胡齐芽, 男, 中国科学院数学与系统科学研究院研究员、博士生导师

电子邮件:hqy@lsec.cc.ac.cn

通信地址:北京市海淀区中关村东路55号数学院南楼704

邮政编码:100190

办公室电话:010-82541863

 

研究概况

   

研究方向

1.     偏微分方程的区域分解方法;

2.     电磁场问题的高效算法;

3.     积分(-微分方程)的高精度方法;

4.     鞍点问题的迭代算法;

5.     无界区域问题的数值方法

成果影响

已在国内外核心期刊上发表论文60余篇,其中SIAM系列等计算数学国际一流刊物上20多篇。 在国际同行中有较大影响的成果有: (1) 对积分方程配置解提出了一种比著名的Sloan迭代更便宜的后处理方法; (2) 首次对鞍点问题设计了实用的非精确Uzawa迭代方法, 引发了许多后继研究工作; (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公开评价为“开创性工作”(pioneering work)

当前的主要研究兴趣

大波数Helmholtz方程(声散射问题)Maxwell方程组(电磁散射问题)的基于平面波离散化的快速算法。

   

奖励信息

1) 获中国科学院数学与系统科学研究院2010年度突出科研成果奖; 
2) 获中国科学院博士生院长奖学金特等奖(1998年); 
3) 获湖南省自然科学优秀论文二等奖(1997)。 

 

教育背景

   

1986年至1988年: 湘潭大学读研究生, 获硕士学位; 

1995年至1998年: 中国科学院数学研究所读博士, 获博士学位 

 

工作经历

   

工作简历

2000.09-至今: 中国科学院数学与系统科学研究院(助理研究员、副研究员、正研究员), 现为二级研究员(教授
1998.09-2000.08
: 中国科学院计算数学研究所(博士后
1988.08-1995.08
: 湘潭大学数学系(副教授

社会兼职

2014.09.01至今: 《数值计算与计算机应用》, 编委

2012.01.01至今: 中国传媒大学兼职教授

 

讲授课程

区域分解方法(博士生课程)  

   

科研活动

   

主要科研项目

1对平面波离散化方法的进一步研究”, 主持, 国家自然科学基金面上项目,2016.01-2019.12 
2
适用于千亿次的高性能计算方法”,参加,国家973重大项目,2010.10-2015.09 

3 “求解电磁散射问题的一类新型有限元方法”,主持, 国家自然科学基金重大研究计划(培育项目)2012.01-2014.12

4用户友好型数值方法研究”, 参加, 国家自然科学基金重点项目,2011.01—2014.12

(5) 若干非线性问题的高效数值方法”,参加,国家自然科学基金重点项目,2006.01-2009.12

6“高性能计算研究”,参加,国家973重大项目,2006.01-2010.12

(7)  “电磁场问题的非匹配网格区域分解方法”, 主持,国家自然科学基金面上项目,2004.01-2006.12 

(8) “大规模科学计算研究”, 参加,国家973重大项目,2001.07-2004.06

 

学术交流

多次应邀出访美国、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。多次应邀在国内、外学术会议上作报告。

   

指导学生情况

已毕业的博士研究生7名; 在读的研究生4名。

 

论文目录(SCI刊物)

 

(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 equa-

tions with singularities, SIAM J. Numer. Anal., 34(1997), No.5, 1698-1707

 

(3) Qiya Hu, Interpolation correction for collocation solutions of Fredholm integro-

differential equations, Math. Comp., 67(1998), No. 223, 987-999

 

(4) Qiya Hu, Geometric meshes and their application to Volterra integro-differential

equations with singularities, IMA J. Numer. Anal., 18(1998), No.1, 151-164

 

(5) Qiya Hu, Multilevel correction for discrete collocation solutions of integral

equations with delay argument, Appl. Numer. Math., 1999, No. 2, 159-171

 

(6) Hermann Brunnner, Qiya Hu and Qun Lin, Geometric meshes in collocation

methods for Volterra integral equations with proportional time delays, IMA. J.

Numer. Anal., 21(2001), No.4, 783-798

 

(7) Qiya Hu and Dehao Yu, Solving singularity problems in unbounded domains by coupling of natural BEM and composite grid FEM, Appl. Numer. Math.,

37(2001), No.1-2, 127-143

 

(8) Qiya Hu and Dehao Yu, A solution method for a certain interface problem

in unbounded domains, Computing, 67(2001), Vol. 67, No. 2, 119-140

 

(9) Qiya Hu, Guoping Liang and Jinzhao Liu, The construction of preconditioner

for domain decomposition methods with Lagrangian multipliers, J. Comp. Math.,

19(2001), No. 2, 213-224

 

(10) Qiya Hu and Jun Zou, An iterative method with variable relaxation pa-

rameters for saddle-point problems, SIAM J. Matrix. Anal. Appl., 23(2001), No.2,

317-338

 

(11) Qiya Hu and Dehao Yu, A coupling of FEM-BEM for Signorini transmission

problems, Science in China (Series A), 31(2001), No.2, 895-906

 

(12) Qiya Hu and Guoping Liang, Accerelation of the two-level multiplicative

Schwarz iterations, Appl. Numer. Math., 41(2002), No. 3, 305-323

 

(13) Qiya Hu and Jun Zou, Two new variants of nonlinear inexact Uzawa algo-

rithms for saddle-point problems, Numer. Math., 93(2002), No. 3, 333-359

 

(14) Qiya Hu and Dehao Yu, A preconditioner for coupling system of natural

boundary element and composite grid finite element, J. Comp. Math., 20(2002),

No.2, p.165-174

 

(15) 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

 

(16) Qiya Hu and Jun Zou, Substructuring preconditioners for saddle-point prob-

lems arising from Maxwell's equations in three dimensions, Math. Comp., 73(2003),

No. 245, 35-61

 

(17) Qiya Hu, Preconditioning Poincar-Steklov operators arising from domain

decompositions with mortar multipliers. IMA J. Numer. Anal. 24(2004), No. 4,

643-669

 

(18) Qiya Hu, Zhongci Shi and Dehao Yu, Efficient solvers for saddle-point problems arising from domain decompositions with Lagrange multipliers, SIAM J. Numer. Anal. 42(2004), No. 3, 905-933

 

(19) Qiya Hu, A non-conforming domain decomposition for Raviart-Thomas vector fields in three dimensions, Sciences in China Series A, Mathematics, 47(2004),

Sup., 190-199

 

(20) Qiya Hu and Dehao Yu, Iteratively solving a kind of Signorini transmission

problem in a unbounded domain. M2AN Math. Model. Numer. Anal., 39 (2005),

no. 4, 715-726.

 

(21) Qiya Hu, Numerical integrations and unit resolution multipliers for domain

decomposition methods with nonmatching grids., Computing 74 (2005), No. 2, 101-129.

 

(22) Hermann Brunner and Qiya Hu, Optimal superconvergence orders of iterated collocation solutions for Volterra integral equations with vanishing delays.

SIAM J. Numer. Anal., 43 (2005), No. 5, 1934-1949 .

 

(23) 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

 

(24) Hermann Brunner and Qiya Hu, Optimal superconvergence results for delay

Volterra integro-differential equations of pantograph type. SIAM J. Numer. Anal.,

45 (2005), No. 3, 986-1004.

 

(25) Qiya Hu, A Regularized Domain Decomposition Method with Lagrange

Multiplier, Advances in Computational Mathematics, 26(2007), No. 4, 367-401

 

(26) Qiya Hu, Shi Shu and Jun Zou, A Mortar Edge Element Method with

nearly Optimal Convergence for Three-dimensional Maxwell's Equations,

 Math. Comput., 2008,Vol. 77, No. 263,  13331353

 

(27) Hermann Brunner and Qiya Hu, Optimal superconvergence results for delay

Volterra integro-di®erential equations of pantograph type. SIAM J. Numer. Anal.,

2007, Vol. 45, No. 3, 986-1004.

 

(28) Qiya Hu Shi Shu and Jun Zou, A mortar edge element method with nearly

optimal convergence for three-dimensional Maxwell's equations Math. Comput.,

2008, Vol. 77, 1333-1353

 

(29) Qiya Hu, Generalized Normal Derivatives and Their Applications in DDMs

with Nonmatching grids and DG methods, Numer. Math. Theor. Meth. App.,

2008, Vol.1, 383-409

 

30Yang Liu, Qiya Hu and Dehao Yu, A non-overlapping domain decomposition

for low-frequency time-harmonic Maxwell's equations in unbounded domains, Adv.

Comput. Math., 2008, Vol.28, 355-382

 

(31) Qiya Hu, Xue-Cheng Tai, and Ragnar Winther, A Saddle Point Approach

to the Computation of Harmonic Maps, SIAM J. Numer. Anal., 2009, Vol.47, No.2,

1500-1523

 

(32) D. Sun, Q. Hu and S. Shu, A domain decomposition method with Lagrange

multiplier based on the pointwise matching condition, International J. of Numer.

Anal. Model., 2009, Vol. 6, No.1, 147-160

 

(33) Qiya Hu, Shi Shu and Junxian Wang, Nonoverlapping Domain Decompo-

sition Methods with a Simple Coarse Space for Elliptic Problems, Math. Comput.,

2010, Vol.79, 2059-2078

 

(34) Qiya Hu and Dehao Yu, A preconditioner for a kind of coupled FEM-BEM

variational inequality, SCIENCE CHINA: Mathematics, 2010, Vol. 53, No. 11,

2811-2830

 

(35) BIN ZHENG, QIYA HU, AND JINCHAO XU, A NONCONFORMING

FINITE ELEMENT METHOD FOR FOURTH ORDER CURL EQUATIONS IN

R3, Math. Comput., 80(2011), 1871-1886

 

(36) XINGDING CHEN AND QIYA HU, INEXACT SOLVERS FOR SADDLE-

POINT SYSTEM ARISING FROM DOMAIN DECOMPOSITION OF LINEAR

ELASTICITY PROBLEMS IN THREE DIMENSIONS, Intern.  J. NUMER.

ANAL. AND MODEl., 8(2011), 156

 

(37) Qiya Hu, Shi Shu and Jun Zou, A discrete weighted Helmholtz decomposi-

tion and its Application, Numer. Math., 2013, Vol. 125, No. 1, pp 153-189

 

(38) Junmin Xiao and Qiya Hu, Multilevel correction for collocation solutions

of Volterra integral equations with proportional delays, Advances in Computational

Mathematics,2013, Vol. 39, No. 3-4, pp 611-644

 

(39) Long Yuan and Qiya Hu, A Solver for Helmholtz System Generated by the

Discretization of Wave Shape FunctionsAdv. Appl. Math. Mech., 2013,Vol. 5, No.

6, pp. 791-808

 

(40) Xingding Chen, Qiya Hu and Junmin Xiao, On the enhanced strain finite element method for incompressible linear elasticity, Applied Numerical Mathematics,

2013, Vol.72, No.1,131-142

 

41Qiya Hu and Long Yuan, A plane wave lest-squares method for time-harmonic Maxwell’s equations in absorbing media, SIAM J. Sci. Comput., 36(2014), No.4, pp.1937–1959

 

(42) Qiya Hu and Long Yuan, A weighted variational formulation based on plane wave basis for discretization of Helmholtz equations, Intern. J. of Numer. Anal. Model., 2014, V. 11, N 3, pp. 587–607;

 

(43) Qiya Hu and Long Yuan, A newton-penalty method for a simplified liquid crystal model, Adv. Comput Math., 2014,  Vo.40, No.2,  pp.201–244

 

44Qiya Hu, Chunmei Liu, Shi Shu and Jun Zou, AN EFFECTIVE PRECONDITIONER FOR A PML SYSTEM FOR ELECTROMAGNETIC SCATTERING PROBLEM, ESAIM: M2AN,  49 (2015), 839854

 

45QIYA 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

 

46LONG YUAN, QIYA HU, AND HENGBIN AN PARALLEL PRECONDITIONERS FOR PLANE WAVE HELMHOLTZ AND MAXWELL SYSTEMS WITH LARGE WAVE NUMBERS INTERN. J. NUMER. ANAL. MODEL.2016,Vol. 13, No. 5, 802–819

 

(47) Qiya Hu and Lin Zhao, Domain Decomposition Preconditioners for the

System Generated by Discontinuous Galerkin Discretization of 2D-3T Heat Conduction Equations, Commun. Comput. Phys., 2017, Vol. 22, No. 4, pp. 1069-1100

 

(48) 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., 2017 (to appear)

 

(49) Qiya Hu and Xun Li,  NOVEL MULTILEVEL PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS, to appear in SIAM J. SCI. COMPUT.

 

(50) Qiya Hu and  Xun Li, EFFICIENT MULTILEVEL PRECONDITIONERS FOR THREE-DIMENSIONAL PLANE WAVE HELMHOLTZ SYSTEMS WITH LARGE WAVE NUMBERS, To appear in MULTISCALE  MODEL. SIMUL.