3

1 Department of Mathematics, University of Houston, Houston, TX 77204, USA
2 Institute of Analysis and Scientific Computing, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
3 Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA 
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Amundson, Neal R.; Caboussat, Alexandre; He, Jiwen; Landry, Chantal; Seinfeld, John H. A dynamic optimization problem related to organic aerosols. Comptes Rendus. Mathématique, Tome 344 (2007) no. 8, pp. 519-522. doi : 10.1016/j.crma.2007.03.002. http://www.numdam.org/articles/10.1016/j.crma.2007.03.002/

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[2] Amundson, N.R.; Caboussat, A.; He, J.W.; Seinfeld, J.H. Primal-dual interior-point method for an optimization problem related to the modeling of atmospheric organic aerosols, J. Optim. Theory Appl., Volume 130 (2006) no. 3, pp. 375-407

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