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Car 3D Model Bundle 2018 Vol.1


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The main objective is to understand the mathematical foundationof electronic structure analysis, to develop and analysis efficient algorithms. W. E and J.F. Lu. The continuum limit and QM-continuum approximation of quantum mechanical models of solids. Comm. Math. Sci., vol. 5, no. 3, pp. 679-696, 2007. General issues in multiscale modeling S. Chen, W. E, Y. Liu and C.-W. Shu. A discontinuous Galerkin implementation of a domain decomposition method for kinetic-hydrodynamic coupling multiscale problems in gas dynamics and device simulations. J. Comput. Phys., vol. 225, no. 2, pp. 1314-1330, 2007. W. E, B. Engquist, X. Li, W. Ren and E. Vanden-Eijnden. Heterogeneous multiscale methods: A review. Comm. Comput. Phys., vol. 2, no. 3, pp. 367-450, 2007.W. E and J.F. Lu. Seamless multiscale modeling via dynamics on fiber bundles. Comm. Math. Sci., vol. 5, no. 3, pp. 649-663, 2007. X. Yue and W. E. The local micro-scale problem in the multiscale modelling of strongly heterogeneous media: Effect of boundary conditions and cell size. J. Comput. Phys., vol. 222, no. 2, pp. 556-572, 2007.S. Chen, W. E and C.-W. Shu. The heterogeneous multiscale method based on the discontinuous galerkin method for hyperbolic and parabolic problems. Multiscale Model. Simul., vol. 3, no. 4, pp. 871-894, 2005.W. E and B. Engquist. The heterogeneous multi-scale method for homogenization problems. Multiscale Methods in Sci. and Eng., pp. 89-110. Lect. Notes in Comput. Sci. Eng., vol. 44, Springer, Berlin, 2005.W. E and P.B. Ming. Analysis of the local quasicontinuum method. Frontiers and Prospects of Contemp. Appl. Math., pp. 18-32. Contemporary Appl. Math., vol. 6, Higher Education Press, Beijing, 2005. W. E, P.B. Ming and P.-W. Zhang. Analysis of the heterogeneous multiscale method for elliptic homogenization problems. J. Amer. Math. Soc., vol. 18, no. 1, pp. 121-156, 2005. W. E, D. Liu and E. Vanden-Eijnden. Analysis of multiscale methods for stochastic differential equations. Comm. Pure Appl. Math., vol. 58, No. 11, 1544-1585, 2005.W. E and B. Engquist. The heterogeneous multiscale method. Second Intl. Congress of Chinese Mathematicians. Proc. of ICCM2001, Taipei, pp. 57-74, New Studies in Advanced Mathematics, vol. 4, Intl. Press, 2004.W. E, X. Li, E. Vanden-Eijnden. Some recent progress in multiscale modeling. Multiscale Modelling and Simulation, pp. 3-22. Lect. Notes Comput. Sci. Eng., vol. 39, Springer, Berlin, 2004. W. E and X.-T. Li. Analysis of the heterogeneous multiscale method for gas dynamics. Methods Appl. Anal., vol. 11, no. 4, pp. 557-572, 2004. W. E and P.B. Ming. Analysis of multiscale methods. J. Comput. Math., vol. 22, no. 2, pp. 210-219, 2004. W. E nd X. Yue. Heterogeneous multiscale method for locally self-similar problems. Comm. Math. Sci., vol. 2, no. 1, pp. 137-144, 2004. W. E. Analysis of the heterogeneous multiscale method for ordinary differential equations. Comm. Math. Sci., vol. 1, no. 3, pp. 423-436, 2003. A. Abdulle and W. E. Finite difference heterogeneous multi-scale method for homogenization problems. J. Comput. Phys., vol. 191, no. 1 pp. 18-39, 2003. L.-T. Cheng and W. E. The heterogeneous multi-scale method for interface dynamics. Recent advances in scientific computing and partial differential equations (Hong Kong, 2002), pp. 43-53, Contemp. Math., vol. 330, Amer. Math. Soc., Providence, RI, 2003. W. E and B. Engquist. The heterogeneous multiscale methods. Comm. Math. Sci., vol. 1, no. 1, pp. 87-132, 2003. W. E and B. Engquist. Multiscale modeling and computation. Notices Amer. Math. Soc., vol. 50, no. 9, pp. 1062-1070, 2003. W. E, B. Engquist and Z. Huang. Heterogeneous multiscale method: A general methodology for multiscale modeling. Phys. Rev. B, vol. 67, no. 9, 092101, 2003. Problems with multiple time scales T. Li, A. Abdulle and W. E. Effectiveness of implicit methods for stiff stochastic differential equations. Comm. Comput. Phys., vol. 3, no. 2, pp. 295-307, 2008. W. E, D. Liu and E. Vanden-Eijnden. Nested st




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