A discontinuous Galerkin implementation of a domain decomposition method for kinetic-hydrodynamic coupling multiscale problems in gas dynamics and device simulations

Journal of Computational Physics

Volumn 225, Issue 2, 2007, Pages 1314-1330

  Chen, Shanqin ^a   E, Weinan ^b   Liu, Yunxian ^c   Shu, Chi Wang ^d  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b PRINCETON UNIVERSITY   (United States)

^c SHANDONG UNIVERSITY   (China)

^d BROWN UNIVERSITY   (United States)

Author keywords

Discontinuous Galerkin method; Domain decomposition method; Gas dynamics; High field model; Hydrodynamics model; Semi conductor device simulation

Indexed keywords

COMPRESSIBILITY OF GASES; GALERKIN METHODS; GAS DYNAMICS; GASES; HYDRODYNAMICS; INTEGRAL EQUATIONS; NUMERICAL METHODS; PROBLEM SOLVING; SEMICONDUCTOR DEVICES; SEMICONDUCTOR DOPING;

DEVICE SIMULATIONS; DISCONTINOUS GALERKIN METHODS; DOMAIN-DECOMPOSITION METHODS; HIGH FIELD MODELS; HYDRODYNAMIC MODELING; MACRO-MODELS; MULTISCALE PROBLEM; SEMI CONDUCTOR DEVICES; SEMI-CONDUCTOR DEVICE SIMULATION; SUBDOMAIN;

DOMAIN DECOMPOSITION METHODS;

EID: 34547596872     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.01.025     Document Type: Article

References (39)

1. Abraham F.F., Broughton J.Q., Bernstein N., and Kaxiras E. Concurrent coupling of length scales: methodology and application. Phys. Rev. B 60 (1999) 2391-2402
2. Abraham F.F., Broughton J.Q., Bernstein N., and Kaxiras E. Spanning the continuum to quantum length scales in a dynamics simulation of brittle fracture. Europhys. Lett. 44 (1998) 783-787
3. Bourgat J.F., Le Tallec P., Perthame B., and Qiu Y. Coupling Boltzmann and Euler equations without overlapping, Domain Decomposition Methods in Science and Engineering. Am. Math. Soc. (1992) 377-398
4. Bourgat J.F., Le Tallec P., and Tidriri M. Coupling Boltzmann and Navier-Stokes equations by friction. J. Comput. Phys. 127 (1996) 227-245
5. Carrillo J.A., Gamba I.M., Majorana A., and Shu C.-W. A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices. Performance and comparisons with Monte Carlo methods. J. Comput. Phys. 184 (2003) 498-525
6. Carrillo J.A., Gamba I.M., and Shu C.-W. Computational macroscopic approximations to the 1-D relaxation-time kinetic system for semiconductors. Physica D 146 (2000) 289-306
7. Cercignani C. Mathematical Methods in Kinetic Theory (1990), Plenum Press, New York
8. Cercignani C., Gamba I., Jerome J., and Shu C.-W. Applicability of the high field model: a preliminary numerical study. VLSI Design 8 (1998) 275-282
9. Cercignani C., Gamba I., Jerome J., and Shu C.-W. Device benchmark comparisons via kinetic, hydrodynamic, and high-field models. Comput. Methods Appl. Mech. Eng. 181 (2000) 381-392
10. Cercignani C., Gamba I., Jerome J., and Shu C.-W. A domain decomposition method for silicon devices. Transport Theory and Statistical Physics 29 (2000) 525-536
11. Cercignani C., Gamba I.M., and Levermore C.D. High field approximations to Boltzmann-Poisson system boundary conditions in a semiconductor. Appl. Math. Lett. 10 (1997) 111-117
12. Cockburn B., Hou S., and Shu C.-W. The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case. Math. Comp. 54 (1990) 545-581
13. Cockburn B., Lin S.-Y., and Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one dimensional systems. J. Comput. Phys. 84 (1989) 90-113
14. Cockburn B., and Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework. Math. Comp. 52 (1989) 411-435
15. Cockburn B., and Shu C.-W. The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems. J. Comput. Phys. 141 (1998) 199-224
16. Cockburn B., and Shu C.-W. The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35 (1998) 2440-2463
17. Cockburn B., and Shu C.-W. Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput. 173 (2001) 173-261
18. Degond P., Jin S., and Mieussens L. A smooth transition model between kinetic and hydrodynamic equations. J. Comput. Phys. 209 (2005) 665-694
19. E W., and Engquist B. The heterogeneous multi-scale methods. Comm. Math. Sci. 1 (2003) 87-132
20. E W., Li X., and Vanden-Eijnden E. Some recent progress in multiscale modeling. In: Attinger S., and Koumoutsakos P. (Eds). Multiscale Modeling and Simulation. Lecture Notes in Computational Science and Engineering Vol. 39 (2004), Springer 3-22
21. Flekkoy E.G., Wagner G., and Feder J. Hybrid model for combined particle and continuum dynamics. Europhys. Lett. 52 (2000) 271-276
22. Hadjiconstantinou N.G. Hybrid atomistic-continuum formulations and the moving contact-line problem. J. Comput. Phys. 154 (1999) 245-265
23. Hadjiconstantinou N.G., and Patera A.T. Heterogeneous atomistic-continuum representation for dense fluid systems. Intl. J. Modern Phys. C 8 (1997) 967-976
24. Jerome J.W. Analysis of Charge Transport, a Mathematical Study of Semiconductor Devices (1996), Springer, Berlin
25. Jiang G., and Shu C.-W. Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126 (1996) 202-228
26. Kadowaki H., and Liu W.K. Bridging multiscale method for localization problems. Comput. Methods Appl. Mech. Eng. 193 (2004) 3267-3302
27. Le Tallec P., and Perlat J.P. Coupling kinetic models with Navier-Stokes equations. CFD Review 2 (1998) 833-855
28. Liu Y., and Shu C.-W. Local discontinuous Galerkin methods for moment models in device simulations: formulation and one dimensional results. J. Comput. Electron. 3 (2004) 263-267
29. Y. Liu, C.-W. Shu, Local discontinuous Galerkin methods for moment models in device simulations: performance assessment and two dimensional results, Appl. Numer. Math., in press.
30. Mandal J.C., and Deshpande S.M. Kinetic flux vector splitting for Euler equations. Comput. Fluids 23 (1994) 447-478
31. Nie X., Chen S., E W., and Robbins M.O. A continuum and molecular dynamics hybrid method for micro- and nano-fluid flow. J. Fluid Mech. 500 (2004) 55-64
32. O'Connell S.T., and Thompson P.A. Molecular dynamics-continuum hybrid computations: a tool for studying complex fluid flows. Phys. Rev. E 52 (1995) R5792-R5795
33. Park H.S., Karpov E.G., Liu W.K., and Klein P.A. The bridging scale for two-dimensional atomistic/continuum coupling. Phil. Mag. A. 85 (2005) 79-113
34. Poupaud F. Derivation of a hydrodynamic system hierarchy for semiconductors from the Boltzmann equation. Appl. Math. Lett. 4 1 (1991) 75-79
35. Qian D., Wagner G.J., and Liu W.K. A multiscale projection method for the analysis of carbon nanotubes. Comput. Methods Appl. Mech. Eng. 193 (2004) 1603-1632
36. Smoller J. Shock Waves and Reaction-Diffusion Equations (1983), Springer-Verlag, Berlin
37. Shu C.-W., and Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77 (1988) 439-471
38. Tiwari S., and Klar A. An adaptive domain decomposition procedure for Boltzmann and Euler equations. J. Comput. Appl. Math. 90 (1998) 223-237
39. Yan J., and Shu C.-W. A local discontinuous Galerkin method for KdV type equations. SIAM J. Numer. Anal. 40 (2002) 769-791