刘发旺教授报告

发布时间:2014年11月17日 作者:   消息来源:科研办    阅读次数:[]

讲座1题目:数值模拟复杂的动力系统及其应用

讲座人:刘发旺教授,澳大利亚昆士兰科技大学数学科学学院      

Professor Fawang Liu

School of Mathematical Sciences

Queensland University of Technology

GPO Box 2434, Brisbane, Qld. 4001

Australia

Phone: 61-07-31381329 (QUT) or 61-(0)410036297 (mobile)

QQ2682942006

Email:f.liu@qut.edu.au

讲座摘要:      

本次讲座主要介绍近二十多年来在澳大利亚昆士兰科技大学从事数值模拟复杂的动力系统及其应用的科学研究项目的经验和体会。科学研究项目主要包括:微波加热问题,快速炼铁问题,燃烧波问题,移动边界和奇异摄动问题 ,吸附传送问题,海水浸入地下水层问题 ,分数阶模型的数值方法回顾,反常次扩散方程,分布阶的偏微分方程,多项分数阶偏微分方程,变分数阶微分方程,分数阶模型在医学中的应用(在人类大脑组织的反常扩散),分数阶模型在生物系统的应用(心脏的电生理系统的数值模拟),分数阶微分方程国内外发展动态。也介绍刘发旺教授的团队在研究分数阶计算的进展,挑战和开放性问题。      

讲座时间: 2014年11月23日下午3点      

讲座地点: 中南大学数理楼一楼报告厅     

讲座2题目:分数阶偏微分方程的数值方法

讲座人:刘发旺教授,澳大利亚昆士兰科技大学数学科学学院      

Professor Fawang Liu

School of Mathematical Sciences

Queensland University of Technology

GPO Box 2434, Brisbane, Qld. 4001

Australia

Phone: 61-07-31381329 (QUT) or 61-(0)410036297 (mobile)

QQ2682942006

Email:f.liu@qut.edu.au

讲座摘要:      

本次讲座将主要介绍一些分数阶计算有关的基本知识以及几类分数阶偏微分方程的数值计算方法,其中包括求解空间分数阶扩散方程的有限差分方法,分别有显式方法,隐式方法,Crank-Nichoson方法以及加权格式;利用一些不同的分析技巧,给出稳定性和收敛性分析;求解空间分数阶的对流-扩散方程的数值方法,分别有L1-和L2-近似,标准和移位的 Grunwald近似,分数阶行方法,显式方法,隐式方法和Crank-Nichoson方法,以及稳定性和收敛性分析的证明;求解变系数的分数阶空间扩散方程的有限体积方法(有限元方法);求解一类反常次扩散方程的隐式方法,引进一新的能量范数,给出了稳定性和收敛性分析,同时也将介绍一个外推技巧和一个改进的收敛阶的技巧。      

讲座时间:2014年11月25日上午九点      

讲座地点:中南大学数理楼一楼报告厅     

 

刘发旺教授是澳大利亚昆士兰科技大学博士生导师,分数阶微分方程数值方法团队的学科带头人。

刘发旺教授1975年毕业于福州大学计算数学专业,毕业后留校工作。1982年获得计算数学硕士学位。1988年被破格提升为福州大学当时最年轻的副教授。刘发旺教授于1988年得到爱尔兰都柏林大学Trinity College提供的奖学金,攻读博士学位。在国际著名的数值分析专家John Miller 教授的指导下,于1991年以优秀的成绩获得了博士学位。从1988年至今,先后在爱尔兰三一学院,爱尔兰都柏林大学学院,澳大利亚昆士兰大学,厦门大学,澳大利亚昆士兰科技大学,从事计算数学和应用数学的教学和科研工作(副教授,博士后,研究员,高级研究员,教授,博士生导师),已主持和承担多项由澳大利亚国家研究基金和中国国家自然科学基金资助的科研项目,受到国内外同行专家的高度好评。2002年6月--2005年12月,回国工作,被聘为厦门大学数学科学学院(一级岗位)教授,并于2005年获得福建省科学进步奖。2006年返回到澳大利亚昆士兰科技大学工作。目前是澳大利亚昆士兰科技大学分数阶微分方程数值方法团队的学科带头人,并多次获得澳大利亚昆士兰科技大学数学类,工程类优秀论文奖。刘发旺教授已指导16名博士研究生和13名硕士研究生,并应邀担任国际Applied Mathematical Modelling, International Journal of Differential Equations,Cogent Mathematics, Progress in Fractional Differentiation and Applications等杂志的编委,国际微分方程杂志分数阶微分方2010,2011,2012,2013年专刊主编,国际应用数学模型的计算方法和数值模型2014年专刊主编,科学世界杂志的分数阶动力系统分析2014专刊的主编。他已发表学术论文210多篇(Sci/EI文章占90%,是已发表的绝大部分文章的通讯作者)。刘发旺教授最近在中国河海大学召开的2012年第五届分数阶微分及其应用国际会议上被授予《Mittag-Leffler Award: FDA Achievement Award》(Mittag-Leffler分数阶微分及其应用成就奖)。      

近几年主要成就及承担的项目:

  • 2013-2016: 分数阶微分方程的高精度数值方法和反常动力学行为,中国国家自然科学基金。      

  • 2012-2014: 复杂动力系统的计算方法及其应用,澳大利亚国家研究基金。      

  • 2008-2012:数值模拟非均质的多孔介质中传送过程的多尺度逼近,昆士兰科技大学和澳大利亚国家研究基金。      

  • 2008-2012:生物系统中的反问题,昆士兰大学,昆士兰科技大学,英国牛津大学和澳大利亚国家研究基金。      

  • 2009-2012:磁共振弥散成像和反常扩散在医学中的应用,昆士兰科技大学和澳大利亚国家研究基金。      

  • 2009-2010:地下水的扩散和传送的分数阶动力模型,昆士兰科技大学研究基金。      

  • 2003-2007:海水在地下水层的扩散和传送,昆士兰科技大学和澳大利亚国家研究基金。      

  • 2003-2005:奇异摄动偏微分方程的数值方法及其应用,中国国家自然科学基金。      

  • 2004-2005:分数阶偏微分方程模拟土壤和植物系统中水和溶质的运动,中澳合作特别基金。      

  • 2000-2002:数值模拟海水入侵地下水层,昆士兰科技大学和澳大利亚国家研究基金。      

PUBLICATIONS LISTS (2013-2014, *Corresponding author)

2014:

[1]F. Liu*,P. Zhuang, I. Turner, V. Anh and K. Burrage, A semi-alternating direction method for a 2-D fractional FitzHugh-Nagumo monodomain model on an approximate irregular domain, J. Comp. Physics, (2014), in press,10.1016/j.jcp.2014.06.001.

[2] X. Hu,F. Liu*,I. Turner, and V. Anh, A numerical investigation of the time distributed-order and two-sided space-fractional advection-dispersion equation, ANZIAM J., (2014), in press.

[3] F. Zeng, C. Li,F. Liuand I. Turner, Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy, SIAM J. Sci. Computing, (2014) , in press.

[4] S. Chen, X. Jiang,F. Liu*and I. Turner, High order unconditionally stable difference schemes for the Riesz space-fractional Telegraph equation, J. Computational and Applied Mathematics, (2014), in press, 10.1016/j.cam.2014.09.028.

[5] H. Ye,F. Liu*and V. Anh, Compact difference scheme for distributed-order time-fractional diffusion-wave equation on bounded domains, J. Comp. Physics, 2014, in press.

[6] S. Chen,F. Liu*,X. Jiang , I. Turner and V. Anh, A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients, Appl. Math. Comp (2014) , in press,10.1016/j.amc.2014.08.031.

[7]F. Liu*,P. Zhuang, I. Turner, V. Anh and K. Burrage, Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model, IEEE Explore Conference Proceedings, Italy, ( 2014), in press.

[8] F. Zeng,F. Liu*,C. Li, K. Burrage, I. Turner and V. Anh, Crank-Nicolson ADI spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation, SIAM Journal on Numerical Analysis, (2014),http://www.siam.org/journals/sinum/x-x/93419.

[9] H. Ye,F. Liu*, V.Anh and I. Turner, Numerical analysis for the time distributed order and Riesz space fractional diffusions on bounded domains, IMA Journal of Applied Mathematics, 227, (2014), 531-540. 10.1016/j.amc.2013.11.015.

[10] H. Zhang,F. Liu*, P. Zhuang, I. Turner and V. Anh, Numerical analysis of a new space-time variable fractional order advection-dispersion equation, Appl. Math. Comp., (2014) in press.

[11] S. Shen,F. Liu*, Q. Liu and V. Anh, Numerical simulation of anomalous infiltration in porous media, , Numerical Algorithm, (2014), in press, DOI: 10.1007/s11075-014-9853-9.

[12] Q. Yu, ,F. Liu*, I. Turner and K. Burrage, Numerical simulation of the fractional Bloch equations, J. Comp. Appl. Math., 255, (2014), 635-651,DOI: 10.1016/j.cam.2013.06.027.

[13] H. Hejazi, T. Moroney andF. Liu. Stability and convergence of a finite volume method for the space fractional advection-dispersion equation, J. Comp. Appl. Math., 255, (2014),684-697, doi.org/10.1016/j.cam.2013.06.039.

[14] H. Ye,F. Liu*, V. Anh and I. Turner , Maximum principle and numerical method for the multi-term time-space Riesz-Caputo fractional differential equations, Appl. Math. Comp., 227 (2014), 531-540,10.1016/j.amc.2013.11.015.

[15] Q. Yang, I. Turner, T. Moroney andF. Liu,A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction-diffusion equations, Applied Mathematical Modelling, 38(15-16) (2014), 3755-3762. http://dx.doi.org/10.1016/j.apm.2014.02.005.

[16] Q. Liu,F. Liu*, I. Turner , V. Anh and Y. Gu,A RBF meshless approach for modeling a fractal mobile/immobile transport model, Appl. Math. Comp., 226, (2014), 336-147,http://dx.doi.org/10.1016/j.amc.2013.10.008.

[17] S. Chen,F. Liu* and K. Burrage, Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media, Computer & Mathematics with Application, 67(9), (2014) , 1673-1681, 10.1016/j.camwa.2014.03.003.

[18] S. Shen,F. Liu*, V. Anh, I. Turner, and J. Chen, A novel numerical approximation for the space fractional advection–dispersion equation, IMA J Appl Math 79(3) (2014) 431-444, doi: 10.1093/imamat/hxs073.

[19]F. Liu*, P. Zhuang, I. Turner, K. Burrage and V. Anh, A new fractional finite volume method for solving the fractional diffusion equation, Applied Mathematical Modelling, Applied Mathematical Modelling, 38(15-16), (2014), 3871-3878, 10.1016/j.apm.2013.10.007.

[10] J. Song, Q. Yu,F. Liu*, and I. Turner, A spatially second-order accurate implicit numerical method for the space and time fractional Bloch-Torrey equation, Numerical Algorithms, 66(4) (2014), 911-932.DOI: 10.1007/s11075-013-9768-x.

[21] P. Zhuang,F. Liu*, I. Turner and Y.T. Gu, Finite volume and finite element methods for solving a one-dimensional space-fractional Boussinesq equation, Applied Mathematical Modelling, 38(15-16), (2014), 3860-3870, 10.1016/j.apm.2013.10.008 .

[22] J. Chen,F. Liu, Q. Liu, I. Turner, V. Anh, K. Burrage, Numerical simulation for the three- dimension fractional sub-diffusion equation, Applied Mathematical Modelling, 38(15-16), (2014), 3695-3705.

[23] H. Ye,F. Liu*,I. Turner and V. Anh, Solutions of Cauchy type problems for space-time Riesz- Caputo fractional wave-diffusion equations, Acta Mathematicae Applicatae Sinica , 2014, in press.

2013:

[24]F. Liu*, M.M. Meerschaert, R. McGough, P. Zhuang and Q. Liu, Numerical methods for solving the multi-term time fractional wave equations, Fractional Calculus \& Applied Analysis, 16(1) (2013), 9-25, DOI: 10.2478/s13540-013-0002-2.

[25] Q. Yu,F. Liu*, I. Turner and K. Burrage, Stability and convergence of an implicit numerical method for the space and time fractional Bloch-Torrey equation, the special issue of Fractional Calculus and Its Applications in-Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, A371: 20120150; (2013),1471-2962, doi:10.1098/rsta.2012.0150.

[26] H. Jiang,F. Liu*, M.M. Meerschaert and R. McGough, Fundamental solutions for the multi-term modified power law wave equations in a finite domain, Electronic Journal of Mathematical Analysis and Applications, 1(1) (2013), 55-66.

[27]J. Chen,F. Liu*, K. Burrage and S. Shen, Numerical techniques for simulating a fractional mathematical model for epidermal wound healing, Journal of Applied Mathematics and Computing, 41, (2013) , 33–47, DOI 10.1007/s12190-012-0591-7。

[28] C. Chen,F. Liu*, I. Turner,V. Anh, Y. Chen, Numerical approximation for a variable-ordernonlinear reaction-subdiffusion equation, Numerical Algorithm, 63, (2013), 265-290, DOI 10.1007/s11075-012-96622-6.

[29] S. Shen,F. Liu*, I. Turner, V. Anh and J. Chen, A characteristic difference method for the variable-order fractional advection-diffusion equation, J. Appl. Math. Computing, 42(1-2), (2013), 371-386, DOI 10.1007/s12190-012-04642-0.

[30] H. Zhang,F. Liu*, M.S. Phanikumar and M.M. Meerschaert, A novel numerical method for the time variable fractional order mobile-immobile advection-dispersion model, Computer & Mathematics with Application, 66, (2013), 693-701, DOI:10.1016/j.camwa.2013.01.031.

[31] Q. Yu,F. Liu*, I. Turner and K. Burrage, Numerical investigation of three types of space and time fractional Bloch-Torrey equations in 2D, Cent. Eur. J. Phys, 11(6) , (2013), 646-665. DOI: 10.2478/s11534-013-0220-6.

[32] Q. Yu,F. Liu*, I. Turner, K. Burrage and V. Vegh, The use of a Riesz fractional differentialbased approach for texture enhancement in image processing, 154, ANZIAM Journal, 54, 2013, C590-C607.

[33] H. Ye,F. Liu*, I. Turner, V. Anh, and K. Burrage, Series expansion solutions for the multi-term time and space fractional partial differential equations in two and three dimensions, Eur. Phys. J., Special Topics222, 1901-1914, (2013),http://epjst.epj.org/10.1140/epjst/e2013-01972-2.

[34]F. Liu*, I. Turner, V. Anh, Q. Yang and K. Burrage, A numerical method for the fractional Fitzhugh-Nagumo monodomain model, 154, ANZIAM Journal, 54, 2013, C608-C629.

[35] F. Zeng, C.P. Li andF. Liu,High-order explicit-implicit numerical methods for nonlinear anomalous diffusion equations, European Physical Journal , 222,2013, 1885-1900.

[36] F. Zeng, C. Li,F. Liuand I. Turner, The use of finite difference/element approximations for solving the time-fractional subdiffusion equation, SIAM J. Sci. Computing, 35(6), (2013) , 2976-3000. DOI:http://dx.doi.org/10.1137/130910865.

[37] H. Hejazi, T. Moroney,F. Liu, A finite volume method for solving the two-sided time-space fractional advection-dispersion equation, Cent. Eur. J. Phys, 11(10), (2013), 1275-1283.

[38] S. Chen,F. Liu*,I. Turner and V. Anh, An implicit numerical method for thetwo-dimensional fractional percolationequation, Appl. Math. Comp., 219 (2013), 4322-4331, 10.1016/j.amc.2012.10.003.

[39] H. Hejazi, T. Moroney andF. Liu. A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients, 154, ANZIAM Journal, 2013, C557-C573.

[40]F. Liu*, S. Chen, I. Turner, K. Burrage and V. Anh, Numerical simulation for two-dimensional Riesz space fractional diffusion equations with a nonlinear reaction term, Cent. Eur. J. Phys, 11(10),(2013), 1221-1232,DOI:102478/s11534-013-0296-z.

[41] C. Chen,F. Liu* and K. Burrage, Numerical methods of the variable-order Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative, IMA J. Appl. Math., 78, (2013), 924-944, 10.1093/imamat/HXR079.

Special Issues:

[1] Fawang Liu, Richard Magin, Changpin Li, Alla Sikorskii, and Santos Bravo Yuste, Analysis of Fractional Dynamic Systems, Hindawi Publishing Corporation, The ScientificWorld Journal Volume 2014, Article ID 760634, 2 pageshttp://dx.doi.org/10.1155/2014/760634.

[2]Fawang Liu,Yuantong Gu,Ian Turner, ICCM2012 - Topical Issue on computational methods, numerical modelling & simulation in Applied Mathematical Modelling, April, 2014, 10.1016/j.apm.2014.04.006.



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