研究领域为高频波、量子输运的建模与计算,分数次微分方程的数值分析和计算,多目标变分与优化的理论和应用。利用半经典极限和多尺度建模来研究高频波和量子输运,得到了既能捕捉到高频波的衍射、量子遂穿等微观效应,而计算量和经典模型相当的多尺度模型和算法。分数次微分方程是最近10几年的一个新兴的方向,在反常扩散、多孔隙介质以及生物等领域得到了很好的应用,在分数次微分方程的极大值原理,边界条件的处理等给出了一些新的观点,并设计了快速有效的数值算法。
(1) Houde Han,Yintzer Shih#,Dongsheng Yin,Tailored Finite Point Methods for Solving Singularly Perturbed Eigenvalue Problems with Higher Eigenvalues,Journal of Scientific Computing , 2017(73): 242–282
(2) H. Brunner#, H. Han and D. Yin,The Maximum Principle for Time-Fractional Diffusion Equations and Its Application, Numerical Functional Analysis and Optimization, 2015(36): 1307–1321
(3) H. Brunner, H. Han and D. Yin#,Artificial boundary conditions and finite difference approximations for a time-fractional diffusion-wave equation on a two-dimensional unbounded spatial domain, Journal of Computational Physics 2014(276): 541-562
(4) S. Jin, D. Wei and D. Yin#, Gaussian beam method for the Schrodinger equation with discontinuous potentials, Journal of Computational and Applied Mathematics, 2014(265): 199-219
(5) D. Yin#, M. Tang and S. Jin, The Gaussian beam method for the Wigner equation with discontinuous potentials, Inverse Problems and Imaging, 2013(3): 1051-1074
(6) D. Yin and C. Zheng#, Composite Gaussian beam approximation method for one dimensional multi-phased wave functions, Communications in Computational Physics, 2012(3): 951-984
(7) D. Yin and C. Zheng#, Gaussian beam formulations and interface conditions for the one-dimensional linear Schrodinger equation, Wave Motion, 2011(48): 310-324
(8) S. Jin and D. Yin#, Computational high frequency waves through curved interfaces viathe Liouville equation and Geometrical Theory of Diffraction, Journal of Computational Physics, 2008(227): 6106-6139
(9) H. Han and D. Yin#, The absorbing boundary conditions for multidimensional Klein-Gordon equations, Communication in Mathematical Sciences, 2007(3): 743-764
(10) H. Han#, D. Yin and Z. Huang, Numerical Solutions of Schrodinger equation in R^3, Numerical Methods for Partial Differential Equations, 2007(3): 511-533