基本信息
胡齐芽  男  博导  中国科学院数学与系统科学研究院
电子邮件: hqy@lsec.cc.ac.cn
通信地址: 北京中关村东路55号中科院数学与系统科学研究院
邮政编码: 100190

研究概况


研究方向


1.  偏微分方程的区域分解方法;
2.  鞍点问题的迭代算法;
3.  电磁场问题的高效算法.

成果影响

已在国际计算数学SCI期刊上发表论文50多篇,  其中在SIAM系列等国际计算数学顶尖刊物上发表20多篇。 在国际同行中有影响的成果有:


1. 对弱奇异积分(积-微分)方程提出了ß-多项式配置方法,并对配置解提出了一种比著名的Sloan迭代更便宜的后处理方法;

相关论文:

(1) Qiya Hu, Stieltjes derivatives and ß-polynomial collocation methods to Volterra Integro-differential equations with singularities, SIAM J. Numer. Anal., 33(1996),No.1, 208-220

(2) Qiya Hu, Superconvergence of numerical solutions to Volterra integral equations with singularities, SIAM J. Numer. Anal., 34(1997), No.5, 1698-1707

 

2.  首次对鞍点问题设计了实用的非精确Uzawa迭代方法, 引发了许多后继工作;

相关论文:

(1) Qiya Hu and Jun Zou, An iterative method with variable relaxation parameters for saddle-point problems, SIAM J. Matrix. Anal. Appl., 23(2001), No.2, 317-338

(2) Qiya Hu and Jun Zou, Two new variants of nonlinear inexact Uzawa algorithms for saddle-point problems, Numer. Math., 93(2002), No. 3, 333-359

(3)Qiya Hu and Jun Zou, Nonlinear inexact Uzawa algorithms for linear and nonlinear saddle-point problems. SIAM J. Optim. 16 (2006), No. 3, 798-825

 

3. 首次对三维Maxwell方程组设计了有效的非重叠区域分解方法, 该项成果被国际同行称为开创性的工作(pioneering work). 

相关论文:

(1) Qiya Hu and Jun Zou, A non-overlapping domain decomposition method for Maxwell's equations in three dimensions, SIAM J. Numer. Anal., 41(2003), No.5, 1682-1708

(2) Qiya Hu and Jun Zou, Substructuring preconditioners for saddle-point problems arising from Maxwell's equations in three dimensions, Math. Comp., 73(2003),No. 245, 35-61

(3)Qiya Hu, Shi Shu and Jun Zou, A discrete weighted Helmholtz decomposition and its Application, Numer. Math., 2013, Vol. 125, No. 1, pp 153-189


4. 对赫姆霍兹方程的平面波离散系统构造了新型平行预条件子,并提出了求解非齐次散射问题的新颖平面波方法.

相关论文:

(1)Qiya Hu and Haiyang ZhangSubstructuring preconditioners for the systems arising from plane wave discretization of Helmholtz equationsSIAM J. Sci. Comput.,2016, Vol. 38, No. 4, pp. 2232-2261

(2) Qiya Hu and  Xun Li,  Efficient multilevel preconditioners for the three-dimensional plane wave Helmholtz systems with large wave numbers,  SIAM:  MULTISCALE MODEL. SIMUL., Vol. 15, No. 3, pp. 1242–1266

(3) Qiya Hu and Long Yuan, A Plane wave method combined with local spectral elements for nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations, Adv. Comput. Math., 44(2018), pp. 245-275

 


当前的主要研究兴趣

时谐Maxwell方程组(电磁散射问题)的区域分解并行算法。

大数据神经网络算法。

招生信息

已有9名研究生如期毕业(尚无学生延期)并获得博士学位,对每个学生都给予具体、细心的指导。每年可招收一名硕博连读学生,研究方向可以有多种选择,欢迎有兴趣的学生联系了解。

招生专业
070102-计算数学
招生方向
区域分解并行算法
电磁场问题的高效算法
机器学习算法

教育背景

1995-09--1998-07   中国科学院数学研究所   博士
学历

 研究生: 1986年至1988年(湘潭大学) 


博士:1995年至1998年(中国科学院数学研究所)

学位

硕士学位:1990年7月(湘潭大学) 

博士学位: 1998年7月(中国科学院数学研究所) 

工作经历

   
工作简历
2000-09~现在, 中国科学院数学与系统科学研究院, 助研,副研,正研
1998-09~2000-08,中国科学院计算数学研究所, 博士后
1988-08~1995-08,湘潭大学, 大学教师(副教授)
社会兼职
2020-09-01-2023-08-31,计算数学, 编委
2017-09-01-2020-08-31,数值计算与计算机应用, 编委
2014-09-01-2017-08-31,数值计算与计算机应用, 编委

教授课程

微积分I-B
微积分II-B
微积分
区域分解方法

专利与奖励

   
奖励信息
(1) 中国科学院数学与系统科学研究院突出科研成果奖, , 院级, 2010
(2) 中国科学院博士院长奖学金, 特等奖, 部委级, 1998
(3) 湖南省自然科学优秀论文, 二等奖, 省级, 1997

出版信息

   
发表论文
(1) A Nodal Finite Element Method for a Thermally Coupled Eddy-Current Problem with Moving Conductors, COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2021, 通讯作者
(2) CONVERGENCE OF THE HIPTMAIR–XU PRECONDITIONER FOR MAXWELL’S EQUATIONS WITH JUMP COEFFICIENTS (I): EXTENSIONS OF THE REGULAR DECOMPOSITION, SIAM J. NUMER. ANAL., 2021, 第 1 作者
(3) Plane wave discontinuous Galerkin methods for the Helmholtz equation and Maxwell equations in anisotropic media, COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2021, 通讯作者
(4) A NOVEL LEAST SQUARES METHOD FOR HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS, SIAM JOURNAL ON NUMERICAL ANALYSIS, 2020, 通讯作者
(5) Generalized plane wave discontinuous Galerkin methods for nonhomogeneous Helmholtz equations with variable wave numbers, INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2020, 通讯作者
(6) A VARIANT OF THE PLANE WAVE LEAST SQUARES METHOD FOR THE TIME-HARMONIC MAXWELL'S EQUATIONS, ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2019, 通讯作者
(7) Error analysis of the plane wave discontinuous galerkin method for maxwell's equations in anisotropic media, COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2019, 通讯作者
(8) COUPLING METHOD OF PLANE WAVE DG AND BOUNDARY ELEMENT FOR ELECTROMAGNETIC SCATTERING, INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2019, 第 1 作者
(9) A substructuring preconditioner with vertex-related interface solvers for elliptic-type equations in three dimensions, ADVANCES IN COMPUTATIONAL MATHEMATICS, 2019, 通讯作者
(10) Uzawa methods for a class of block three-by-three saddle-point problems, NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2019, 第 3 作者
(11) A plane wave method combined with local spectral elements for nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations, ADVANCES IN COMPUTATIONAL MATHEMATICS, 2018, 通讯作者
(12) Comparisons of three kinds of plane wave methods for the Helmholtz equation and time-harmonic Maxwell equations with complex wave numbers, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 第 2 作者
(13) atwostepsmethodbasedonplanewavefornonhomogeneoushelmholtzequationsininhomogeneousmedia, NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2018, 通讯作者
(14) The plane wave methods combined with local spectral finite elements for the wave propagation in anisotropic media, ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2018, 第 2 作者
(15) NOVEL MULTILEVEL PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS, SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2017, 通讯作者
(16) Domain Decomposition Preconditioners for the System Generated by Discontinuous Galerkin Discretization of 2D-3T Heat Conduction Equations, COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2017, 通讯作者
(17) EFFICIENT MULTILEVEL PRECONDITIONERS FOR THREE-DIMENSIONAL PLANE WAVE HELMHOLTZ SYSTEMS WITH LARGE WAVE NUMBERS, MULTISCALE MODELING & SIMULATION, 2017, 通讯作者
(18) PARALLEL PRECONDITIONERS FOR PLANE WAVE HELMHOLTZ AND MAXWELL SYSTEMS WITH LARGE WAVE NUMBERS, INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2016, 第 2 作者
(19) SUBSTRUCTURING PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS, SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2016, 通讯作者
(20) 自适应结构网格并行应用支撑软件框架研究2011年度报告, 2011 Annual Report for the Program Entitled "Parallel Adaptive Structured Mesh Applications Infrastruture", 科技创新导报, 2016, 第 5 作者
(21) AN EFFECTIVE PRECONDITIONER FOR A PML SYSTEM FOR ELECTROMAGNETIC SCATTERING PROBLEM, ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2015, 通讯作者
(22) 复波数helmholtz方程和时谐maxwell方程组的平面波间断petrovgalerkin方法, 数值计算与计算机应用, 2015, 第 2 作者
(23) A newton-penalty method for a simplified liquid crystal model, ADVANCES IN COMPUTATIONAL MATHEMATICS, 2014, 通讯作者
(24) A PLANE-WAVE LEAST-SQUARES METHOD FOR TIME-HARMONIC MAXWELL'S EQUATIONS IN ABSORBING MEDIA, SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2014, 通讯作者
(25) A WEIGHTED VARIATIONAL FORMULATION BASED ON PLANE WAVE BASIS FOR DISCRETIZATION OF HELMHOLTZ EQUATIONS, INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2014, 通讯作者
(26) On the enhanced strain finite element method for incompressible linear elasticity, APPLIED NUMERICAL MATHEMATICS, 2013, 通讯作者
(27) Multilevel correction for collocation solutions of Volterra integral equations with proportional delays, ADVANCES IN COMPUTATIONAL MATHEMATICS, 2013, 通讯作者
(28) A discrete weighted Helmholtz decomposition and its Applications, Numer. Math., 2013, 第 1 作者
(29) A discrete weighted Helmholtz decomposition and its application, NUMERISCHE MATHEMATIK, 2013, 第 1 作者
(30) An Effective Combined Finite Element-Upwind Finite Volume Method for a Transient Multiphysics Two-Phase Transport Model of a Proton Exchange Membrane Fuel Cell, JOURNAL OF FUEL CELL SCIENCE AND TECHNOLOGY, 2013, 第 3 作者
(31) A Solver for Helmholtz System Generated by the Discretization of Wave Shape Functions, ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2013, 通讯作者
(32) Numerical Study of a 3D Two-Phase PEM Fuel Cell Model Via a Novel Automated Finite Element/Finite Volume Program Generator, COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2012, 第 3 作者
(33) Numerical Study of a 3D Two-Phase PEM Fuel Cell Model Via a Novel Automated Finite Element/Finite Volume Program Generator, COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2012, 第 3 作者
(34) A NONCONFORMING FINITE ELEMENT METHOD FOR FOURTH ORDER CURL EQUATIONS IN R-3, MATHEMATICS OF COMPUTATION, 2011, 第 2 作者
(35) INEXACT SOLVERS FOR SADDLE-POINT SYSTEM ARISING FROM DOMAIN DECOMPOSITION OF LINEAR ELASTICITY PROBLEMS IN THREE DIMENSIONS, INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2011, 第 2 作者
(36) apreconditionerforakindofcoupledfembemvariationalinequality, SCIENCE CHINA-MATHEMATICS, 2010, 通讯作者
(37) NONOVERLAPPING DOMAIN DECOMPOSITION METHODS WITH A SIMPLE COARSE SPACE FOR ELLIPTIC PROBLEMS, MATHEMATICS OF COMPUTATION, 2010, 通讯作者
(38) 一种求解H(curl)型椭圆问题的非重叠DDM预条件子, A PRECONDITIONER BASED ON NONOVERLAPPING DOMAIN DECOMPOSITION FOR SOLVING H(curl) ELLIPTIC PROBLEM, 计算数学, 2010, 第 2 作者
(39) 一类耦合的有限元边界元变分不等式的预条件子, 中国科学数学, 2010, 第 1 作者
(40) 一类耦合的有限元-边界元变分不等式的预条件子 谨以此文致《中国科学》创刊六十周年, 中国科学:数学, 2010, 第 1 作者
(41) A SADDLE POINT APPROACH TO THE COMPUTATION OF HARMONIC MAPS, SIAM JOURNAL ON NUMERICAL ANALYSIS, 2009, 通讯作者
(42) 求解Maxwell线性元鞍点系统的基于HX预条件子的Uzawa算法, UZAWA ALGORITHM BASED ON HX PRECONDITIONER FOR SOLVING MAXWELL SADDLE-POINT SYSTEM, 数值计算与计算机应用, 2009, 第 2 作者
(43) Generalized Normal Derivatives and Their Applications in DDMs with Nonmatching Grids and DG Methods, NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2008, 通讯作者
(44) A mortar edge element method with nearly optimal convergence for three-dimensional Maxwell's equations, MATHEMATICS OF COMPUTATION, 2008, 通讯作者
(45) A regularized domain decomposition method with Lagrange multiplier, ADVANCES IN COMPUTATIONAL MATHEMATICS, 2007, 第 1 作者
(46) DOMAIN DECOMPOSITION WITH NON-MATCHING GRIDS FOR COUPLING OF FEM AND NATURAL BEM, DOMAIN DECOMPOSITION WITH NON-MATCHING GRIDS FOR COUPLING OF FEM AND NATURAL BEM, 系统科学与复杂性:英文版, 2005, 第 2 作者
(47) A PRECONDITIONER FOR THREE-DIMENSIONAL DOMAIN DECOMPOSITION METHODS WITH LAGRANGE MULTIPLIERS, A preconditioner for three-dimensional domain decomposition methods with lagrange multipliers, 系统科学与复杂性:英文版, 2003, 第 1 作者
(48) Two new variants of nonlinear inexact Uzawa algorithms for saddle-point problems, NUMERISCHE MATHEMATIK, 2002, 
(49) 抛物问题的拉格朗日乘水区域分解法, 计算数学, 2000, 第 1 作者
(50) 积分算子方程的连续型配置方法, 计算数学, 1998, 第 1 作者
(51) 非匹配网格区域分解方法研究, 1998, 第 1 作者
(52) 某些奇异积分方程配置解的高阶“插值”, 高等学校计算数学学报, 1998, 第 1 作者
(53) Lagrangian乘子区域分解法的一类预条件子, 计算数学, 1998, 第 2 作者
(54) 多滞量积分方程基于高阶插值的分步配置方法, 计算数学, 1997, 第 1 作者

科研活动

   
科研项目
( 1 ) 对平面波离散化方法的进一步研究, 主持, 国家级, 2016-01--2019-12
( 2 ) 适用于千亿次的高性能计算方法, 参与, 国家级, 2010-10--2015-09
( 3 ) 变波数亥姆霍兹方程和时谐麦克斯韦方程组的平面波型方法研究, 主持, 国家级, 2021-01--2024-12

合作情况

多次出访美国、加拿大、挪威、香港等地的知名大学, 与国际同行建立了良好的合作关系。

指导学生

已指导学生

陈星玎  博士研究生  070102-计算数学  

肖俊敏  博士研究生  070102-计算数学  

袁龙  博士研究生  070102-计算数学  

张海洋  博士研究生  070102-计算数学  

李璇  博士研究生  070102-计算数学  

胡少亮  博士研究生  070102-计算数学  

赵林  博士研究生  070102-计算数学  

宋荣荣  博士研究生  070102-计算数学  

王泽中  博士研究生  070102-计算数学  

杨鹏飞  博士研究生  070102-计算数学  

现指导学生

王丽绮  博士研究生  070102-计算数学  

李冠达  硕士研究生  070102-计算数学  

李子逸  博士研究生  070102-计算数学