Lunji Song
Professor of Institute of Computational Mathematics.
Email：song@lzu.edu.cn
Ph.D.Lanzhou University, 2009, Applied Mathematics
Biography
My Bachelor and Master degrees in Mathematics were received in Lanzhou University, China. As a doctoral student mentored by Prof. Yujiang Wu since 2006, and jointly supervised by Prof. Roger Temam, I visited ISCAM at Indiana University, Bloomington, USA and received my PhD degree in 2009. I also visited NTU (Singapore), Beijing Computational Science Research Center and Alabama University. During 2015-2016, I conducted my postdoc research on numerical methods for interface problems in Math Department at Alabama University, USA.
Social experience
Editorial Board Member of AIMS Mathematics
Member of Society for Industrial and Applied Mathematics (SIAM)
Member of Chinese Mathematical Society (CMS)
Member of the China Society for Industrial and Applied Mathematics (CSIAM)
Teaching and guiding the situation of graduate students
Numerical Analysis, Numerical Methods for Partial differential Equations, Linear Algebra, Calculus, The Mystery of Algorithms and Programs, Mathematical Modeling, Seminar for Graduate students, Undergraduate Students’ Thesis
Project results
1. NSFC general project, Weak Galerkin finite element methods and their applications on time-harmonic Helmholtz scattering interface problems in an unbounded domain, 2022-2025, PI
2. NSFC Youth Fund Project, High-precision internal penalty discontinuous Galerkin method for high-frequency Helmholtz scattering problems in unbounded areas, 2012-2014, PI
3. NSFC Tianyuan Mathematics Youth Fund Project, Multi-layer preconditioning method of discontinuous Galerkin method, 2011, PI
4. NSFC-Guangdong Provincial Joint Fund, Supercomputing Science Applied Research Special, 2016-2017, PI
5. NSFC (Gansu) general project, Numerical Algorithm and Theoretical Analysis of Hartree-Fock Equation, 2018-2020, PI
6. NSFC (Gansu) Project, Application and Analysis of Discontinuous Galerkin Method in Nonlinear Problems, 2014-2016, PI
7. The Fundamental Research Funds for the Central Universities, Lanzhou University, PI
Research interests
Discontinuous Galerkin FEMs for Helmholtz scattering problems in exterior domains, incompressible fluid flows, and parabolic problems; Weak Galerkin FEM for interface problems; Superconvergence of gradient recovery techniques for discontinuous Galerkin methods and its applications.
Publications
[1] Song, Lunji; Zhao, Shan; Liu, Kaifang A relaxed weak Galerkin method for elliptic interface problems with low regularity. Appl. Numer. Math. 128 (2018), 65–80.
[2] Song, Lunji; Zhao, Shan Symmetric interior penalty Galerkin approaches for two-dimensional parabolic interface problems with low regularity solutions. J. Comput. Appl. Math. 330 (2018), 356–379.
[3] Song, Lunji; Liu, Kaifang; Zhao, Shan A weak Galerkin method with an over-relaxed stabilization for low regularity elliptic problems. J. Sci. Comput. 71 (2017), no. 1, 195–218.
[4] Song, Lunji; Yang, Chaoxia Convergence of a second-order linearized BDF-IPDG for nonlinear parabolic equations with discontinuous coefficients. J. Sci. Comput. 70 (2017), no. 2, 662–685.
[5] Song, Lunji; Zhang, Zhimin Superconvergence property of an over-penalized discontinuous Galerkin finite element gradient recovery method. J. Comput. Phys. 299 (2015), 1004–1020.
[6] Song, Lunji; Zhang, Zhimin Polynomial preserving recovery of an over-penalized symmetric interior penalty Galerkin method for elliptic problems. Discrete Contin. Dyn. Syst. Ser. B 20 (2015), no. 5, 1405–1426.
[7] Song, Lunji; Gie, Gung-Min; Shiue, Ming-Cheng Interior penalty discontinuous Galerkin methods with implicit time-integration techniques for nonlinear parabolic equations. Numer. Methods Partial Differential Equations 29 (2013), no. 4, 1341–1366.
[8] Song, Lunji; Zhang, Jing; Wang, Li-Lian A multi-domain spectral IPDG method for Helmholtz equation with high wave number. J. Comput. Math. 31 (2013), no. 2, 107–136.
[9] Song, Lunji; Wu, Yujiang Nonlinear stability of reaction-diffusion equations using wavelet-like incremental unknowns. Appl. Numer. Math. 68 (2013), 83–107.
Honor and Award
1. Cuiying Good Teacher (Education Mentor Type), Lanzhou University, 2022
2. LONG-JI Education Teaching Backbone Award in 2021, Lanzhou University
3. Leader of a National First-Class Undergraduate Course Since 2020
4. Anshuo Teaching Award, 2020
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