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

Pages: 123 - 132, Issue Special, September 2009

 Abstract        Full Text (244.9K)              

Alexandre Caboussat - University of Houston, Department of Mathematics, 4800 Calhoun Rd, Houston, Texas 77204 - 3008, United States (email)
Allison Leonard - University of Houston, Department of Mathematics, 4800 Calhoun Rd, Houston, TX 77204-3008, United States (email)

Abstract: 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:  Differential-algebraic equations, weakly coupling, Schur complement, fast/slow decomposition, air quality modeling
Mathematics Subject Classification:  Primary: 65L05, 65L80, 65F05; Secondary: 70K70

Received: June 2008;      Revised: June 2009;      Published: September 2009.