正在建设中. 欢迎各位提宝贵意见和积极参与!
吴金彪老师计划中的讨论班安排
注意: 开学后, 他将可能根据参加讨论班的对象
对内容作适当的调整.
下学期的讨论班的内容只是有一些初步设想, 目前想可能在如下方面给学生出题:
热弹性力学方程组的解析解和数值解.
反应扩散方程的稳定化格式.
Stokes方程的数值解.
汤华中老师计划中的讨论班安排
注意: 开学后, 我将可能根据参加讨论班的对象对内容作适当的调整.
- 主要内容
- 能量方法应用于初边值问题
- Laplace 变换方法应用于初边值问题
- 能量方法应用于差分近似
- Laplace 变换方法应用于差分近似
- Laplace 变换方法应用于全离散近似: 模态分析(Normal Mode Analysis)
- Normal mode Analysis 的应用
- 有限差分近似的离散算子近似
- Mimetic Finite Difference
- Normal mode Analysis 的应用
- W.N. E and J.G. Liu, Projection method II: Godunov-Ryabenki analysis, SIAM J. Numer. Anal., 33(4),1996, pp.1597-1621.
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- 参考文献
- B. Gustafsson,
H.-O. Kreiss, and J. Oliger, Time Dependent
Problems and Difference Methods, John Wiley & Sons, INc., 1995.
- L. Margolin, M. Shashkov, and P. Smolarkiewicz, A Discrete Operator Calculus for Finite Difference Approximations, Comput. Methods Appl. Mech. Engrg., 187 (2000), pp. 365--383. - (pdf)
- M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler, and I. Yotov. Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals, LA-UR-03-7904, Submitted to Mathematics of Computation. --- (ps)
- Y. Kuznetsov, K. Lipnikiov and M. Shashkov, Mimetic Finite-Difference Method on Polygonal Meshes, LA-UR-03-7608 (pdf)
- K. Lipnikov, J. Morel, and M. Shashkov, Mimetic Finite Difference Methods for Diffusion Equations on Non-orthogonal AMR Meshes, LA-UR-03-1765, Submitted to Journal of Computational Physics.
- J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic Finte Difference Methods for Diffusion Equations, Computational Geosciences, 6 (2002), pp. 333-352. - (pdf)
- J. Campbell, J. M. Hyman and and M. Shashkov, Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids Computers & Mathematics with Applications, 44 (2002), 157-173. (ps).
- J. Hyman, M. Shashkov and S. Steinberg, The Effect of Inner Products for Discrte Vector Fields on the Accuracy of Mimetic Finite Difference Methods, An International Journal of Computers & Mathematics with Applications, 42 (2001), pp. 21527-1547. -- (ps)
- R. Liska, V. Ganzha, and C. Zenger, Mimetic Finite DIfference Methods for Elliptic Equations on Unstructured Grids, LA-UR-01-6955. (ps) Also published as TUM-I0108, Dezember 01, Institut fuer Informatic der Technishen Universitat Muenchen. -- (ps)
- M. Berndt, K. Lipnikov, J. D. Moulton, and M. Shashkov, Convergence of Mimetic Finite Difference Discretizations of the Diffusion Equation, East-West Journal on Numerical Mathematics, Vol. 9, # 4, (2001), pp. 253--316. -- (ps)
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J.E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Fourth- and sixth-order conservative finite-difference approximations of the divergence and gradient, Applied Numerical Mathematics 37 (2001) pp. 171--187. (pdf)
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J. Hyman, J. Morel, M. Shashkov, and S. Steinberg, Mimetic Finite Difference for Diffusion equations, LA-UR-01-2334, Submitted to Journal of Computational Geosciences. (ps).
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J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion, Progress in Electromagnetic Research, PIER 32 (2001), pp. 89--121. -- (ps)
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J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358 (revised version), Journal of Computational Physics, 170 (2001), pp. 338--372. -- (pdf)
- J. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell's Equations, Journal of Computational Physics, 151, pp. 881--909 (1999). -- (pdf)
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J. Morel, M. Hall and M. Shashkov, A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes, LA-UR-99-4358, Submitted to Journal of Computational Physics. -- (pdf)
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J. M. Hyman and M. Shashkov, The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods, SIAM Journal on Numerical Analysis, Volume 36, No. 3, pp. 788--818, (1999) . -- (pdf)
- J. M. Hyman and M. Shashkov, The Approximation of Boundary Conditions for Mimetic Finite Difference Methods, Computers & Mathematics with Applications, 36 (1998) pp. 79--99. -- (pdf)
- J. E. Morel. R. M. Roberts and M. J. Shashkov, A Local Support-Operators Diffusion Discretization Scheme Journal of Computational Physics, 144, pp. 17--51, (1998). --(pdf)
- 讨论方式和目的
- 读, 讲, 实践相结合;
- 初步学会查阅文献, 并开展一些科研工作