English 清华大学 旧版入口 人才招聘

黄忠亿

  • 教授
  • 电话:(010)62796893
  • 邮箱:zhongyih@tsinghua.edu.cn

基本信息

博士(清华大学,1999),教授、博导

系党委副书记、学位分委会副主席

中国工业与应用数学学会常务副秘书长

中国计算数学分会常务委员

《计算数学》、《计算物理》、《高等学校计算数学学报》编委

工作履历

2008.12–现在, 清华大学数学科学系,教授

2002.12–2008.12,清华大学数学科学系,副教授

2000.09–2002.01,美国普林斯顿大学PACM,博士后

1999.04–2002.12,清华大学数学科学系,讲师

研究领域

计算数学与科学工程计算,机器学习理论及其应用

所授课程

《数值分析》、《科学与工程计算基础》、《偏微分方程数值解法》、《有限元方法》、《差分方法》、《无界区域上偏微分方程的数值解及其应用》

奖励与荣誉

2020  获国家杰出青年科学基金资助

2013  获优秀青年科学基金资助

2008  获清华大学基础研究人才计划资助

2008  获BAIL2008国际会议颁发的Pieter Hemker奖(2/3)

2002  获北京市科学技术二等奖(4/6)

学术成果

        在多尺度数学物理问题的建模、分析和数值模拟等方面取得了一系列重要创新性成果,并成功应用于材料科学、流体力学、图像处理、金融数学、人工智能等领域:系统研究了多尺度椭圆/抛物问题的高效数值解法,提出了基于特征展开的有限点法/直接线法,可以自然得到描述问题奇性的具有一致收敛性的高精度数值解;系统研究了多尺度双曲问题的高效数值方法,提出并发展了量身定做有限胞/点方法和基于Bloch分解的(随机Galerkin)算子分裂拟谱方法,计算量比传统方法低一个参数量级以上;对无界区域发展方程、拟线性问题和分数阶问题等提出了准确和高精度人工边界条件。

  Mathematics of Computation, Numerische Mathematik, SIAM 系列杂志, Journal of Computational Physics 等国际顶尖杂志上发表论文50余篇,研究成果被国际学术界的300多名学者在100余种SCI收录期刊上引用了800余次(Google Scholar 引用1200余次)。


主要论著:

[55] An iterative splitting method for pricing European options under the Heston model. (with Hongshan Li), Appl. Math. Comput. 387, 125424, 12 pp., 2020.

[54] Artificial Boundary Method for European Pricing Option Problem, (with Hongshan Li),  East Asian J Appl. Math.,10(4): 7 46-773 , 2020.

[53] Transparent boundary conditions and numerical computation for singularly perturbed telegraph equation on unbounded domain. (with Wang Kong), Numer. Math. 145: 345–382, 2020.

[52] Convergence Analysis on Stochastic Collocation Methods for the Linear Schrodinger Equation with Random Inputs, (with Zhizhang Wu), Adv. Appl. Math. Mech., 12: 30-56, 2020.

[51] Image segmentation using the Cahn-Hilliard equation, (with Wenli Yang, Wei Zhu), J. Sci. Comput. 79 (2): 1057-1077, 2019.

[50] Asymptotic analysis and numerical method for singularly perturbed eigenvalue problems, (with Wang Kong), SIAM J. Sci. Comput., 40 (5): A3293-A3321, 2018.

[49] An Efficient Tailored Finite Point Method for Rician Denoising and Deblurring, (with Wenli Yang, Wei Zhu), Commun. Comput. Phys, 24(4): 1169-1195, 2018.

[48] The direct method of lines for elliptic problems in star-shaped domains, (with Zhizhang Wu, Wei-Cheng Wang, Yi Yang), J. Comput. Appl. Math, 327: 350-361, 2017.

[47] Tailored finite point method for parabolic problems, (with Yi Yang), Comput. Meth. Appl. Math., 16: 543-562, 2016.

[46] A Bloch decomposition-based stochastic Galerkin method for quantum dynamics with a random external potential, (with Zhizhang Wu), J. Comput. Phys. 317: 257-275, 2016.

[45] Monotone finite point method for non-equilibrium radiation diffusion equations, (with Y. Li), BIT Numer. Math. 56: 659-679, 2016.

[44] An equation decomposition based tailored finite point method for linearized incompressible flow in two dimensional space, (with Y. Li, H. Han), Comput. Meth. Appl. Math. 15 (1): 39-58, 2015.

[43] Numerical simulations of X-rays Free Electron Lasers (XFEL), (with P. Antonelli, A. Athanassoulis, P. Markowich), Multiscale Model. Simul. 12 (4): 1607-1621, 2014.

[42] The Tailored finite point method, (with H. Han), Comput. Meth. Appl. Math., 14 (3): 321-345, 2014.

[41] A Semi-discrete tailored finite point method for a class of anisotropic diffusion problems, (with H. Han and W. Ying), Comput. Math. Appl. 65 (11): 1760-1774, 2013.

[40] An Iterative Method based on equation decomposition for the fourth-order singular perturbation problem, (with H. Han and S. Zhang), Numer. Meth. Part. D. E. 29 (3): 961-978, 2013.

[39] A class of nonconforming quadrilateral finite elements for incompressible flow, (with Y. Li), Sci. China Math. 56 (2): 379-393, 2013.

[38] Tailored finite point method based on exponential bases for convection-diffusion-reaction equation, (with H. Han), Math. Comput. 82 (281): 213-226, 2013.

[37] Gaussian Beam Methods for the Dirac Equation in the Semi-classical Regime, (with H. Wu, S. Jin and D. Yin), Commun. Math. Sci. 10 (4): 1301–1315, 2012.

[36] Tailored finite cell method for solving Helmholtz equation in layered heterogeneous medium, (with X. Yang), J. Comput. Math. 30 (4): 381–391, 2012.

[35] An equation decomposition method for the numerical solution of a fourth-order elliptic singular perturbation problem, (with H. Han), Numer. Meth. Part. D. E, 28 (3): 942-953, 2012.

[34] Tailored finite point method for numerical simulation of partial differential equations, In L. Ji et al (eds.), AMS/IP Studies in Advanced Mathematics, Vol 51, Cambridge: AMS/IP. 2012, pp. 593-608

[33] Tailored finite point method for first order wave equation, (with X. Yang), J. Sci. Comput., 49 (3): 351-366, 2011.

[32] Tailored finite point method for steady-state reaction-diffusion equation, (with H. Han), Comm. Math. Sci., 8 (4): 887-899, 2010.

[31] Bloch Decomposition-Based Gaussian Beam Method for the Schr¨odinger equation with Periodic Potentials, (with S. Jin, H. Wu and X. Yang), J. Comput. Phys., 229 (13): 4869-4883, 2010.

[30] Numerical simulation of trapped dipolar quantum gases: Collapse studies and vortex dynamics, (with P. Markowich, and C. Sparber), Kinetic and Related Models, 3 (1):181-194, 2010.

[29] Bloch Decomposition method for waves in periodic media, (with S. Jin, P. Markowich, and C. Sparber), Series in Contemporary Applied Mathematics, CAM 15 (2010), Some Problems on Nonlinear Hyperbolic Equations and Applications, pp. 161-188.

[28] Tailored finite point method for a singular perturbation problem with variable coefficients in two dimensions, (with H. Han), J Sci. Comput., 41 (2): 200-220, 2009.

[27] Tailored finite point method for the interface problem, Netw. Heterog. Media, 4 (1): 91-106, 2009.

[26] On the Bloch decomposition based spectral method for wave propagation in periodic media, (with S. Jin, P. Markowich, and C. Sparber), Wave Motion, 46 (1): 15-28, 2009.

[25] A Hybrid Phase-Flow Method for Hamiltonian Systems with Discontinuous Hamiltonians, (with S. Jin, H. Wu), SIAM J Sci. Comput., 31(2):1303-1321, 2008.

[24] A Tailored finite point method for the Helmholtz equation with high wave numbers in heterogeneous medium, (with H. Han), J Comput. Math., 26 (5):728-739, 2008.

[23] A Tailored finite point method for a singular perturbation problem on an unbounded domain, (with H. Han and B. Kellogg), J Sci. Comput., 36 (2): 243-261, 2008.

[22] Numerical simulation of the nonlinear Schroedinger equation with multi-dimensional periodic potentials, (with S. Jin, P. Markowich, and C. Sparber), Multiscale Model. Simul. , 7 (2): 539-564, 2008.

[21] Exact artificial boundary conditions for quasilinear elliptic equation in unbounded domains, (with H. Han and D. Yin), Comm. Math. Sci., 6 (1): 71-82, 2008.

[20] Numerical solutions of Schrodinger equations in R3, (with H. Han and D. Yin), Numer. Meth. For Diff. Eqns, 23 (3): 511-533, 2007.

[19] A Bloch decomposition based split-step pseudo spectral method for quantum dynamics with periodic potentials, (with S. Jin, P. Markowich, and C. Sparber), SIAM J Sci. Comput., 29 (2): 515-538, 2007.

[18] Numerical Simulation for Crack Propagation in Two-Dimensional, (in Chinese) (with Q. Liu), J. Tsinghua University, 46 (9): 1604-1607, 2006.

[17] Wavelet-Galerkin method for reaction-diffusion equation, (in Chinese) (with X. Yang and L. Zhu), J. Tsinghua University, 46 (3): 392-395, 2006.

[16] Numerical Study of a Domain Decomposition Method For a Two-Scale Linear Transport Equation, (with X. Yang, F. Golse, S. Jin), Netw. Heterog. Media, 1(1):143-166, 2006.

[15] A time-splitting spectral method for Maxwell-Dirac system, (with S. Jin, P. Markowich, C. Sparber, C. Zheng), J. Comput. Phys., 208 (2): 761-789, 2005.

[14] Exact artificial boundary conditions for Schrodinger equation in R2, (with H. Han) Comm. Math. Sci., 2 (1): 79-94, 2004.

[13] Heterogeneous multi-scale method: A general methodology for multi-scale modeling, (with W. E and B. Engquist) Phys. Rev. B, 67 (9): 092101, 2003.

[12] High accuracy numerical method of thin-film problems in micromagnetics, J. Comput. Math. 21 (1): 33-40, 2003.

[11] A dynamic atomistic-continuum method for the simulation of crystalline materials, (with W. E), J. Comput. Phys. 182 (1): 234-261, 2002.

[10] Exact and Approximating Boundary Conditions for the Parabolic Problems on Unbounded Domains, (with H. Han), Comput. Math. Appl., 44 (5-6): 655-666, 2002.

[9] A Class of Artificial Boundary Conditions for Heat Equation in Unbounded Domains, (with H. Han), Comput. Math. Appl., 43 (6-7): 889-900, 2002.

[8] The discrete method of separation of variables for composite material problems, (with H. Han), Int. J. Fracture 112 (4): 379-402, 2001.

[7] Matching conditions in atomistic-continuum modeling of materials, (with W. E), Phys. Rev. Lett., 87 (13): 5501-5504, 2001.

[6] Numerical simulations of fracture problems by coupling the FEM and the direct method of lines, (with W. Bao and H. Han), Comput. Method Appl. Mech. Eng., 190 (37-38): 4831-4846, 2001.

[5] Wavelet-Galerkin method for the singular perturbation problem with boundary layers, Tsinghua Science & Technology, 5(4): 365-369, 2000.

[4] The discrete method of separation of variables for computation of stress intensity factors, (with H. Han and W. Bao), Chinese J. Comput. Phys., 17(5): 483-496, 2000.

[3] The direct method of lines for the numerical solutions of interface problem, (with H. Han), Comput. Method Appl. Mech. Eng., 171(1): 61-75, 1999.

[2] A semi-discrete numerical procedure for composite material problems, (with H. Han), Mathematical Sciences and Applications Vol. 12(1999), Advances in numerical mathematics, pp. 35-44.

[1] A semi-discrete method for the solution of elliptic equation with singularities, (with H. Han), CSIAM98 VI: 17 (1998), pp.541-545.


人才培养

指导在读博士生15名:刘安宁,胡奕啸,王夏恺,戴淼钰,王昊宇,朱晓鹏,冯立,罗鑫,许先粮,杜婷,黄维佳,王跃然,吴诗童,吴天昊,解雯佳

指导毕业博士7名:柴利慧(2013),杨祎(2016),李野(2016),杨文莉(2018),孔旺(2019),伍智璋(2019),李洪姗(2020)

指导毕业硕士9名:刘强(2006),曹亮(2007),齐鹏(2008),王宇晗(2008),郑双超(2011),齐振民(2012),谢潇宇(2015),刘志成(2016),尤思博(2017)