姓名: 王海永

性别:

出生日期: 1983-09-23


职位: 副教授

电话:

Email: haiyongwang@hust.edu.cn

个人主页:


基本情况 Basic


				

教育背景 Educational background

Ph.D. in Mathematics, 09/2007 — 12/2010
School of Mathematics and Statistics
Central South University
Changsha, 410083
Hunan Province
Supervisor: Professor Shuhuang Xiang

B.Sc. in Mathematics, 09/2001 — 06/2005
School of Mathematics and Statistics
Central South University
Changsha, 410073
Hunan Province

工作经历 Work experience

Associate Professor in Mathematics, 01/2013 — present
School of Mathematics and Statistics
Huazhong University of Science and Technology
Wuhan, 430074
Hubei Province

Postdoc Research Fellow, 03/2011 — 12/2012
Department of Computer Science
University of Leuven
Celestijnenlaan 200A, 3001 Leuven
Belgium
       

研究方向 Research fields

1. Numerical methods for highly oscillatory problems
    Starting from my PhD, I am interested in efficient methods for highly oscillatory integrals such as numerical steepest descent methods, Filon-type methods and Levin-type methods. 
2. Quadrature
    Gauss and Clenshaw-Curtis quadrature are two improtant methods for computing integrals numerically. Their convergence rates for various functions are of interest. Especially, I am interested in convergence rate and acceleration of Clenshaw-Curtis quadrature for singular functions. 
3. Spectral methods
    Spectral expansions in terms of Jacobi, Legendre and Chebyshev polynomials are widely used in solving differential equations. Typically, these expansion coefficients can not be calculated exactly and numerical algorithms should be developed to provide approximation. I am interested in developing fast and accurate methods for the computation of Jacobi coefficients. Meanwhile, I am also interested in the optimal estimatie of these spectral expansion coefficients.    
4.Barycentric interpolation 
   Barycentric interpolation formula is a fast and stable method for computing the polynomial interpolant numerically. In practice, most attention is paid to the Chebyshev roots and extreme points. Here, I am interested in the Legendre and Jacobi points and explicit barycentric weights for these points are given which enables us to evaluate the corresponding polynomial interpolants efficiently.   

科研成果 Scientific achievements

Publications:
14. Wang Haiyong and Huybrechs Daan, Fast and accurate computation of Chebyshev coefficients in the complex plane, IMA Journal of Numerical Analysis, to appear, 2016. 
13. Wang Haiyong, On the optimal estimates and comparison of Gegenbauer expansion coefficients, SIAM Journal on Numerical Analysis, 54(3), 1557–1581, 2016
12. Wang Haiyong, Huybrechs Daan and Vandewalle Stefan, Explicit barycentric weights for polynomial interpolation in the roots or extrema of classical orthogonal polynomials, Mathematics of Computation, 83 (290), 2893—2914, 2014 
11. Asheim Andreas, Deano Alfredo, Huybrechs Daan and Wang Haiyong, A Gaussian quadrature rule for oscillatory integrals on a bounded interval, Discrete and Continuous Dynamical Systems A, 34 (3), 883—901, 2014
10. Xiang Shuhuang, He Guo and Wang Haiyong, On fast and stable implementation of Clenshaw-Curtis and Fejér-type quadrature rules, Abstract and Applied Analysis, Volume 2014, Article ID 436164, 2014
9. Wang Haiyong, Zhang Lun and Huybrechs Daan, Asymptotic expansions and fast computation of oscillatory Hilbert transforms, Numerische Mathematik, 123 (4),  709—743, 2013
8. Wang Haiyong and Xiang Shuhuang, On the convergence rates of Legendre approximation, Mathematics of Computation, 81 (278), 861—877, 2012
7. Xiang Shuhuang, Cho Yeol Je, Wang Haiyong and Brunner Hermann, Clenshaw-Curtis-Filon-type methods for highly oscillatory Bessel transforms and applications, IMA Journal of Numerical Analysis, 31 (4), 1281—1314, 2011
6. Wang Haiyong and Xiang Shuhuang, Asymptotic expansion and Filon-type methods for a Volterra integral equation with a highly oscillatory kernel, IMA Journal of Numerical Analysis, 31 (2), 469—490, 2011
5. Xiang Shuhuang and Wang Haiyong, Fast integration of highly oscillatory integrals with exotic oscillators, Mathematics of Computation, 79 (270), 829—844, 2010
4. Xiang Shuhuang, Chen Xiaojun and Wang Haiyong, Error bounds for approximation in Chebyshev points, Numerische Mathematik, 116 (3), 463—491, 2010
3. Wang Haiyong and Xiang Shuhuang, On the evaluation of Cauchy principal value integrals of oscillatory functions, Journal of Computational and Applied Mathematics, 234 (1), 95—100, 2010
2. Wang Haiyong and Xiang Shuhuang, Uniform approximations to Cauchy principal value integrals of oscillatory functions, Applied Mathematics and Computation, 215 (5), 1886—1894, 2009      
1. Xiang Shuhuang and Wang Haiyong, On the Levin iterative methods for oscillatory integrals, Journal of Computational and Applied Mathematics, 217 (1), 38—45, 2008

Preprints:
1. Wang Haiyong and Huybrechs Daan, Fast and accurate computation of Jacobi expansion coefficients of analytic functions, arXiv:1404.2463, 2014
2. Wang Haiyong, Convergence rate and acceleration of Clenshaw-Curtis quadrature for functions with endpoint singularities, arXiv:1401.0638, 2014.
3. Wang Haiyong and Zhang Lun, Jacobi polynomials on the Bernstein ellipse, arXiv:1703.04243, 2017.

      

其它 Other

每年都会收到一些报考研究生的邮件,以下是相关的两点说明:
(1)如果您确信对计算数学的课题研究有非常浓厚的兴趣,或者您已经计划好未来继续攻读博士,非常欢迎联系;
(2)也许您还不确定对学术研究是否有兴趣,但是您确信在未来几年里能够在学校里专心读书的,欢迎联系;
此外有两个建议
(1)如果您在同一时间联系多个指导老师,建议不要考虑我;
(2)在联系我之前,建议您了解一下我的研究方向和问题。