Commun. Comput. Phys., 12 (2012), pp. 981-1005.

Boosted Hybrid Method for Solving Chemical Reaction Systems with Multiple Scales in Time and Population Size

Yucheng Hu 1*, Assyr Abdulle 2, Tiejun Li 1

1 Laboratory of Mathematics and Applied Mathematics and School of Mathematical Sciences, Peking University, Beijing 100871, China.
2 Mathematics Section, Ecole Polytechnique Federale de Lausanne, CH-1015 Lausanne, Switzerland.

Received 19 April 2011; Accepted (in revised version) 30 November 2011
Available online 28 March 2012


A new algorithm, called boosted hybrid method, is proposed for the simulation of chemical reaction systems with scale-separation in time and disparity in species population. For such stiff systems, the algorithm can automatically identify scale-separation in time and slow down the fast reactions while maintaining a good approximation to the original effective dynamics. This technique is called boosting. As disparity in species population may still exist in the boosted system, we propose a hybrid strategy based on coarse-graining methods, such as the tau-leaping method, to accelerate the reactions among large population species. The combination of the boosting strategy and the hybrid method allow for an efficient and adaptive simulation of complex chemical reactions. The new method does not need a priori knowledge of the system and can also be used for systems with hierarchical multiple time scales. Numerical experiments illustrate the versatility and efficiency of the method.

AMS subject classifications: 65C05, 65C20

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Key words: Chemical reaction, multiscale, boosting, hybrid method.

*Corresponding author.
Email: (Y. Hu), (A. Abdulle), (T. Li)

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