Publications

Book

Jie Shen, Tao Tang and Li-Lian Wang. Spectral Methods: Algorithms, Analysis and Applications. Springer Series in Computational Mathematics, Volume 41, Springer, 2011.   Contents   Erratum (updated on Dec. 28, 2015)   Matlab Codes   Book Performance Report (2016) and Reviews

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Papers in refereed journals (Google Citations)

2017
68 Spectral element methods on hybrid triangular and quadrilateral meshes (with Jingliang Li, Heping Ma and Hua Wu). International Journal of Numerical Analysis and Modelling, Accepted, 2017 [Invited paper for the special issue in memory of Professor Benyu Guo (1942-2016)]. [PDF]
67 Laguerre functions and their applications to tempered fractional differential equations on infinite intervals (with Sheng Chen and Jie Shen). Journal of Scientific Computing, Accepted, 2017. [PDF]
66 A perfect absorbing layer for high-order simulation of wave scattering problems (with Zhiguo Yang). Lecture Notes in Computational Sciences and Engineering, Accepted, 2017. [Part of the plenary lecture at ICOSAHOM2016, Brazil] [PDF]
65 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. Accepted, 2017. [PDF]
64 A review of prolate spheroidal wave functions from the perspective of spectral methods. Journal of Mathematical Study. Vol. 50 (2), 101-143, 2017. [A review paper contributed to JMS]. [PDF]
63 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]
62 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]
61 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]
60 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]
59 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]
2016
58 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]
57 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]
56 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]
55 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]
2015
54 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]
53 Accurate simulation of circular and elliptic cylindrical invisibility cloaks (with Zhiguo Yang). Communications in Computational Physics, Vol. 17(3), 822-849, 2015. [PDF]
52 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]
51 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]
50 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]
2014
49 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]
48 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]
47 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]
46 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]
45 Superconvergence of Jacobi-Gauss-type spectral interpolation (with Xiaodan Zhao and Zhimin Zhang). Journal of Scientific Computing, Vol. 59(3), 667-687, 2014. [PDF]
2013
44 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]
43 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]
42 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]
41 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]
2012
40 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]
39 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]
38 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]
37 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]
2011
36 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]
35 On spectral approximations by generalized Slepian functions (with Jing Zhang). Numerical Mathematics: Theory, Methods and Applications, Vol. 4, 296-318, 2011. [PDF]
34 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]
33 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]
32 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]
2010
31 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]
30 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]
29 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]
28 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]
27 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]
26 A collocation method with exact imposition of mixed boundary conditions (with Zhongqing Wang). Journal of Scientific Computing, Vol. 42, 291-317, 2010. [PDF]
25 Analysis of spectral approximations using prolate spheroidal wave functions. Mathematics of Computation, Vol. 79, No. 270, 807-827, 2010. [PDF]
2009
24 Interpolation approximations based on Gauss-Lobatto-Legendre-Birkhoff quadrature (with Benyu Guo). Journal of Approximation Theory, Vol. 161, 142-173, 2009. [PDF]
23 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]
22 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]
21 On spectral approximations in elliptic geometries using Mathieu functions (with Jie Shen). Mathematics of Computation, Vol. 78, No. 266, 815-844, 2009. [PDF]
20 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]
19 Generalized Jacobi polynomials/functions and their applications (with Benyu Guo and Jie Shen). Applied Numerical Mathematics, Vol. 59, 1011-1028, 2009. [PDF]
2008
18 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]
2007
17 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]
16 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]
15 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]
14 Error analysis of spectral method on a triangle (with Benyu Guo). Advances in Computational Mathematics, Vol. 26, No. 4, 473-496, 2007. [PDF]
2006
13 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]
12 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]
11 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]
10 Stair Laguerre pseudospectral method for differential equations on the half line (with Benyu Guo). Advances in Computational Mathematics, Vol. 25, 305-322, 2006. [PDF]
9 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]
8 Mixed Fourier-Jacobi spectral method (with Benyu Guo). Journal of Mathematical Analysis and Applications, Vol. 315, No. 1, 8-28, 2006. [PDF]
<2006
7 Spectral approximation of the Helmholtz equation with high wave numbers (with Jie Shen). SIAM Journal on Numerical Analysis, Vol. 43, 623-644, 2005. [PDF]
6 Error analysis for mapped Jacobi spectral methods (with Jie Shen). Journal of Scientific Computing, Vol. 24, No. 2, 183-218, 2005. [PDF]
5 Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces (with Benyu Guo). Journal of Approximation Theory, Vol. 128, No. 1, 1-41, 2004. [PDF]
4 Error analysis for mapped Legendre spectral and pseudospectral methods (with Jie Shen). SIAM Journal on Numerical Analysis, Vol. 42, 326-349, 2004. [PDF]
3 Jacobi spectral methods for multiple-dimensional singular differential equations (with Benyu Guo). Journal of Computational Mathematics, Vol. 21, No. 3, 325-338, 2003.
2 Non-isotropic Jacobi spectral method (with Benyu Guo). Contemporary Mathematics, Vol. 329, 157-169, 2003.
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]

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Papers in refereed conference proceedings

1 Fast and accurate computation of exact nonreflecting boundary condition for Maxwell’s equations (with Xiaodan Zhao). Accepted by the conference: The 29th International Review of Progress in Applied and Computational Electromagnetics (ACES2013), 2013. [PDF]
2 Robust edge detection using Mumford-Shah and binary level set method (with Yuying Shi and Xue-Cheng Tai). Accepted by The Applied and Compuational Electromagnetic Society Lecture Notes in Computer Sciences. Proceeding of International Conference on Scale Space and Variational Methods in Computer Vision (SSVM2011), 2011. [PDF]
3 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]

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