General tooth boundary conditions for equation free modeling

SIAM Journal on Scientific Computing

Volumn 29, Issue 4, 2007, Pages 1495-1510

  Roberts, A J ^a   Kevrekidis, I G ^b  

^a UNIVERSITY OF SOUTHERN QUEENSLAND   (Australia)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

Coupling boundary conditions; Gap tooth scheme; High order consistency; Multiscale computation

Indexed keywords

BOLTZMANN EQUATION; DYNAMICAL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; INTERPOLATION; MOLECULAR DYNAMICS;

COUPLING BOUNDARY CONDITION; EQUATION-FREE MODELS; GAP-TOOTH SCHEME; HIGH ORDER CONSISTENCY; HIGH-ORDER; HIGHER-ORDER; MACROSCALES; MICROSCOPIC LEVELS; MICROSCOPIC SIMULATION; MULTISCALE COMPUTATION;

BOUNDARY CONDITIONS;

EID: 35748963495     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/060654554     Document Type: Article

References (21)

1. V. BALAKOTAIAH AND H.-C. CHANG, Hyperbolic homogenized models for thermal and solutal dispersion, SIAM J. Appl. Math., 63 (2003), pp. 1231-1258.
2. J. CARR, Applications of Center Manifold Theory, Applied Math. Sci. 35, Springer-Verlag, New York, 1981.
3. Z. CHEN AND T. Y. HOU, A mixed multiscale finite element method for elliptic problems with oscillating coefficients, Math. Comp., 72 (2002), pp. 541-576.
4. A. J. CHORIN AND P. STINIS, Problem Reduction, Renormalization, and Memory, Technical report, http://arXiv.org/abs/math.NA/ 0503612, 2005.
5. J. DOLBOW, M. A. KHALEEL, AND J. MITCHELL, Multiscale Mathematics Initiative: A Roadmap. Report from the 3rd DoE Workshop on Multiscale Mathematics, Technical report, Department of Energy, Washington, DC, http://www.sc.doe.gov/ascr/Research/AM/MultiscaleMathWorkshop3. pdf, 2004.
6. S.-I. EI, K. FUJII, AND T. KUNIHIRO, Renormalization-group method for reduction of evolution equations: Invariant manifolds and envelopes, Ann. Physics, 280 (2000), pp. 236-298.
7. C. W. GEAR, J. LI, AND I. G. KEVREKIDIS, The gap-tooth method in particle simulations, Phys. Lett. A, 316 (2003), pp. 190-195.
8. B. GUSTAFSSON AND J. MOSSINO, Non-periodic explicit homogenization and reduction of dimension: The linear case, IMA J. Appl. Math., 68 (2003), pp. 269-298.
9. T. Y. HOU AND X.-H. WU, A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comput. Phys., 134 (1997), pp. 169-189.
10. I. G. KEVREKIDIS, C. W. GEAR, J. M. HYMAN, P. G. KEVREKIDIS, O. RUNBORG, AND K. THEODOROPOULOS, Equation-free, coarse-grained multiscale computation: Enabling microscopic simulators to perform system level tasks, Comm. Math. Sci., 1 (2003), pp. 715-762.
11. Y. A. KUZNETSOV, Elements of Applied Bifurcation Theory, Appl. Math. Sci. 112, Springer-Verlag, New York, 1995.
12. T. MACKENZIE, Create Accurate Numerical Models of Complex Spatio-Temporal Dynamical Systems with Holistic Discretisation, Ph.D. thesis, University of Southern Queensland, Queensland, Australia, 2005.
13. B. MUDAVANHU AND R. E. O'MALLEY, A new renormalization method for the asymptotic solution of weakly nonlinear vector systems, University of Washington, Seattle, WA, 2003.
14. NATIONAL PHYSICAL LABORATORY, Modern Computing Methods, 2nd ed., Notes on Applied Science 16, Her Majesty's Stationery Office, London, 1961.
15. A. J. ROBERTS, Low-dimensional modeling of dynamics via computer algebra, Comput. Phys. Comm., 100 (1997), pp. 215-230.
16. A. J. ROBERTS, Holistic discretisation ensures fidelity to Burgers' equation, Applied Numer. Math., 37 (2001), pp. 371-396.
17. A. J. ROBERTS, Holistic discretization illuminates and enhances the numerical modeling of differential equations, in Topics in Applied and Theoretical Mathematics and Computer Science, V. V. Kluev and N. E. Mastorakis, eds., WSEAS, Athens, Greece, 2001, pp. 81-89.
18. A. J. ROBERTS, A holistic finite difference approach models linear dynamics consistently, Math. Comp., 72 (2002), pp. 247-262.
19. A. J. ROBERTS AND I. G. KEVREKIDIS, Higher order accuracy in the gap-tooth scheme for largescale dynamics using microscopic simulators, ANZIAM J., 46 (2004/2005), pp. C637-C657.
20. G. SAMAEY, I. G. KEVREKIDIS, AND D. ROOSE, Damping factors for the gap-tooth scheme, in Multiscale Modeling and Simulation, S. Attinger and P. Koumoutsakos, eds., Lect. Notes Comput. Sci. Eng. 39, Springer-Verlag, New York, 2004, pp. 93-102.
21. G. SAMAEY, D. ROOSE, AND I. G. KEVREKIDIS, The gap-tooth scheme for homogenization problems, Multiscale Model. Simul., 4 (2005), pp. 278-306.