计算数学教研室--崔霞
姓名：崔霞
邮箱：cui_xia@iapcm.ac.cn
职称：研究员
导师资格：博导
所属培养单位、教研团队：北京应用物理与计算数学研究所 计算数学教研室
学历工作经历简介：
1993年于山东大学获得计算数学及其应用软件专业学士学位，1996、1999年于山东大学分别获得计算数学专业硕士/博士学位。1999年7月-2001年5月于北京应用物理与计算数学研究所从事博士后研究。2001年5月至今，在北京应用物理与计算数学研究所工作。担任美国数学会Mathematical Reviews评论员，AMC、JCAM等期刊审稿人。
研究方向简介：
招生专业：计算数学；研究方向：偏微分方程数值解。多年从事偏微分方程数值解法、特别是辐射流体力学中多维辐射扩散及相关问题的数值方法研究，包括有限差分、有限体积、有限元方法以及并行与迭代加速方法研究。目前主要研究方向：扩散问题非结构网格上有限体积计算方法、高效并行方法、非线性离散格式与迭代加速方法设计与性质分析、辐射流体力学耦合问题计算方法等。
主要研究成果：
在国内外重要学术刊物发表论文50余篇。作为负责人，主持完成国家自然科学基金项目4项。
1.J. Fang, Z. J. Shen, X. Cui (*), A coupled nonlinear finite element scheme for anisotropic diffusion equation with nonlinear capacity term, Journal of Computational and Applied Mathematics, https://doi.org/10.1016/j.cam.2023.115512.
2.Y. J. Gong, G. W. Yuan, X. Cui (*), Existence of a fully implicit solution with second-order time evolution for strong nonlinear diffusion equation, Applied Mathematics Letters, 117 (2021) 107091.
3.H. Zheng, G. W. Yuan, X. Cui (*), A second-order space-time accurate scheme for nonlinear diffusion equation with general capacity term, Numerical Methods for Partial Differential Equations, 36:6 (2020) 1845-1867
4.Y. M. Zhang, X. Cui, G. W. Yuan, Nonlinear iteration acceleration solution for equilibrium radiation diffusion equation, ESAIM: Mathematical Modelling and Numerical Analysis, 54:5 (2020) 1465-1490.
5.F. Zhao, X. Cui, G. W. Yuan, Iterative acceleration methods with second-order time accuracy for nonlinear diffusion equations, Advances in Computational Mathematics, 46:7 (2020). https://doi.org/10.1007/s10444-020-09756-4.
6.X. Cui, G. W. Yuan, Z. J. Shen, An efficient solving method for nonlinear convection diffusion equation, International Journal of Numerical Methods for Heat & Fluid Flow, 28:1 (2018) 173-187.
7.X. Cui, Z. J. Shen, G. W. Yuan, Asymptotic-preserving discrete schemes for non-equilibrium radiation diffusion problem in spherical and cylindrical symmetrical geometries, Communications in Computational Physics, 23:1 (2018) 198-229.
8.X. Cui, G. W. Yuan, Z. J. Shen, Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion, Journal of Computational Physics, 313 (2016) 415-429.
9.X. Cui, G. W. Yuan, J. Y. Yue, Numerical analysis and iteration acceleration of a fully implicit scheme for nonlinear diffusion problem with second-order time evolution, Numerical Methods for Partial Differential Equations, 32:1 (2016) 121-140.
10.X. Cui, G. W. Yuan, J. Y. Yue, An efficient nonlinear iteration scheme for nonlinear parabolic-hyperbolic system, Journal of Computational and Applied Mathematics, 236:2 (2011) 253-264.
11.X. Cui, J. Y. Yue, G. W. Yuan, Nonlinear scheme with high accuracy for nonlinear coupled parabolic-hyperbolic system, Journal of Computational and Applied Mathematics, 235:12 (2011) 3527-3540.
12.X. Cui, J. Y. Yue, A nonlinear iteration method for solving a two-dimensional nonlinear coupled system of parabolic and hyperbolic equations, Journal of Computational and Applied Mathematics, 234:2 (2010) 343-364.
13.X. Cui, Finite volume numerical analysis for parabolic equation with Robin boundary condition, Journal of Computational Mathematics, 23:2 (2005) 165-176.
14.X. Cui, AD Galerkin analysis for nonlinear pseudo-hyperbolic equations, Journal of Computational Mathematics, 21:2 (2003) 125-134.
15.X. Cui, ADFE method with high accuracy for nonlinear parabolic integro- differential system with nonlinear boundary conditions, Acta Mathematica Scientia, 22B:4 (2002) 473-483.
