Areas of Focus
- High-dimensional numerical methods
- Discrete modeling and combinatorial optimization
- Computational quantum mechanics
- Spectral theory and algorithms
- Numerical solutions of differential equations
- Computational complexity
Work Experience
- 2024- Professor, Peking University
- 2012-2023 Associate Professor, Peking University
- 2010-2012 Assistant Professor, Peking University
- 2014 Visiting Research Scholar, University of Seville
- 2014 Visiting Research Scholar, Chinese University of Hong Kong
- 2012 Visiting Research Scholar, Princeton University
- 2009-2010 Postdoctoral Fellow, Hong Kong University of Science and Technology
- 2007-2008 Visiting Research Scholar, University of North Carolina
Academic Background & Achievements
- 2009 PhD: Peking University
- 2003 Bachelor: Peking University
Publications
- A characteristic-spectral-mixed scheme for six-dimensional Wigner-Coulomb dynamics, Yunfeng Xiong, Yong Zhang, Sihong Shao, 2023
- Nonlocalization of singular potentials in quantum dynamics, Sihong Shao, Lili Su, 2023
- Adaptive Hermite spectral methods in unbounded domains, Tom Chou, Sihong Shao, Mingtao Xia, 2023
- Noncollinear density functional theory, Zhichen Pu, Hao Li, Ning Zhang, Hong Jiang, Yiqin Gao, Yunlong Xiao, Qiming Sun, Yong Zhang, Sihong Shao, 2023
- A higher-order accurate operator splitting spectral method for the Wigner-Poisson system, Zhenzhu Chen, Haiyan Jiang, Sihong Shao, 2022
- A frequency-dependent p-adaptive technique for spectral methods, Mingtao Xia, Sihong Shao, Tom Chou, 2021
- Efficient scaling and moving techniques for spectral methods in unbounded domains, Mingtao Xia, Sihong Shao, Tom Chou, 2021
- Lovász extension and graph cut, Kung-Ching Chang, Sihong Shao, Dong Zhang, Weixi Zhang, 2021
- Nonsmooth critical point theory and applications to the spectral graph theory, Kung-Ching Chang, Sihong Shao, Dong Zhang, Weixi Zhang, 2021
- Branching random walk solutions to the Wigner equation, Sihong Shao, Yunfeng Xiong, 2020
- A high order efficient numerical method for 4-D Wigner equation of quantum double-slit interferences, Zhenzhu Chen, Sihong Shao, Wei Cai, 2019
- Externally driven nonlinear Dirac equation revisited: theory and simulations, Niurka R. Quintero, Sihong Shao, Renato Alvarez-Nodarse, Franz G. Mertens, 2019
- Numerical methods for the Wigner equation with unbounded potential, Zhenzhu Chen, Yunfeng Xiong, Sihong Shao, 2019
- The Wigner branching random walk: Efficient implementation and performance evaluation, Yunfeng Xiong, Sihong Shao, 2019
- A branching random walk method for many-body Wigner quantum dynamics, Sihong Shao, Yunfeng Xiong, 2019
- Cheeger's cut, maxcut and the spectral theory of 1-Laplacian on graphs, Kung-Ching Chang, Sihong Shao, Dong Zhang, 2017
- Nonlinear Dirac equation solitary waves under a spinor force with different components, Franz G. Mertens, Fred Cooper, Sihong Shao, Niurka R. Quintero, Avadh Saxena, A. R. Bishop, 2017
- Nodal domains of eigenvectors for 1-Laplacian on graphs, Kung-Ching Chang, Sihong Shao, Dong Zhang, 2017
- Boundary treatments in non-equilibrium Green's function (NEGF) methods for quantum transport in nano-MOSFETs, Wei Cai, Haiyan Jiang, Pingwen Zhang, Sihong Shao, 2008
- A Schwarz generalized eigen-oscillation spectral element method (GeSEM) for 2-D high frequency electromagnetic scattering in dispersive inhomogeneous media, Wei Cai, Xia Ji, Jiguang Sun, Sihong Shao, 2008
- Nonlinear Dirac equation solitary waves under a spinor force with different components, A.R. Bishop, Fred Cooper, Franz G. Mertens, Niurka R. Quintero, Avadh Saxena, Sihong Shao, 2017
- A variational model for two-phase immiscible electro-osmotic flows, Tiezheng Qian, Sihong Shao, 2012
- Relativistic explicit correlation: Coalescence conditions and practical suggestions, Zhendong Li, Wenjian Liu, Sihong Shao, 2012
- Adaptive conservative cell average spectral element methods for transient Wigner equation in quantum transport, Wei Cai, Tiao Lu, Sihong Shao, 2011
- Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory, Weinan E, Lin Lin, Sihong Shao, 2013
- Interaction of solitary waves with a phase shift in a nonlinear Dirac model, Huazhong Tang, Sihong Shao, 2008
- Accurate calculation of Green's function of the Schroedinger equation in a block layered potential, Wei Cai, Huazhong Tang, Sihong Shao, 2006
- Higher-order accurate Runge-Kutta discontinuous Galerkin methods for a nonlinear Dirac model, Huazhong Tang, Sihong Shao, 2006
- Interaction for the solitary waves of a nonlinear Dirac model, Huazhong Tang, Sihong Shao, 2005
- Numerical methods for nonlinear Dirac equation, Huazhong Tang, Jian Xu, Sihong Shao, 2013
- Analysis of the time reversible Born-Oppenheimer molecular dynamics, Lin Lin, Jianfeng Lu, Sihong Shao, 2014
- The 1-Laplacian Cheeger Cut: Theory and Algorithms, K.C. Chang, Dong Zhang, Sihong Shao, 2015
- Multi-hump solitary waves of a nonlinear Dirac equation, Huazhong Tang, Dongyi Wei, Jian Xu, Sihong Shao, 2015
- Stability of solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity, Fred Cooper, Avinash Khare, Franz G. Mertens, Niurka R. Quintero, Avadh Saxena, Sihong Shao, 2014
- Feature-scale simulations of particulate slurry flows in chemical mechanical polishing by smoothed particle hydrodynamics, Wei Cai, Dong Wang, Changhao Yan, Xuan Zeng, Sihong Shao
Awards
- 2021 Peking University Huang Tingfang/Xinhe Young Outstanding Scholar Award
- 2020 Peking University Outstanding PhD Thesis Advisor
- 2019 Beijing Institute for Artificial Intelligence 'Zhiyuan Young Scientist'
- 2015 Procter & Gamble Teaching Award
- 2013, 2017 Peking University Outstanding Class Teacher (twice)
- 2011 Peking University Outstanding PhD Thesis Third Prize
- 2008 Peking University Los Angeles Scholarship
- 2007 Peking University May Fourth Scholarship
- 2006 Peking University Huawei Scholarship
- 2005, 2006, 2008 Peking University Academic Innovation Award (three times)
- 2005 Peking University Samsung Scholarship
- 2005 Chinese Society for Computational Mathematics Outstanding Young Paper Competition First Prize
- 2004, 2007 Peking University Academic Excellence Award (twice)
