學歷工作經歷簡介
1993年于山東大學獲得計算數學及其套用軟體專業學士學位,1996、1999年于山東大學分別獲得計算數學專業碩士/博士學位。1999年7月-2001年5月於北京套用物理與計算數學研究所從事博士後研究。2001年5月至今,在北京套用物理與計算數學研究所工作。擔任美國數學會Mathematical Reviews評論員,AMC、JCAM等期刊審稿人。
研究方向簡介
招生專業:計算數學;研究方向:偏微分方程數值解。多年從事偏微分方程數值解法、特別是輻射流體力學中多維輻射擴散及相關問題的數值方法研究,包括有限差分、有限體積、有限元方法以及並行與疊代加速方法研究。主要研究方向:擴散問題非結構格線上有限體積計算方法、高效並行方法、非線性離散格式與疊代加速方法設計與性質分析、輻射流體力學耦合問題計算方法等。
主要研究成果
在國內外重要學術刊物發表論文50餘篇。作為負責人,主持完成國家自然科學基金項目4項。
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).
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.