MATH 273A: Scientific Computation
Fall quarter, 2005
TOPICS IN APPLIED MATHEMATICS AND COMPUTATIONAL SCIENCE
Instructor: Bo Li
REFERENCES
General: Crystalline Defects, Elasticity, Fluid Mechanics,
Numerical ODE and PDE
- Crystalline Defects
- D. Hull and D. J. Bacon, Introduction to Dislocations, 4th ed.,
Butterworth-Heinemann, 2001.
- C. Kittel, Introduction to Solid State Physics,, 7th ed., Wiley, 1996.
- R. Phillips, Crystals, Defects and Microstructures : Modeling Across Scales,
Cambridge University Press, 2001.
- Elasticity
- L. D. Landau and E. M. Lifshitz, Theory of Elasticity,
3rd ed., Butterworth-Heinemann, 1986.
- A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity,
4th ed., Dover, 1944.
- I. S. Sokolnikoff, Mathematical Theory of Elasticity, 2nd ed., Krieger, 1983.
- Fluid Mechanics
- G. K. Batchelor, An Introduction to Fluid Dynamics, Cambridge University
Press, 1967.
- I. M. Cohen and P. K. Kundu, Fluid Mechanics, Academic Press, 2004.
- I. G. Currie, Fundamental Mechanics of Fluids, 2nd ed., McGraw-Hill, 1993.
- L. D. Landau and E. M. Lifshitz, Fluid Mechanics, 2nd ed.,
Butterworth-Heinemann, 1987.
- Numerical ODE and PDE
- O. Axelsson and V. A. Barker, Finite Element Solution of Boundary Value
Problems: Theory and Computation, Academic Press, 1984.
- D. Braess, Finite Elements: Theory, Fast Solvers, and Applications
in Solid Mechanics, Cambridge University Press, 2001.
- C. W. Gear, Numerical Initial Value Problems in Ordinary Differential
Equations, Prentice Hall, 1971.
- E. Hairer and G. Wanner, Solving Ordinary Differential
Equations, II, 2nd ed., Springer-Verlag, 1996.
- T. J. R. Hughes, The Finite Element Method, Dover, 2000.
- C. Johnson, Numerical Solution of Partial Differential Equations
by the Finite Element Method, Cambridge University Press, 1987.
- R. J. LeVeque, Numerical Methods for Conservation Laws, 2nd ed.,
Birkh\344user Verlag, 1992.
- K. W. Morton and D. F. Mayers, Numerical Solution of Partial Differential
Equations, Cambridge University Press, 1995.
- J. C. Strikwerda, Finite Difference Schemes and Partial Differential
Equations, Chapman & Hall, 1989.
- O. C. Zienkiewicz, The Finite Element Method, 3rd ed, McGraw-Hill,
New York, 1977.
Multiscale Methods
- The quasicontinuum method
-
R. E. Miller and E. B. Tadmor,
The quasicontinuum method: Overview, applications and current directions,
J. Computer-Aided Materials Design, 9, 203-239, 2002.
-
V. B. Shenoy, R. Miller, E. B. Tadmor, D. Rodney, R. Phillips and M. Ortiz,
An adaptive finite element approach to atomic-scale mechanics - the quasicontinuum method,
J. Mech. Phys. Solids, 47, 611-642, 1999.
-
J. Knap J and M. Ortiz, An analysis of the quasicontinuum method,
J. Mech. Phys. Solids, 49, 1899-1923, 2001.
- The heterogeneous multiscale method
- A. Abdulle and W. E, Finite difference heterogeneous multi-scale method
for homogenization problems, J. Comput. Phys., 191, 18-39, 2003.
- W. E, Analysis of the heterogeneous multiscale method for ordinary
differential equations, Comm. Math. Sci., 1(3), 423-436, 2003.
- W. E, B. Engquist, X. Li, W. Ren, E. Vanden-Eijnden, The
heterogeneous multiscale method: A review, preprint, 2005.
- W. E, P. Ming, and P. Zhang, Analysis of the heterogeneous multiscale method
for elliptic homogenization problems, J. Amer. Math Soc., 8, 121-156, 2004.
- B. Engquist and R. Tsai, Heterogeneous multiscale methods for stiff
ordinary differential equations, preprint, 2004.
- X. Yue and W. E, The local microscale problem in the multiscale modelling of
strongly heterogeneous media: effect of boundary conditions and cell size,
preprint, 2005.
- Coupling molecular dynamics and continuum simulations
- E. B. Tadmor, G. S. Smith, N. Bernstein, and E. Kaxiras,
Mixed finite element and atomistic formulation for complex crystals,
Phys. Rev. B, 59, 235-245, 1999.
- J. Q. Broughton, F. F. Abraham, N. Bernstein, and E. Kaxiras,
Concurrent coupling of length scales: Methodology and application,
Phys. Rev. B, 60(4), 2391-2403, 1999.
- W. E and Z. Huang, Matching conditions in atomistic-continuum modeling of materials,
Phys. Rev. Lett., 87(13), 135501, 2001.
- X. B. Nie, S. Y. Chen, W. E., and M. O. Robbins, A continuum and molecular
dynamics hybrid method for micro-and nano-fluid flow,
J. Fluid Mech., 500, 55-64, 2004.
- T. Qian and X.-P. Wang, Driven cavity flow: From molecular dynamics to
continuum hydrodynamics, Multiscale Model. Simul., 3(4), 749-763, 2005.
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Interface Dynamics
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Energy Minimization
Last updated by Bo Li on October 17, 2005.