American Institute of Mathematical Sciences

Advanced
2009, 2009(Special): 123-132. doi: 10.3934/proc.2009.2009.123

Numerical solution and fast-slow decomposition of a population of weakly coupled systems

Alexandre Caboussat 1, and  Allison Leonard 2,

1. 

University of Houston, Department of Mathematics, 4800 Calhoun Rd, Houston, Texas 77204 - 3008
2. 

University of Houston, Department of Mathematics, 4800 Calhoun Rd, Houston, TX 77204-3008, United States

Received  June 2008 Revised  June 2009 Published  September 2009

The modeling of the microphysics of a population of atmospheric particles interacting through a common medium leads to the solution of a large system of weakly coupled differential-algebraic equations. An implicit time discretization of the system of differential-algebraic equations is solved with a Newton method at each time step. The structure of the global system and the sparsity of the Newton matrix allow the efficient use of a Schur complement approach for the decoupling of the various subsystems at the discrete level. A numerical approach for the decomposition of the population into fast and slow subsystems is proposed. Numerical results are presented for organic atmospheric particles to illustrate the properties of the method.
Keywords: Schur complement, Differential-algebraic equations, air quality modeling, weakly coupling, fast/slow decomposition.
Mathematics Subject Classification: Primary: 65L05, 65L80, 65F05; Secondary: 70K70.
Citation: Alexandre Caboussat, Allison Leonard. Numerical solution and fast-slow decomposition of a population of weakly coupled systems. Conference Publications, 2009, 2009 (Special) : 123-132. doi: 10.3934/proc.2009.2009.123
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