Publications (by Topic)

PDEs with Nonlocal/Singular Operators
11 On diagonal dominance of FEM stiffness matrix of fractional Laplacian and maximum principle preserving schemes for the fractional Allen-Cahn equation (with Hongyan Liu, Changtao Sheng and Huifang Yuan). Journal of Scientific Computing, 86, 19, 2021. [PDF]
10 On explicit form of the FEM stiffness matrix for the integral fractional Laplacian on non-uniform meshes (with Hongbin Chen and Changtao Sheng). Applied Mathematics Letters, Vol. 133, 106864, 2021. [PDF]
9 Fast Fourier-like mapped Chebyshev spectral-Galerkin methods for PDEs with integral fractional Laplacian in unbounded domains (with Changtao Sheng, Jie Shen, Tao Tang and Huifang Yuan). SIAM Journal on Numerical Analysis, Vol. 58 (5): 2435-2464, 2020. [PDF]
8 Rational spectral methods for PDEs involving fractional Laplacian in unbounded domains (with Tao Tang, Huifang Yuan and Tao Zhou). SIAM Journal on Scientific Computing, Vol. 42, No. 42, A585-A611, 2020. [PDF]
7 A new spectral method using nonstandard singular basis functions for time-fractional differential equations (with Wenjie Liu and Shuhuang Xiang). Communications on Applied Mathematics and Computation , Vol. 1 (2): 207-230, 2019. [PDF]
6 Generalised Müntz Spectral Galerkin Methods for Singularly Perturbed Fractional Differential Equations (with Sun Tao, and Ruiqing Liu). East Asian Journal on Applied Mathematics . Vol. 8, 611-633 2018 [Invited for contribution to a special issue]. [PDF]
5 A spectral collocation method for nonlinear fractional boundary value problems with a caputo derivative (with Chuanli Wang and Zhongqing Wang). Journal of Scientific Computing. Vol. 76 (1), 166-188, 2018. [PDF]
4 Laguerre functions and their applications to tempered fractional differential equations on infinite intervals (with Sheng Chen and Jie Shen). Journal of Scientific Computing, Vol. 74 (3), 1286–1313, 2018. [PDF]
3 A new framework for solving fractional optimal control problems using fractional pseudospectral methods (with Xiaojun Tang and Yang Shi). Automatica, Vol. 78, 333-340, 2017. [PDF]
2 Optimal fractional integration preconditioning and error analysis of fractional collocation method using nodal generalized Jacobi functions (with Can Huang, Yujian Jiao and Zhimin Zhang). SIAM Journal on Numerical Analysis, Vol. 54(6), 3357–3387, 2016. [PDF]
1 Generalized Jacobi functions and their applications to fractional differential equations (with Sheng Chen and Jie Shen). Mathematics of Computation, Vol. 85 (300), 1603-1638, 2016. [PDF]

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Acoustic and Electromagnetic Wave Scattering
17 A truly exact perfect absorbing layer for time-harmonic acoustic wave scattering problems (with Zhiguo Yang and Yang Gao). To appear in SIAM Journal on Scientific Computing, 2021. [PDF]
16 Analysis of a backward Euler-type scheme for Maxwell’s equations in a Havriliak-Negami dispersive medium (with Yubo Yang and Fanhai Zeng). To appear in ESAIM: Mathematical Modelling and Numerical Analysis, 2021. [PDF]
15 On time-domain NRBC for Maxwell’s equations and its application in accurate simulation of electromagnetic invisibility cloaks (with Bo Wang, Zhiguo Yang and Shidong Jiang). Journal of Scientific Computing, 86, 20, 2021. [PDF]
14 An efficient iterative method for solving multiple scattering in locally inhomogeneous media (with Bo Wang, Ziqing Xie and Rui Zhang). Computer Methods in Applied Mechanics and Engineering , Vol. 358, 112642, 2020. [PDF]
13 Wavenumber explicit analysis for time-harmonic Maxwell equations in a spherical shell and spectral approximations (with Lina Ma, Jie Shen and Zhiguo Yang). IMA Journal of Numerical Analysis. Vol. 38 (2), 810-851, 2018. [PDF]
12 An accurate spectral method for the transverse magnetic mode of Maxwell equations in Cole-Cole media (with Can Huang). Advances in Computational Mathematics. Vol. 45, 707–734, 2019. [PDF]
11 A perfect absorbing layer for high-order simulation of wave scattering problems (with Zhiguo Yang). Spectral and high order methods for partial differential equations—ICOSAHOM 2016. Lect. Notes Comput. Sci. Eng., 119, 81–101 . Springer, Cham, 2017. [Part of the plenary lecture at ICOSAHOM2016, Brazil] [PDF]
10 Seamless integration of global Dirichlet-to-Neumann boundary condition and spectral elements for transformation electromagnetics (with Zhiguo Yang, Zhijian Rong, Bo Wang and Baile Zhang). Computer Methods in Applied Mechanics and Engineering, Vol. 301, 137-163, 2016. [PDF]
9 Analysis of transient electromagnetic scattering from a three-dimensional open cavity (with Peijun Li and Aihua Wood). SIAM Journal on Applied Mathematics, Vol. 75(4), 1675-1699, 2015. [PDF]
8 Accurate simulation of circular and elliptic cylindrical invisibility cloaks (with Zhiguo Yang). Communications in Computational Physics, Vol. 17(3), 822-849, 2015. [PDF]
7 Spectral approximation of time-harmonic Maxwell equations in three-dimensional exterior domains (with Lina Ma and Jie Shen). International Journal of Numerical Analysis and Modelling, Vol. 12,343-365, 2015. [PDF]
6 On L^2-stability analysis of time-harmonic acoustic scattering problems with exact nonreflecting boundary conditions (with Bo Wang). Journal of Mathematical Study, Vol. 1, No. 1, 65-84, 2014. [PDF]
5 A multi-domain spectral IPDG method for Helmholtz equation with high wave number (with Lunji Song and Jing Zhang). Journal Of Computational Mathematics, Vol. 31, 107-136, 2013. [PDF]
4 Fast and accurate computation of time-domain acoustic scattering problems with exact nonreflecting boundary conditions (with Bo Wang and Xiaodan Zhao). SIAM Journal on Applied Mathematics, Vol. 72, No. 6, 1869-1898, 2012. [PDF]
3 An efficient and accurate spectral method for acoustic scattering in elliptic domains (with Jie Shen and Qirong Fang). Numerical Mathematics: Theory, Methods and Applications, Vol. 2, No. 3, 258-274, 2009. [PDF]
2 Analysis of a spectral-Galerkin approximation to the Helmholtz equation in exterior domains (with Jie Shen). SIAM Journal on Numerical Analysis, Vol. 45, 1954-1978, 2007. [PDF]
1 Spectral approximation of the Helmholtz equation with high wave numbers (with Jie Shen). SIAM Journal on Numerical Analysis, Vol. 43, 623-644, 2005. [PDF]

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Spectral/Spectral-element Methods

A. Spectral Approximation Theory
8 Asymptotics of Generalized Gegenbauer functions of fractional degree (with Wenjie Liu). Journal of Approximation Theory, Vol. 253, 105378, 2020. [PDF]
7 Optimal error estimates for Chebyshev approximation of functions with limited regularity in fractional Sobolev-type spaces (with Wenjie Liu and Huiyuan Li). Mathematics of Computation, Vol. 88 (320): 2857-2895, 2019. [PDF]
6 Superconvergence of Jacobi-Gauss-type spectral interpolation (with Xiaodan Zhao and Zhimin Zhang). Journal of Scientific Computing, Vol. 59(3), 667-687, 2014. [PDF]
5 Sharp error bounds for Jacobi expansions and Gegenbauer-Gauss quadrature of analytic functions (with Xiaodan Zhao and Ziqing Xie). SIAM Journal on Numerical Analysis, Vol. 51, No. 3, 1443-1469, 2013. [PDF]
4 On exponential convergence of Gegenbauer interpolation and spectral differentiation (with Ziqing Xie and Xiaodan Zhao). Mathematics of Computation, Vol. 82, No. 282, 1017-1036, 2013. [PDF]
3 Interpolation approximations based on Gauss-Lobatto-Legendre-Birkhoff quadrature (with Benyu Guo). Journal of Approximation Theory, Vol. 161, 142-173, 2009. [PDF]
2 Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces (with Benyu Guo). Journal of Approximation Theory, Vol. 128, No. 1, 1-41, 2004. [PDF]
1 Jacobi interpolation approximations and their applications to singular differential equations (with Benyu Guo). Advances in Computational Mathematics, Vol. 14, No. 3, 227-276, 2001. [PDF]

B. PSWF Spectral Methods
10 Ball prolate spheroidal wave functions in arbitrary dimensions (with Jing Zhang, Huiyuan Li and Zhimin Zhang). Applied and Computational Harmonic Analysis. Vol. 48, 539-569, 2020. [PDF]
9 A review of prolate spheroidal wave functions from the perspective of spectral methods. Journal of Mathematical Study. Vol. 50 (2), 101-143, 2017. [PDF]
8 Optimal spectral schemes based on generalized prolate spheroidal wave functions of order -1 (with Jing Zhang, Huiyuan Li and Zhimin Zhang). Journal of Scientific Computing, Vol. 70, 451-477, 2017. [PDF]
7 On hp-convergence of prolate spheroidal wave functions and a new well-conditioned prolate-collocation scheme (with Jing Zhang and Zhimin Zhang). Journal of Computational Physics, Vol. 268, 377-398, 2014. [PDF]
6 On spectral approximations by generalized Slepian functions (with Jing Zhang). Numerical Mathematics: Theory, Methods and Applications, Vol. 4, 296-318, 2011. [PDF]
5 An improved estimate of PSWF approximation and approximation by Mathieu functions (with Jing Zhang). Journal of Mathematical Analysis and Applications, Vol. 379, 35-47, 2011. [PDF]
4 A prolate-element method for nonlinear PDEs on the sphere (with Jing Zhang and Zhijian Rong). Journal of Scientific Computing, Vol. 47, 73-92, 2011. [PDF]
3 A new generalization of the PSWFs with applications to spectral approximations on quasi-uniform grids (with Jing Zhang). Applied and Computational Harmonic Analysis, Vol. 29, No. 3, 523-545, 2010. [PDF]
2 Analysis of spectral approximations using prolate spheroidal wave functions. Mathematics of Computation, Vol. 79, No. 270, 807-827, 2010. [PDF]
1 On spectral approximations in elliptic geometries using Mathieu functions (with Jie Shen). Mathematics of Computation, Vol. 78, No. 266, 815-844, 2009. [PDF]

C. Well-conditioned Collocation Methods
6 On approximate inverse of Hermite and Laguerre collocation differentiation matrices and new collocation schemes in unbounded domains (with Chao Zhang, Dongqin Gu and Wenjie Liu). Journal of Computational and Applied Mathematics. Vol. 344, 553–571, 2018. [PDF]
5 A new collocation scheme using non-polynomial basis functions (with Chao Zhang and Wenjie Liu). Journal of Scientific Computing, Vol. 70, 793–818, 2017. [PDF]
4 Well-conditioned fractional collocation methods using fractional Birkhoff interpolation basis (with Yujian Jiao and Can Huang). Journal of Computational Physics, Vol. 305, 1-28, 2016. [PDF]
3 A well-conditioned collocation method using a pseudospectral integration matrix (with Michael D. Samson and Xiaodan Zhao). SIAM Journal on Scientific Computing, Vol. 36(3), A907-A929, 2014. [PDF]
2 A Legendre-Gauss collocation method for nonlinear delay differential equations (with Zhongqing Wang). Discrete and Continuous Dynamical Systems-B, Vol. 13, No. 3, 685-708, 2010 [PDF]
1 A collocation method with exact imposition of mixed boundary conditions (with Zhongqing Wang). Journal of Scientific Computing, Vol. 42, 291-317, 2010. [PDF]

D. Spectral-element Methods
9 A new triangular spectral element method II: Mixed formulation and hp-error estimates (with Bingzhen Zhou, Bo Wang and Ziqing Xie). Numerical Mathematics: Theory, Methods and Applications. Vol. 12, 72-97, 2019.[Invited for contribution] [PDF]
8 Spectral element methods on hybrid triangular and quadrilateral meshes (with Jingliang Li, Heping Ma and Hua Wu). International Journal of Numerical Analysis and Modelling. Vol. 15(12), 111-133, 2018 [Invited paper for the special issue in memory of Professor Benyu Guo (1942-2016)]. [PDF]
7 Accurate calculation of spherical and vector spherical harmonic expansions via spectral element grids (with Bo Wang and Ziqing Xie).
Advances in Computational Mathematics , Vol. 44 (2), 951-985, 2018.		 [PDF]
6 An unfitted hybridizable DG method for the Poisson interface problem and its error analysis (with Haixia Dong, Bo Wang and Ziqing Xie). IMA Journal of Numerical Analysis, Vol. 37, 444–476, 2017. [PDF]
5 A new triangular spectral-element method I: Implementation and analysis on a triangle (with Michael Samson and Huiyuan Li). Numerical Algorithms, Vol. 64, 519-547, 2012. [PDF]
4 A new spectral method on triangles (with Youyun Li, Huiyuan Li and Heping Ma). Lecture Notes in Computational Sciences and Engineering. Proceeding of International Conference on Spectral and High-Order Methods (ICOSAHOM09), 237-246, 2010. [PDF]
3 A spectral method on tetrahedra using rational basis functions (with Huiyuan Li). International Journal of Numerical Analysis and Modelling, Vol. 7, No. 2, 330-355, 2010. [PDF]
2 A triangular spectral element method using fully tensorial rational basis functions (with Jie Shen and Huiyuan Li). SIAM Journal on Numerical Analysis, Vol. 47, No. 3, 1619-1650, 2009. [PDF]
1 Error analysis of spectral method on a triangle (with Benyu Guo). Advances in Computational Mathematics, Vol. 26, No. 4, 473-496, 2007. [PDF]

E. Miscellaneous Spectral Algorithms: Sparse Grids, GJP/GJFs, Rational Approximation etc.
17 Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains (with Jie Shen and Haijun Yu). Journal of Computational and Applied Mathematics, Vol. 256, 264-275, 2014. [PDF]
16 Sparse spectral approximations of high-dimensional problems based on hyperbolic cross (with Jie Shen). SIAM Journal on Numerical Analysis, Vol. 48, No. 3, 1087-1109, 2010. [PDF]
15 Generalized Jacobi polynomials/functions and their applications (with Benyu Guo and Jie Shen). Applied Numerical Mathematics, Vol. 59, 1011-1028, 2009. [PDF]
14 Optimal spectral-Galerkin methods using generalized Jacobi polynomials (with Benyu Guo and Jie Shen). Journal of Scientific Computing, Vol. 27, No. 1-3, 305-322, 2006. [PDF]
13 Legendre and Chebyshev dual-Petrov-Galerkin methods for hyperbolic equations (with Jie Shen). Computer Methods in Applied Mechanics and Engineering, Vol. 196, 3785-3797, 2007. [PDF]
12 Laguerre and composite Legendre-Laguerre dual-Petrov-Galerkin methods for third-order equations (with Jie Shen). Discrete and Continuous Dynamical Systems-B, Vol. 6, No. 6, 1381-1402, 2006. [PDF]
11 Some recent advances on spectral methods for unbounded domains (with Jie Shen). Communications in Computational Physics, Vol. 5, No. 2-4, 195-241, 2009. [PDF]
10 Error analysis for mapped Jacobi spectral methods (with Jie Shen). Journal of Scientific Computing, Vol. 24, No. 2, 183-218, 2005. [PDF]
9 Error analysis for mapped Legendre spectral and pseudospectral methods (with Jie Shen). SIAM Journal on Numerical Analysis, Vol. 42, 326-349, 2004. [PDF]
8 Integration process of ordinary differential equations based on Laguerre-Radau interpolations (with Benyu Guo, Zhongqing Wang and Hongjiong Tian). Mathematics of Computation, Vol. 77, 181-199, 2008. [PDF]
7 Fourierization of the Legendre-Galerkin method and a new space-time spectral method (with Jie Shen). Applied Numerical Mathematics, Vol. 57, 710-720, 2007. [PDF]
6 Modified Laguerre pseudospectral method refined by multidomain Legendre pseudospectral approximation (with Benyu Guo). Journal of Computational and Applied Mathematics, Vol. 190, 304-324, 2006. [PDF]
5 Stair Laguerre pseudospectral method for differential equations on the half line (with Benyu Guo). Advances in Computational Mathematics, Vol. 25, 305-322, 2006. [PDF]
4 Generalized Laguerre interpolation and pseudospectral method for unbounded domains (with Benyu Guo and Zhongqing Wang). SIAM Journal on Numerical Analysis, Vol. 43, No. 6, 2567-2589, 2006. [PDF]
3 Mixed Fourier-Jacobi spectral method (with Benyu Guo). Journal of Mathematical Analysis and Applications, Vol. 315, No. 1, 8-28, 2006. [PDF]
2 Jacobi spectral methods for multiple-dimensional singular differential equations (with Benyu Guo). Journal of Computational Mathematics, Vol. 21, No. 3, 325-338, 2003.
1 Non-isotropic Jacobi spectral method (with Benyu Guo). Contemporary Mathematics, Vol. 329, 157-169, 2003.

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PDE-based Image Processing
9 Generalizing Mumford-Shah model for multiphase piecewise smooth image segmentation (with Ying Gu, Wei Xiong and Jierong Cheng). IEEE Transactions on Image Processing, Vol. 26, No. 2, 942-952, 2017. [PDF]
8 Convergence rate of overlapping domain decomposition methods for the ROF model based on a dual formulation (with Huibin Chang, Xue-Cheng Tai and Danping Yang). SIAM Journal On Imaging Sciences, Vol 8(1), 564-591, 2015. [PDF]
7 A fast edge detection algorithm using binary labels (with Yuying Shi, Ying Gu and Xue-Cheng Tai). Inverse Problem and Imaging, Vol. 9(2), 551-578, 2015. [PDF]
6 Adaptive wavelet collocation methods for image segmentation using TV-Allen-Cahn type models (with Zhijian Rong and Xue-Cheng Tai). Advances in Computational Mathematics, Vol. 38, No. 1, 101-131, 2013. [PDF]
5 A direct approach towards global minimization for multiphase labeling and segmentation problems (with Ying Gu and Xue-Cheng Tai). IEEE Transactions on Image Processing, Vol. 21, No. 5, 2399-2411, 2012. [PDF]
4 Geometry of total variation regularized L^p-model (with Yuying Shi and Xue-Cheng Tai). Journal of Computational and Applied Mathematics, Vol. 236, 2223-2234, 2012. [PDF]
3 Fast algorithms for the anisotropic LLT model in image denoising (with Zhifeng Pang and Yufei Yang). East Asian Journal on Applied Mathematics, Vol. 1, No. 3, 264-283, 2011. [PDF]
2 Efficient dual algorithms for image segmentation using TV-Allen-Cahn type models (with Ying Gu). Communications in Computational Physics, Vol. 9, No. 4, 859-877, 2011. [PDF]
1 A two-level domain decomposition method for image restoration (with Jing Xu and Xue-Cheng Tai). Inverse Problem and Imaging, Vol. 4, No. 3, 523-545, 2010. [PDF]

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