Assistant Professor Yong-Yong Cai

Applied and Computational Mathematics

Office Location
Room B211

Ph.D in Applied Mathematics, National University of Singapore, 2012

M.S in Pure and Applied Mathematics, Peking University, 2007

B.S in Pure and Applied Mathematics, Peking University, 2004


Professional Employment

Yongyong Cai received his Ph.D. in Applied Mathematics, National University of Singapore in 2012, supervised by Professor Weizhu Bao. Afterwards, he became a visiting assistant professor at University of Wisconsin Madison from 2012-2013, and also a visiting post-doc research associate at University of Maryland, College Park during 2013. Then he worked as a research associate/visiting assistant professor at Purdue University, West Lafayette during 2013-2016. Now, he is the assistant professor at Beijing Computational Science Research Center.

Research Interests

Partial differential equations and applied analysis
Nonlinear Schrodinger equation and applications in Bose-Einstein condensation
Phase-field equations and applications
Highly oscillatory dispersive equation and applications
Numerical analysis and scientific computing


SIAM Travel Award to SIAM Conference on Computational Science and Engineering (CSE) 2013
SIAM Student Chapter Certificate of Recognition, 2012.
Top graduate research award in Faculty of Science 2011, National University of Singapore, Singapore
First prize, The 7th East Asia SIAM Student Paper Prize, 2011.
Marie Curie Early Stage Training (MEST) fellowship (DEASE), European Union (Jan.-Jun. 2009, Jan.-Aug. 2010).
President Scholarship, (2007); research scholarship (2007-2011), National University
of Singapore, Singapore.

Representative Publications
1.  Yongyong Cai, Weizhu Bao, Xiaowei Jia, Qinglin Tang; A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Dirac Equation in the Nonrelativistic Limit Regime; SIAM J. Numer. Anal. 54, 3, 1785-1812, 2016
2.  Yongyong Cai, Weizhu Bao, Jia Yin, Xiaowei Jia; Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime; Sci China Math, 59, 2016
3.  Yongyong Cai, Weizhu Bao, Xinran Ruan; Mean- eld regime and Thomas-Fermi approximations of trapped Bose-Einstein condensates with higher order interactions in one and two dimensions; Journal of Physics B: Atomic, Molecular and Optical Physics; 49, 12, 2016
4.  Yongyong Cai, Weizhu Bao; Ground states and dynamics of spin-orbit-coupled Bose-Einstein condensates; SIAM J. on Applied Math.; 75, 492-517, 2015
5.  Yongyong Cai, Weizhu Bao, Xiaofei Zhao; A uniformly accurate multiscale time integrator pseudospectral method for the Klein-Gordon equation in the nonrelativistic limit regime; SIAM J. Numer. Anal.; 52, 2488-2511, 2014
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