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An Observational and Modeling Study of Extratropical Transition of Hurricane Sandy in 2012

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Journal of Ocean University of China 2015年第5期14卷 783-794页

作者： fu dan LI Pengyuan fu Gang Department of Meteorology Ocean University of China

Around 30 October 2012, Hurricane Sandy made landfall along the New Jersey shoreline after its completion of extratropical transition and transformation into an extratropical cyclone. The strong gale induced a catastrophic storm surge, and caused 72 death and damage of more than $50 billion. In this paper, the evolutionary process and spatial structure of the Hurricane Sandy during its extratropical transition were investigated by using Weather Research and Forecasting （WRF） version 3.3.1 modeling resuits and National Center for Environmental Prediction （NCEP） Coupled Forecast System model version 2 reanalysis datasets （CFSv2）. It is found that during the upper-level trough interaction on 29 October, Sandy gradually fused with a pre-existing mid-latitude low-pressure system, and finished the re-intensification. WRF modeling results showed that the second peak occurred mainly due to the enhanced vertical motion, reduced vertical wind shear as well as the supplement of potential vorticity resulting from trough interaction over the southeast of Great Lakes. The cold continental air from the back of trough was encircled within the warm core system cyclonically, forming the characteristic of warm seclusion.

关键词： Hurricane Sandy extratropical transition mid latitude trough WRF modeling

A two-grid algorithm based on Newton iteration for the stream function form of the Navier-Stokes equations

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Applied Mathematics(A Journal of Chinese Universities) 2011年第3期26卷 368-378页

作者： SHAO Xin-ping HAN dan-fu Department of Mathematics Zhejiang University Hangzhou 310027 China

In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems （with same stiffness matrix but different right-hand side） on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.

关键词： Two-grid algorithm Navier-Stokes equations Stream function form Reynolds number Newton iteration.

Quadrature-free spline method for two-dimensional Navier-Stokes equation

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Applied Mathematics(A Journal of Chinese Universities) 2008年第1期23卷 31-42页

作者： HU Xian-liang HAN dan-fu Dept. of Math. Zhejiang Univ. Hangzhou 310027 China.

In this paper, a quadrature-free scheme of spline method for two-dimensional Navier- Stokes equation is derived, which can dramatically improve the efficiency of spline method for fluid problems proposed by Lai and Wenston（2004）. Additionally, the explicit formulation for boundary condition with up to second order derivatives is presented. The numerical simulations on several benchmark problems show that the scheme is very efficient.

关键词： quadrature-free spline method Navier-Stokes equation.

The shape optimization of the arterial graft design by level set methods

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Applied Mathematics(A Journal of Chinese Universities) 2016年第2期31卷 205-218页

作者： JIANG Dong HAN dan-fu HU Xian-liang School of Mathematical Sciences Zhejiang University Department of Mathematics Hangzhou Normal University

The goal of the arterial graft design problem is to find an optimal graft built on an occluded artery, which can be mathematically modeled by a fluid based shape optimization problem. The smoothness of the graft is one of the important aspects in the arterial graft design problem since it affects the flow of the blood significantly. As an attractive design tool for this problem, level set methods are quite efficient for obtaining better shape of the graft. In this paper, a cubic spline level set method and a radial basis function level set method are designed to solve the arterial graft design problem. In both approaches, the shape of the arterial graft is implicitly tracked by the zero-level contour of a level set function and a high level of smoothness of the graft is achieved. Numerical results show the efficiency of the algorithms in the arterial graft design.

关键词： Arterial graft Shape optimization Level set method Adjoint variable method.

THE CONVERGENCE ON A FAMILY OF ITERATIONS WITH CUBIC ORDER

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Journal of Computational Mathematics 2001年第5期19卷 467-474页

作者： dan-fu Han (Department of Mathematics, Zhejiang University, Hangzhou 310028, China) 浙江大学浙江杭州 310028

Establishes a convergent theorem for a family of iterations with cubic order by using general convergence hypotheses. Disadvantage of using the cubic majorizing function; Convergence of the majorizing sequence; Overvi... 详细信息

关键词： convergence majorizing method gamma-condition error estimate

Objective optical quality and visual outcomes after the PresbyMAX monocular ablation profile

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International Journal of Ophthalmology(English edition) 2020年第7期13卷 1060-1065页

作者： dan fu Jing Zhao Xing-Tao Zhou Eye and ENT Hospital of fudan University Shanghai 200030China NHC Key Laboratory of Myopia fudan University Shanghai200030China Shanghai Research Center of Ophthalmology and Optometry Shanghai200030China

AIM:To assess objective visual quality after presbyopia correction using the Presby MAX monocular ***:This prospective,nonrandomized study included 28 eyes from 18 patients(mean age 50.4±5.6 y)who underwent presbyopia correction with the Presby MAX monocular *** and binocular visual acuities were evaluated preoperatively,1 d,1 wk,1,3 mo,and 1 y after *** quality was analyzed by HartmannShack wavefront aberration supported cornea *** transfer function(MTF)cutoff frequency,Strehl ratio,and objective scattering index(OSI)were analyzed using an optical quality analysis ***:One year after surgery,100%and 94.4%of patients achieved binocular uncorrected distance and near visual acuity of 20/25,*** the last visit Spherical aberration and total higher aberration were higher than the corresponding preoperative levels(P<0.001);however,no significant difference was found in MTF,OSI,or Strehl *** decreases in OSI and MTF mainly occurred in the nondominant *** was no significant difference in optical quality between the dominant and nondominant eyes,except for spherical aberration and horizontal coma(P<0.05).CONCLUSION:The Presby MAX monocular mode is safe and effective for presbyopia *** has little effect on optical quality,though short-term degraded optical quality occurred mainly in the bi-aspheric ablated eyes.

关键词： presbyopia monovision optical quality PresbyMAX

Modified two-grid method for solving coupled Navier-Stokes/Darcy model based on Newton iteration

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Applied Mathematics(A Journal of Chinese Universities) 2015年第2期30卷 127-140页

作者： SHEN Yu-jing HAN dan-fu SHAO Xin-ping Department of Mathematics Zhejiang University Department of Mathematics Hangzhou Normal University School of Science Hangzhou Dianzi University

A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is given, which shows that the same order of accuracy can be achieved as solving the system directly in the fine mesh when h = H2. Both theoretical analysis and numerical experiments illustrate the efficiency of the algorithm for solving the coupled problem.

关键词： Navier-Stokes equation Darcy's law interface coupling two-grid algorithm Newton iteration

A second order isoparametric finite element method for elliptic interface problems

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Applied Mathematics(A Journal of Chinese Universities) 2013年第1期28卷 57-74页

作者： FANG Xu-fa HAN dan-fu HU Xian-liang Department of Mathematics Zhejiang University

A second order isoparametric finite element method （IPFEM） is proposed for elliptic interface problems. It yields better accuracy than some existing second-order methods, when the coefficients or the flux across the immersed curved interface is discontinuous. Based on an initial Cartesian mesh, a mesh optimization strategy is presented by employing curved boundary elements at the interface, and an incomplete quadratic finite element space is constructed on the optimized mesh. It turns out that the number of curved boundary elements is far less than that of the straight one, and the total degree of freedom is almost the same as the uniform Cartesian mesh. Numerical examples with simple and complicated geometrical interfaces demonstrate the efficiency of the proposed method.

关键词： Isoparametric element elliptic problem curved boundary element interface element immersed interface problem.

THE CONVERGENCE OF DURAND-KERNER METHOD FOR SIMULTANEOUSLY FINDING ALL ZEROS OF THE POLYNOMIAL

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Journal of Computational Mathematics 2000年第6期18卷 567-570页

作者： dan-fu Han (Department of Mathematics, Zhejiang University, Hangzhou 310028, China) 浙江大学浙江杭州 310028

In this paper we propose the two kinds of different criterions and use them to judge the convergence of Durand-Kerner method and to compare the obtained results with other methods. [ABSTRACT FROM AUTHOR]

关键词： Durand-Kerner method convergence two kinds of criterions