教育经历
2009 北京大学 博士
2003 北京大学 学士
2003 北京大学 学士
工作经历
2012- 北京大学数学科学学院 副教授
2010-2012 北京大学数学科学学院 助理教授
2014-2014 西班牙塞维利亚大学数学研究所 客座研究学者
2014-2014 香港中文大学系统工程与工程管理系 客座研究学者
2012-2012 美国普林斯顿大学应用与计算数学系 客座研究学者
2009-2010 香港科技大学数学系 博士后
2007-2008 美国北卡大学数学与统计系 客座研究学者
2010-2012 北京大学数学科学学院 助理教授
2014-2014 西班牙塞维利亚大学数学研究所 客座研究学者
2014-2014 香港中文大学系统工程与工程管理系 客座研究学者
2012-2012 美国普林斯顿大学应用与计算数学系 客座研究学者
2009-2010 香港科技大学数学系 博士后
2007-2008 美国北卡大学数学与统计系 客座研究学者
代表作
Kung-Ching Chang, Sihong Shao, Dong Zhang, Weixi Zhang, Lovász extension and graph cut, Communications in Mathematical Sciences, accepted on 2 November 2020.
Kung-Ching Chang*, Sihong Shao, Dong Zhang, Weixi Zhang, Nonsmooth critical point theory and applications to the spectral graph theory, SCIENCE CHINA Mathematics, doi.org/10.1007/s11425-019-1625-8, published online on 20 March 2020.
Sihong Shao, Yunfeng Xiong, Branching random walk solutions to the Wigner equation, SIAM Journal on Numerical Analysis 58 (2020) 2589.
Zhenzhu Chen, Sihong Shao*, Wei Cai, A high order efficient numerical method for 4-D Wigner equation of quantum double-slit interferences, Journal of Computational Physics 396 (2019) 54.
Niurka R. Quintero, Sihong Shao*, Renato Alvarez-Nodarse, Franz G. Mertens, Externally driven nonlinear Dirac equation revisited: theory and simulations, Journal of Physics A: Mathematical and Theoretical 52 (2019) 155401.
Zhenzhu Chen, Yunfeng Xiong, Sihong Shao*, Numerical methods for the Wigner equation with unbounded potential, Journal of Scientific Computing 79 (2019) 345.
Yunfeng Xiong, Sihong Shao*, The Wigner branching random walk: Efficient implementation and performance evaluation, Communications in Computational Physics 25 (2019) 871.
Sihong Shao*, Yunfeng Xiong, A branching random walk method for many-body Wigner quantum dynamics, Numerical Mathematics: Theory, Methods and Applications 12 (2019) 21.
Kung-Ching Chang*, Sihong Shao, Dong Zhang, Cheeger's cut, maxcut and the spectral theory of 1-Laplacian on graphs, SCIENCE CHINA Mathematics 60 (2017) 1963.
Franz G. Mertens, Fred Cooper, Sihong Shao, Niurka R. Quintero, Avadh Saxena*, A. R. Bishop, Nonlinear Dirac equation solitary waves under a spinor force with different components, Journal of Physics A: Mathematical and Theoretical 50 (2017) 145201.
Kung-Ching Chang, Sihong Shao*, Dong Zhang, Nodal domains of eigenvectors for 1-Laplacian on graphs, Advances in Mathematics 308 (2017) 529.
With Wei Cai (蔡伟), Haiyan Jiang (姜海燕), Pingwen Zhang (张平文), Boundary treatments in non-equilibrium Green's function (NEGF) methods for quantum transport in nano-MOSFETs, Journal of Computational Physics 227 (2008) 6553.
With Wei Cai (蔡伟), Xia Ji (季霞), Jiguang Sun (孙继广), A Schwarz generalized eigen-oscillation spectral element method (GeSEM) for 2-D high frequency electromagnetic scattering in dispersive inhomogeneous media, Journal of Computational Physics 227 (2008) 9933.
With A.R. Bishop, Fred Cooper, Franz G. Mertens, Niurka R. Quintero, Avadh Saxena, Nonlinear Dirac equation solitary waves under a spinor force with different components, Journal of Physics A: Mathematical and Theoretical 50 (2017) 145201.
With Tiezheng Qian (钱铁铮), A variational model for two-phase immiscible electro-osmotic flows, Communications in Computational Physics 11 (2012) 831.
With Zhendong Li (李振东), Wenjian Liu (刘文剑), Relativistic explicit correlation: Coalescence conditions and practical suggestions, Journal of Chemical Physics 136 (2012) 144117.
With Wei Cai (蔡伟), Tiao Lu (卢朓), Adaptive conservative cell average spectral element methods for transient Wigner equation in quantum transport, Communications in Computational Physics 9 (2011) 711.
With Weinan E (鄂维南), Lin Lin (林霖), Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory, Journal of Computational Physics 245 (2013) 205.
With Zhendong Li (李振东), Wenjian Liu (刘文剑), Coalescence conditions of relativistic wave functions, DOI 10.1007/978-3-642-41611-8_8-1, Handbook of Relativistic Quantum Chemistry, Springer-Verlag Berlin Heidelberg 2015.
With Huazhong Tang (汤华中), Interaction of solitary waves with a phase shift in a nonlinear Dirac model, Communications in Computational Physics 3 (2008) 950.
With Wei Cai (蔡伟), Huazhong Tang (汤华中), Accurate calculation of Green's function of the Schroedinger equation in a block layered potential, Journal of Computational Physics 219 (2006) 733.
With Huazhong Tang (汤华中), Higher-order accurate Runge-Kutta discontinuous Galerkin methods for a nonlinear Dirac model, Discrete and Continuous Dynamical Systems-Series B 6 (2006) 623.
With Huazhong Tang (汤华中), Interaction for the solitary waves of a nonlinear Dirac model, Physics Letters A 345 (2005) 119.
With Huazhong Tang (汤华中), Jian Xu (徐健), Numerical methods for nonlinear Dirac equation, Journal of Computational Physics 245 (2013) 131.
With Lin Lin (林霖), Jianfeng Lu (鲁剑锋), Analysis of the time reversible Born-Oppenheimer molecular dynamics, Entropy 16 (2014) 110.
With K.C. Chang (张恭庆), Dong Zhang (张栋), The 1-Laplacian Cheeger Cut: Theory and Algorithms, Journal of Computational Mathematics 33 (2015) 443. [arXiv:1603.01687]. http://arxiv.org/abs/1603.01687
With Huazhong Tang (汤华中), Dongyi Wei (韦东奕), Jian Xu (徐健), Multi-hump solitary waves of a nonlinear Dirac equation, Communications in Mathematical Sciences 13 (2015), 1219. (arXiv:1311.7453)
With Fred Cooper, Avinash Khare, Franz G. Mertens, Niurka R. Quintero, Avadh Saxena, Stability of solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity, Physical Review E 90 (2014) 032915.
With Wei Cai (蔡伟), Dong Wang (王冬), Changhao Yan (严昌浩), Xuan Zeng (曾璇), Feature-scale simulations of particulate slurry flows in chemical mechanical polishing by smoothed particle hydrodynamics, Communications in Computational Physics 16 (2014) 1389.
With Dong Wang (王冬), Yisong Zhou (周逸松), Efficient implementation of smoothed particle hydrodynamics (SPH) with plane sweep algorithm, Communications in Computational Physics 19 (2016) 770.
With K.C. Chang (张恭庆), Dong Zhang (张栋), Nodal Domains of Eigenvectors for 1-Laplacian on Graphs, Advances in Mathematics 308 (2017) 529 [arXiv:1602.07472].
With Zhendong Li (李振东), Wenjian Liu (刘文剑), Basic structures of relativistic wave functions, DOI 10.1007/978-3-642-41611-8_7-1, Handbook of Relativistic Quantum Chemistry, Springer-Verlag Berlin Heidelberg 2015.
With Zhendong Li (李振东), Wenjian Liu (刘文剑), Relativistic explicit correlation: Problems and solutions, DOI 10.1007/978-3-642-41611-8_9-1, Handbook of Relativistic Quantum Chemistry, Springer-Verlag Berlin Heidelberg 2015.
With Fred Cooper, Avinash Khare, Franz G. Mertens, Niurka R. Quintero, Avadh Saxena, Nonlinear Dirac equation solitary waves in the presence of external driving forces, Journal of Physics A: Mathematical and Theoretical 49 (2016) 065402.
With Jean Michel Sellier, Comparison of Deterministic and Stochastic Methods for Time-Dependent Wigner Simulations, Journal of Computational Physics 300 (2015) 167.
With Zhenzhu Chen (陈珍珠), Yunfeng Xiong (熊云丰), An advective-spectral-mixed method for time-dependent many-body Wigner simulations, SIAM Journal on Scientific Computing 38 (2016) B491 [arXiv:1602.08853].
With Zhendong Li (李振东), Wenjian Liu (刘文剑), Classifications and canonical forms of tensor product expressions in the presence of permutation symmetries, arXiv:1604.06156, April, 2016.
With K.C. Chang (张恭庆), Dong Zhang (张栋), Spectrum of the signless 1-Laplacian and the dual Cheeger constant on graphs, Submitted, Jul. 2016 [arXiv:1607.00489].
Kung-Ching Chang*, Sihong Shao, Dong Zhang, Weixi Zhang, Nonsmooth critical point theory and applications to the spectral graph theory, SCIENCE CHINA Mathematics, doi.org/10.1007/s11425-019-1625-8, published online on 20 March 2020.
Sihong Shao, Yunfeng Xiong, Branching random walk solutions to the Wigner equation, SIAM Journal on Numerical Analysis 58 (2020) 2589.
Zhenzhu Chen, Sihong Shao*, Wei Cai, A high order efficient numerical method for 4-D Wigner equation of quantum double-slit interferences, Journal of Computational Physics 396 (2019) 54.
Niurka R. Quintero, Sihong Shao*, Renato Alvarez-Nodarse, Franz G. Mertens, Externally driven nonlinear Dirac equation revisited: theory and simulations, Journal of Physics A: Mathematical and Theoretical 52 (2019) 155401.
Zhenzhu Chen, Yunfeng Xiong, Sihong Shao*, Numerical methods for the Wigner equation with unbounded potential, Journal of Scientific Computing 79 (2019) 345.
Yunfeng Xiong, Sihong Shao*, The Wigner branching random walk: Efficient implementation and performance evaluation, Communications in Computational Physics 25 (2019) 871.
Sihong Shao*, Yunfeng Xiong, A branching random walk method for many-body Wigner quantum dynamics, Numerical Mathematics: Theory, Methods and Applications 12 (2019) 21.
Kung-Ching Chang*, Sihong Shao, Dong Zhang, Cheeger's cut, maxcut and the spectral theory of 1-Laplacian on graphs, SCIENCE CHINA Mathematics 60 (2017) 1963.
Franz G. Mertens, Fred Cooper, Sihong Shao, Niurka R. Quintero, Avadh Saxena*, A. R. Bishop, Nonlinear Dirac equation solitary waves under a spinor force with different components, Journal of Physics A: Mathematical and Theoretical 50 (2017) 145201.
Kung-Ching Chang, Sihong Shao*, Dong Zhang, Nodal domains of eigenvectors for 1-Laplacian on graphs, Advances in Mathematics 308 (2017) 529.
With Wei Cai (蔡伟), Haiyan Jiang (姜海燕), Pingwen Zhang (张平文), Boundary treatments in non-equilibrium Green's function (NEGF) methods for quantum transport in nano-MOSFETs, Journal of Computational Physics 227 (2008) 6553.
With Wei Cai (蔡伟), Xia Ji (季霞), Jiguang Sun (孙继广), A Schwarz generalized eigen-oscillation spectral element method (GeSEM) for 2-D high frequency electromagnetic scattering in dispersive inhomogeneous media, Journal of Computational Physics 227 (2008) 9933.
With A.R. Bishop, Fred Cooper, Franz G. Mertens, Niurka R. Quintero, Avadh Saxena, Nonlinear Dirac equation solitary waves under a spinor force with different components, Journal of Physics A: Mathematical and Theoretical 50 (2017) 145201.
With Tiezheng Qian (钱铁铮), A variational model for two-phase immiscible electro-osmotic flows, Communications in Computational Physics 11 (2012) 831.
With Zhendong Li (李振东), Wenjian Liu (刘文剑), Relativistic explicit correlation: Coalescence conditions and practical suggestions, Journal of Chemical Physics 136 (2012) 144117.
With Wei Cai (蔡伟), Tiao Lu (卢朓), Adaptive conservative cell average spectral element methods for transient Wigner equation in quantum transport, Communications in Computational Physics 9 (2011) 711.
With Weinan E (鄂维南), Lin Lin (林霖), Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory, Journal of Computational Physics 245 (2013) 205.
With Zhendong Li (李振东), Wenjian Liu (刘文剑), Coalescence conditions of relativistic wave functions, DOI 10.1007/978-3-642-41611-8_8-1, Handbook of Relativistic Quantum Chemistry, Springer-Verlag Berlin Heidelberg 2015.
With Huazhong Tang (汤华中), Interaction of solitary waves with a phase shift in a nonlinear Dirac model, Communications in Computational Physics 3 (2008) 950.
With Wei Cai (蔡伟), Huazhong Tang (汤华中), Accurate calculation of Green's function of the Schroedinger equation in a block layered potential, Journal of Computational Physics 219 (2006) 733.
With Huazhong Tang (汤华中), Higher-order accurate Runge-Kutta discontinuous Galerkin methods for a nonlinear Dirac model, Discrete and Continuous Dynamical Systems-Series B 6 (2006) 623.
With Huazhong Tang (汤华中), Interaction for the solitary waves of a nonlinear Dirac model, Physics Letters A 345 (2005) 119.
With Huazhong Tang (汤华中), Jian Xu (徐健), Numerical methods for nonlinear Dirac equation, Journal of Computational Physics 245 (2013) 131.
With Lin Lin (林霖), Jianfeng Lu (鲁剑锋), Analysis of the time reversible Born-Oppenheimer molecular dynamics, Entropy 16 (2014) 110.
With K.C. Chang (张恭庆), Dong Zhang (张栋), The 1-Laplacian Cheeger Cut: Theory and Algorithms, Journal of Computational Mathematics 33 (2015) 443. [arXiv:1603.01687]. http://arxiv.org/abs/1603.01687
With Huazhong Tang (汤华中), Dongyi Wei (韦东奕), Jian Xu (徐健), Multi-hump solitary waves of a nonlinear Dirac equation, Communications in Mathematical Sciences 13 (2015), 1219. (arXiv:1311.7453)
With Fred Cooper, Avinash Khare, Franz G. Mertens, Niurka R. Quintero, Avadh Saxena, Stability of solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity, Physical Review E 90 (2014) 032915.
With Wei Cai (蔡伟), Dong Wang (王冬), Changhao Yan (严昌浩), Xuan Zeng (曾璇), Feature-scale simulations of particulate slurry flows in chemical mechanical polishing by smoothed particle hydrodynamics, Communications in Computational Physics 16 (2014) 1389.
With Dong Wang (王冬), Yisong Zhou (周逸松), Efficient implementation of smoothed particle hydrodynamics (SPH) with plane sweep algorithm, Communications in Computational Physics 19 (2016) 770.
With K.C. Chang (张恭庆), Dong Zhang (张栋), Nodal Domains of Eigenvectors for 1-Laplacian on Graphs, Advances in Mathematics 308 (2017) 529 [arXiv:1602.07472].
With Zhendong Li (李振东), Wenjian Liu (刘文剑), Basic structures of relativistic wave functions, DOI 10.1007/978-3-642-41611-8_7-1, Handbook of Relativistic Quantum Chemistry, Springer-Verlag Berlin Heidelberg 2015.
With Zhendong Li (李振东), Wenjian Liu (刘文剑), Relativistic explicit correlation: Problems and solutions, DOI 10.1007/978-3-642-41611-8_9-1, Handbook of Relativistic Quantum Chemistry, Springer-Verlag Berlin Heidelberg 2015.
With Fred Cooper, Avinash Khare, Franz G. Mertens, Niurka R. Quintero, Avadh Saxena, Nonlinear Dirac equation solitary waves in the presence of external driving forces, Journal of Physics A: Mathematical and Theoretical 49 (2016) 065402.
With Jean Michel Sellier, Comparison of Deterministic and Stochastic Methods for Time-Dependent Wigner Simulations, Journal of Computational Physics 300 (2015) 167.
With Zhenzhu Chen (陈珍珠), Yunfeng Xiong (熊云丰), An advective-spectral-mixed method for time-dependent many-body Wigner simulations, SIAM Journal on Scientific Computing 38 (2016) B491 [arXiv:1602.08853].
With Zhendong Li (李振东), Wenjian Liu (刘文剑), Classifications and canonical forms of tensor product expressions in the presence of permutation symmetries, arXiv:1604.06156, April, 2016.
With K.C. Chang (张恭庆), Dong Zhang (张栋), Spectrum of the signless 1-Laplacian and the dual Cheeger constant on graphs, Submitted, Jul. 2016 [arXiv:1607.00489].
科研项目
2019/1-2021/12 计算量子力学 国家自然科学基金委员会
2015/1-2018/12 多体Dirac-Coulomb方程的显相关波函数方法 国家自然科学基金委员会
2014/1-2016/12 磁流体动力学(MHD)方程的高阶约束输运有限元方法 国家自然科学基金委员会
2012/1-2014/12 非线性Dirac方程的计算和分析 高等学校博士学科点专项科研基金
2012/1-2014/12 多相不相混电渗流的建模和计算 国家自然科学基金委员会
2010/11-2012/10 化学机械抛光中复杂流体现象的建模和计算 复旦大学专用集成电路与系统国家重点实验室
2015/1-2018/12 多体Dirac-Coulomb方程的显相关波函数方法 国家自然科学基金委员会
2014/1-2016/12 磁流体动力学(MHD)方程的高阶约束输运有限元方法 国家自然科学基金委员会
2012/1-2014/12 非线性Dirac方程的计算和分析 高等学校博士学科点专项科研基金
2012/1-2014/12 多相不相混电渗流的建模和计算 国家自然科学基金委员会
2010/11-2012/10 化学机械抛光中复杂流体现象的建模和计算 复旦大学专用集成电路与系统国家重点实验室
主讲课程
智能、量子与计算讨论班（课程介绍见 http://scholar.pku.edu.cn/ssh）
2021.9 组合最优化算法 数学科学学院研究生及高年级本科生
2021.3 谱方法 数学科学学院研究生及高年级本科生
2020.9 数学分析(III) 信息科学技术学院、元培学院 2019级本科生
2020.2 数学分析(II) 信息科学技术学院、元培学院 2019级本科生
2019.9 数学分析(I) 信息科学技术学院、元培学院 2019级本科生
2019.2 谱方法 数学科学学院研究生及高年级本科生
2018.9 数学分析(III) 信息科学技术学院、元培学院 2017级本科生
2018.2 数学分析(II) 信息科学技术学院、元培学院 2017级本科生
2017.9 数学分析(I) 信息科学技术学院、元培学院 2017级本科生
2017.2 计算流体力学 数学科学学院研究生及高年级本科生
2016.9 数学分析(III) 信息科学技术学院、元培学院 2015级本科生
2016.2 数学分析(II) 信息科学技术学院、元培学院 2015级本科生
2015.9 数学分析(I) 信息科学技术学院、元培学院 2015级本科生
2015.2 谱方法 数学科学学院研究生及高年级本科生
2013.9 数学分析(III) 信息科学技术学院2012级本科生
2013.2 数学分析(II) 信息科学技术学院2012级本科生
2012.9 数学分析(I) 信息科学技术学院2012级本科生
2011.9 数学分析(III) 信息科学技术学院2010级本科生
2011.2 数学分析(II) 信息科学技术学院2010级本科生
2010.9 数学分析(I) 信息科学技术学院2010级本科生
2021.9 组合最优化算法 数学科学学院研究生及高年级本科生
2021.3 谱方法 数学科学学院研究生及高年级本科生
2020.9 数学分析(III) 信息科学技术学院、元培学院 2019级本科生
2020.2 数学分析(II) 信息科学技术学院、元培学院 2019级本科生
2019.9 数学分析(I) 信息科学技术学院、元培学院 2019级本科生
2019.2 谱方法 数学科学学院研究生及高年级本科生
2018.9 数学分析(III) 信息科学技术学院、元培学院 2017级本科生
2018.2 数学分析(II) 信息科学技术学院、元培学院 2017级本科生
2017.9 数学分析(I) 信息科学技术学院、元培学院 2017级本科生
2017.2 计算流体力学 数学科学学院研究生及高年级本科生
2016.9 数学分析(III) 信息科学技术学院、元培学院 2015级本科生
2016.2 数学分析(II) 信息科学技术学院、元培学院 2015级本科生
2015.9 数学分析(I) 信息科学技术学院、元培学院 2015级本科生
2015.2 谱方法 数学科学学院研究生及高年级本科生
2013.9 数学分析(III) 信息科学技术学院2012级本科生
2013.2 数学分析(II) 信息科学技术学院2012级本科生
2012.9 数学分析(I) 信息科学技术学院2012级本科生
2011.9 数学分析(III) 信息科学技术学院2010级本科生
2011.2 数学分析(II) 信息科学技术学院2010级本科生
2010.9 数学分析(I) 信息科学技术学院2010级本科生
社会兼职
2013/12/29-今 北京计算数学学会 理事
荣誉获奖
2015 宝洁教师奖
2013 北京大学2012-2013学年度优秀班主任
2011 北京大学优秀博士学位论文三等奖
2008 北京大学洛杉矶奖学金
2007 北京大学五四奖学金
2006 北京大学华为奖学金
2005, 2006, 2008 北京大学学术类创新奖（三次）
2005 北京大学三星奖学金
2005 中国计算数学学会优秀青年论文竞赛一等奖
2004, 2007 北京大学学习优秀奖（二次）
2013 北京大学2012-2013学年度优秀班主任
2011 北京大学优秀博士学位论文三等奖
2008 北京大学洛杉矶奖学金
2007 北京大学五四奖学金
2006 北京大学华为奖学金
2005, 2006, 2008 北京大学学术类创新奖（三次）
2005 北京大学三星奖学金
2005 中国计算数学学会优秀青年论文竞赛一等奖
2004, 2007 北京大学学习优秀奖（二次）