Coupling algorithms for calculating sensitivities of smoluchowski's coagulation equation

SIAM Journal on Scientific Computing

Volumn 32, Issue 2, 2010, Pages 635-655

  Man, Peter L W ^a   Norris, James R ^b   Bailleul, Ismael F ^b   Kraft, Markus ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Coagulation; Coupling; Modeling; Sensitivity; Simulation; Smoluchowski

Indexed keywords

PARAMETER ESTIMATION; STOCHASTIC SYSTEMS;

CENTRAL DIFFERENCE; COUPLING ALGORITHMS; MARCUS-LUSHNIKOV PROCESS; MODELING; PARAMETRIC DERIVATIVES; SENSITIVITY; SIMULATION; SMOLUCHOWSKI; SMOLUCHOWSKI COAGULATION EQUATION; STOCHASTIC ALGORITHMS;

COAGULATION;

EID: 77950835710     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/09075679X     Document Type: Article

References (20)

1. A. ElBECK AND W. WAGNER, Stochastic particle approximations for Smoluchoski's coagulation equation, Ann. Appl. Probab., 11 (2001), pp. 1137-11 65. (Pubitemid 33571757)
2. A. ElBECK AND W. WAGNER, An efficient stochastic algorithm for studying coagulation dynamics and gelation phenomena, SIAM J. Sci. Comput., 22 (2000), pp. 802-821. (Pubitemid 32546982)
3. M. GoODSON AND M. KRAFT, An efficient stochastic algorithm for simulating nano-particle dynamics, J. Comput. Phys., 183 (2002), pp. 210-232. (Pubitemid 36100556)
4. A. KOLODKO AND K. SABELFELD, Stochastic particle methods for Smoluchowski coagulation equation: Variance reduction and error estimations, Monte Carlo Methods Appl., 9 (2003), pp. 315-339.
5. H. BRIESEN, Hierarchical characterization of aggregates for Monte Carlo simulations,AIChE J., 52 (2006), pp. 2436-2446. (Pubitemid 44013407)
6. H. ZHAO, A. MAISELS, T. MATSOUKAS, AND C. ZHENG, Analysis of four Monte Carlo methods for the solution of population balances in dispersed systems, Powder Technol., 173 (2007), pp. 38-50. (Pubitemid 46454402)
7. A. BRAUMANN, M. J. GOODSON, M. KRAFT, AND P. R. MORT, Modelling and validation of granulation with heterogeneous binder dispersion and chemical reaction, Chem. Eng. Sci., 62 (2007), pp. 4717-4728. (Pubitemid 47176537)
8. R. I. A. PATTERsON AND M. KRAFT, Models for the aggregate structure of soot particles, Combust. Flame, 151 (2007), pp. 160 - 172. (Pubitemid 47374105)
9. H. B. ZHAO AND C. G. ZHENG, A new event-driven constant-volume method for solution of the time evolution of particle size distribution, J. Comput. Phys., 228 (2009), pp. 1412-1428.
10. A. VlKHANSKY AND M. KRAFT, A Monte Carlo methods for identification and sensitivity analysis of coagulation processes, J. Comput. Phys., 200 ( 2004), pp. 50-59. (Pubitemid 39238560)
11. A. VIKHANSKY, M. KRAFT, M. SIMON, S. SCHMIDT, AND H. J. BART, Droplets population balance in a rotating disc contactor: An inverse prob lem approach, AIChE J., 52 (2006), pp. 1441-1450. (Pubitemid 43815807)
12. S. ASMUSSEN AND P. W. GLYNN, Stochastic Simulation: Algorithms and Analysis, Springer, New York, 2007, pp. 224 - 230.
13. R. I. A. PATTERSON, J. SINGH, M. BALTHASAR, M. KRAFT, AND J. R. NORRIS, The linearprocess deferment algorithm: A new technique for solving population balance equations, SIAM J. Sci. Comput., 28 (2006), pp. 303-320.
14. J. R. NORRIS, Smoluchowski's coagulation equation: Uniqueness, nonuniqueness and a hydrodynamic limit for the stochastic coalescent, Ann. App l. Probab., 9 (1999), pp. 78 - 109.
15. I. JEON, Existence of gelling solutions for coagulation-fragmentation equations, Comm. Math. Phys., 194 (1998), pp. 541 - 567. (Pubitemid 128360080)
16. R. I. A. PATTERSON, J. SINGH, M. BALTHASAR, M. KRAFT, AND W. WAGNER, Extending stochastic soot simulation to higher pressures, Combu st. Flame, 145 (2006), pp. 638-642.
17. N. MORGAN, M. KRAFT, M. BALTHASAR, D. WONG, M. FRENKLACH, AND P. MITCHELL, Numerical simulations of soot aggregation in premixed laminar flames, Proc. Combust. Inst., 31 (2007), pp. 693-700. (Pubitemid 47424441)
18. M. CELNIK, R.I.A.PATTERSON, M. KRAFT, AND W. WAGNER, Coupling a stochastic soot population balance to gas-phase chemistry using operator splitting, Combust. Flame, 148 (2007), pp. 158-176. (Pubitemid 46072801)
19. D. J. ALDOUS, Deterministic and stochastic models for coalescence (aggregation and coagulation): A review of the mean-field theory for probabilists, Bernoulli, 5 (1999), pp. 3-48.
20. P. L. W. MAN, M. KRAFT, AND J. R. NORRIS, Coupling algorithms for calculating sensitivities of population balances, in Numerical Analysis and Ap plied Mathematics, AIP Conf. Proc. 1048, Amer. Inst. Phys., Melville, NY, 2008, pp. 927-930.