Low-variance direct Monte Carlo simulations using importance weights

ESAIM: Mathematical Modelling and Numerical Analysis

Volumn 44, Issue 5, 2010, Pages 1069-1083

  Al Mohssen, Husain A ^a   Hadjiconstantinou, Nicolas G ^a  

^a Massachusetts Institute of Technology   (United States)

Author keywords

DSMC; Microscale gas flow; Variance reduction

Indexed keywords

EID: 77956742472     PISSN: 28227840     EISSN: 28047214     Source Type: Journal    
DOI: 10.1051/m2an/2010052     Document Type: Article

References (28)

1. F.J. Alexander, A.L. Garcia and B.J. Alder, Cell size dependence of transport coefficients in stochastic particle algorithms. Phys. Fluids 10 (1998) 1540-1542.
2. H.A. Al-Mohssen, An Excursion with the Boltzmann Equation at Low Speeds: Variance-Reduced DSMC. Ph.D. Thesis, Massachusetts Institute of Technology, Dept. of Mechanical Engineering, Cambridge (2010).
3. H.A. Al-Mohssen and N.G. Hadjiconstantinou, Yet Another Variance Reduction Method for Direct Monte Carlo Simulations of Low-Signal Flows, in 26th International Symposium on Rarefied Gas Dynamics, T. Abe Ed., AIP, Kyoto (2008) 257-262.
4. L.L. Baker and N.G. Hadjiconstantinou, Variance reduction for Monte Carlo solutions of the Boltzmann equation. Phys. Fluids 17 (2005) 051703.
5. L.L. Baker and N.G. Hadjiconstantinou, Variance-reduced particle methods for solving the Boltzmann equation. J. Comput. Theor. Nanosci. 5 (2008) 165-174.
6. L.L. Baker and N.G. Hadjiconstantinou, Variance-reduced Monte Carlo solutions of the Boltzmann equation for low-speed gas flows: A discontinuous Galerkin formulation. Int. J. Numer. Methods Fluids 58 (2008) 381-402.
7. G.A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press (1994).
8. C. Cercignani, The Boltzmann equation and its applications. Springer-Verlag (1988).
9. C. Cercignani, Mathematical Methods in Kinetic Theory. Plenum Press (1990).
10. C. Cercignani, Slow Rarefied Flows: Theory and Application to Micro-Electro-Mechanical Systems. Springer (2006).
11. J. Chun and D.L. Koch, A direct simulation Monte Carlo method for rarefied gas flows in the limit of small Mach number. Phys. Fluids 17 (2005) 107107.
12. A. Doucet and X. Wang, Monte Carlo methods for signal processing: a review in the statistical signal processing context. IEEE Signal Process. Mag. 22 (2005) 152-170.
13. A.L. Garcia and W. Wagner, Time step truncation error in direct simulation Monte Carlo. Phys. Fluids 12 (2000) 2621-2633.
14. P. Glasserman, Monte Carlo Methods in Financial Engineering. Springer (2004).
15. N.G. Hadjiconstantinou, Analysis of discretization in the direct simulation Monte Carlo. Phys. Fluids 12 (2000) 2634-2638.
16. N.G. Hadjiconstantinou, The limits of Navier-Stokes theory and kinetic extensions for describing small-scale gaseous hydrodynamics. Phys. Fluids 18 (2006) 111301.
17. N.G. Hadjiconstantinou, A.L. Garcia, M.Z. Bazant and G. He, Statistical error in particle simulations of hydrodynamic phenomena. J. Comput. Phys. 187 (2003) 274-297.
18. T.M.M. Homolle and N.G. Hadjiconstantinou, Low-variance deviational simulation Monte Carlo. Phys. Fluids 19 (2007) 041701.
19. T.M.M. Homolle and N.G. Hadjiconstantinou, A low-variance deviational simulation Monte Carlo for the Boltzmann equation. J. Comput. Phys. 226 (2007) 2341-2358.
20. C.D. Landon, Weighted Particle Variance Reduction of Direct Simulation Monte Carlo for the Bhatnagar-Gross-Krook Collision Operator. M.S. Thesis, Massachusetts Institute of Technology, Dept. of Mechanical Engineering, Cambridge (2010).
21. H.C. Ottinger, B.H.A.A. van den Brule and M.A. Hulsen, Brownian configuration fields and variance reduced CONNFFESSIT. J. Non-Newton. Fluid Mech. 70 (1997) 255-261.
22. W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical Recipes. Cambridge University Press (2007).
23. G.A. Radtke and N.G. Hadjiconstantinou, Variance-reduced particle simulation of the Boltzmann transport equation in the relaxation-time approximation. Phys. Rev. E 79 (2009) 056711.
24. R.Y. Rubinstein, Simulation and the Monte Carlo Method. Wiley (1981).
25. D.W. Scott, Multivariate Density Estimation. John Wiley & Sons (1992).
26. Y. Sone, Kinetic Theory and Fluid Dynamics. Birkhauser (2002).
27. W. Wagner, A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation. J. Stat. Phys. 66 (1992) 1011-1044.
28. W. Wagner, Deviational Particle Monte Carlo for the Boltzmann Equation. Monte Carlo Methods Appl. 14 (2008) 191-268.