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Du, Qiang

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Author ID: du.qiang Recent zbMATH articles by "Du, Qiang"
Published as: Du, Q.; Du, Qiand; Du, Qiang
Homepage: http://www.columbia.edu/~qd2125/
External Links: MGP · Wikidata · dblp
Documents Indexed: 234 Publications since 1988, including 1 Book
all top 5

Co-Authors

15 single-authored
35 Gunzburger, Max D.
22 Ju, Lili
18 Tian, Xiaochuan
12 Liu, Chun
10 Wang, Desheng
10 Wang, Xiaoqiang
8 Lehoucq, Richard B.
8 Yang, Jiang
8 Zhu, Liyong
7 Chen, Long-Qing
7 Mengesha, Tadele
7 Peterson, Janet S.
7 Yu, Peng
7 Zhang, Lei
6 Tao, Yunzhe
6 Zhang, Jingyan
6 Zhou, Kun
5 Li, Tien-Yien
5 Tian, Li
5 Zhang, Jiwei
4 Bao, Weizhu
4 Chapman, Stephen Jonathan
4 Dai, Shibin
4 Emelianenko, Maria
4 Ryham, Rolf J.
4 Sun, Qi
4 Zheng, Chunxiong
4 Zhou, Zhi
3 Ding, Shijin
3 Huang, Zhan
3 Li, Manlin
3 Lu, Jianfang
3 Remski, Joan
3 Zhang, Yanzhi
2 Chen, Zhiming
2 Dawson, Clint N.
2 Deang, Jennifer M.
2 D’Elia, Marta
2 Ding, Jiu
2 Feng, Weiming
2 Gray, Paul A.
2 Hou, L. Steven
2 Hu, Shiyi
2 Hyon, Yunkyong
2 Jin, Ming
2 Lee, Hwi-Young
2 Lee, Jeehyun
2 Li, Changpin
2 Li, Xiao
2 Lin, Fang Hua
2 Ma, Yanping
2 Ming, Ju
2 Nicolaides, Roy A.
2 Parks, Michael L.
2 Qiao, Zhonghua
2 Tian, Hao
2 Wang, Chang-Yi
2 Wang, Jiakou
2 Wu, Xiaonan
2 Yuan, Guangwei
2 Zeng, Zhonggang
2 Zhang, Jian
2 Zhang, Wei
2 Zhao, Xuying
2 Zhao, Yanxiang
2 Zhu, Wenxiang
2 Zou, Jun
1 Aftalion, Amandine
1 Burkardt, John V.
1 Carrillo de la Plata, José Antonio
1 Chabaud, Brandon M.
1 Chang, Chien-Cheng
1 Chen, An
1 Chen, Falai
1 Chen, Gui-Qiang G.
1 Chen, Jie
1 Chiu, Chichia
1 Chung, Tsz Shun Eric
1 Das, Sovan Lal
1 Defterli, Ozlem
1 Dong, Cheng
1 Dupont, Todd F.
1 Faber, Vance
1 Feng, Xiaobing
1 Gu, Ran
1 Guo, Ben-Yu
1 Han, Houde
1 Hesthaven, Jan S.
1 Hoskins, Meghan Henty
1 Hou, Lisheng
1 Hu, Jiashun
1 Hu, Shaoyi
1 Huang, Yunqing
1 Huang, Zhaohui
1 Kamm, James R.
1 Keller, Rachael T.
1 Layton, William J.
1 Le, Thinh
1 Lee, Hyesuk Kwon
1 LeFloch, Philippe Gerard
...and 47 more Co-Authors
all top 5

Serials

32 SIAM Journal on Numerical Analysis
15 Journal of Computational Physics
13 SIAM Journal on Applied Mathematics
10 SIAM Journal on Scientific Computing
9 Computer Methods in Applied Mechanics and Engineering
9 Mathematics of Computation
7 Journal of Scientific Computing
6 Discrete and Continuous Dynamical Systems. Series B
6 Multiscale Modeling & Simulation
6 Communications in Mathematical Sciences
6 Communications in Computational Physics
5 Computers & Mathematics with Applications
5 Journal of Computational and Applied Mathematics
5 SIAM Journal on Mathematical Analysis
4 Journal of Mathematical Analysis and Applications
4 SIAM Review
3 Archive for Rational Mechanics and Analysis
3 IMA Journal of Numerical Analysis
3 Nonlinearity
3 Applied Mathematics and Computation
3 Physica D
3 European Journal of Applied Mathematics
3 Journal of Elasticity
3 International Journal of Numerical Analysis and Modeling
3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
2 International Journal for Numerical Methods in Engineering
2 Numerische Mathematik
2 Journal of Computational Mathematics
2 Numerical Methods for Partial Differential Equations
2 Discrete and Continuous Dynamical Systems
2 Communications on Pure and Applied Analysis
2 Numerical Mathematics: Theory, Methods and Applications
2 Communications on Applied Mathematics and Computation
1 Applicable Analysis
1 Journal of Mathematical Biology
1 Journal of Mathematical Physics
1 Letters in Mathematical Physics
1 Mathematical Methods in the Applied Sciences
1 ZAMP. Zeitschrift für angewandte Mathematik und Physik
1 Chaos, Solitons and Fractals
1 BIT
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Quarterly of Applied Mathematics
1 Mathematica Numerica Sinica
1 Parallel Computing
1 Computational Mechanics
1 Science in China. Series A
1 Economics Letters
1 International Journal of Computational Geometry & Applications
1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
1 Stochastic Processes and their Applications
1 Advances in Mathematical Sciences and Applications
1 Numerical Linear Algebra with Applications
1 Advances in Computational Mathematics
1 Fractional Calculus & Applied Analysis
1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics
1 Acta Mathematica Sinica. English Series
1 Foundations of Computational Mathematics
1 Computational Methods in Applied Mathematics
1 Mathematical Biosciences and Engineering
1 CBMS-NSF Regional Conference Series in Applied Mathematics
1 Kinetic and Related Models
1 Science China. Mathematics
1 Journal of Mathematical Research with Applications
1 Nonlinear Analysis. Theory, Methods & Applications

Publications by Year

Citations contained in zbMATH

204 Publications have been cited 3,840 times in 2,055 Documents Cited by Year
Centroidal Voronoi tessellations: Applications and algorithms. Zbl 0983.65021
Du, Qiang; Faber, Vance; Gunzburger, Max
201
1999
Analysis and approximation of nonlocal diffusion problems with volume constraints. Zbl 1422.76168
Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun
172
2012
Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow. Zbl 1061.82025
Bao, Weizhu; Du, Qiang
131
2004
Analysis and approximation of the Ginzburg-Landau model of superconductivity. Zbl 0787.65091
Du, Qiang; Gunzburger, Max D.; Peterson, Janet S.
131
1992
A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws. Zbl 1266.26020
Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun
122
2013
A phase field approach in the numerical study of the elastic bending energy for vesicle membranes. Zbl 1116.74384
Du, Qiang; Liu, Chun; Wang, Xiaoqiang
113
2004
Numerical analysis of a continuum model of phase transition. Zbl 0744.65089
Du, Qiang; Nicolaides, R. A.
100
1991
Mathematical and numerical analysis of linear peridynamic models with nonlocal boundary conditions. Zbl 1220.82074
Zhou, Kun; Du, Qiang
83
2010
A finite difference domain decomposition algorithm for numerical solution of the heat equation. Zbl 0732.65091
Dawson, Clint N.; Du, Qiang; Dupont, Todd F.
80
1991
Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions. Zbl 1086.74024
Du, Qiang; Liu, Chun; Wang, Xiaoqiang
76
2006
Finite element methods with matching and nonmatching meshes for Maxwell equations with discontinuous coefficients. Zbl 0964.78017
Chen, Zhiming; Du, Qiang; Zou, Jun
71
2000
Analysis and comparison of different approximations to nonlocal diffusion and linear peridynamic equations. Zbl 1295.82021
Tian, Xiaochuan; Du, Qiand
62
2013
Analysis of a linear fluid-structure interaction problem. Zbl 1039.35076
Du, Q.; Gunzburger, M. D.; Hou, L. S.; Lee, J.
60
2003
Global existence and uniqueness of solutions on the time-dependent Ginzburg- Landau model for superconductivity. Zbl 0843.35019
Du, Qiang
57
1994
Asymptotically compatible schemes and applications to robust discretization of nonlocal models. Zbl 1303.65098
Tian, Xiaochuan; Du, Qiang
52
2014
A phase field formulation of the Willmore problem. Zbl 1125.35366
Du, Qiang; Liu, Chun; Ryham, Rolf; Wang, Xiaoqiang
48
2005
Mathematical analysis for the peridynamic nonlocal continuum theory. Zbl 1269.45005
Du, Qiang; Zhou, Kun
47
2011
Modelling and simulations of multi-component lipid membranes and open membranes via diffuse interface approaches. Zbl 1143.92001
Wang, Xiaoqiang; Du, Qiang
46
2008
Numerical approximation of some linear stochastic partial differential equations driven by special additive noises. Zbl 1030.65002
Du, Qiang; Zhang, Tianyu
46
2002
Analysis and applications of the exponential time differencing schemes and their contour integration modifications. Zbl 1080.65074
Du, Qiang; Zhu, Wenxiang
43
2005
Constrained centroidal Voronoi tessellations for surfaces. Zbl 1036.65101
Du, Qiang; Gunzburger, Max D.; Ju, Lili
40
2003
Fractional diffusion on bounded domains. Zbl 06418052
Defterli, Ozlem; D’Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Rich; Meerschaert, Mark M.
38
2015
Analysis of a phase field Navier-Stokes vesicle-fluid interaction model. Zbl 1172.74016
Du, Qiang; Li, Manlin; Liu, Chun
38
2007
Analysis of a Ladyzhenskaya model for incompressible viscous flow. Zbl 0712.76039
Du, Qiang; Gunzburger, Max D.
38
1991
Nonlocal constrained value problems for a linear peridynamic Navier equation. Zbl 1297.74051
Mengesha, Tadele; Du, Qiang
36
2014
Dynamics of rotating Bose-Einstein condensates and its efficient and accurate numerical computation. Zbl 1141.35052
Bao, Weizhu; Du, Qiang; Zhang, Yanzhi
36
2006
Numerical studies of discrete approximations to the Allen-Cahn equation in the sharp interface limit. Zbl 1198.82045
Zhang, Jian; Du, Qiang
35
2009
Grid generation and optimization based on centroidal Voronoi tessellations. Zbl 1024.65118
Du, Qiang; Gunzburger, Max
35
2002
The bond-based peridynamic system with Dirichlet-type volume constraint. Zbl 1381.35177
Mengesha, Tadele; Du, Qiang
34
2014
Energetic variational approaches in modeling vesicle and fluid interactions. Zbl 1183.74056
Du, Qiang; Liu, Chun; Ryham, Rolf; Wang, Xiaoqiang
34
2009
A posteriori error analysis of finite element method for linear nonlocal diffusion and peridynamic models. Zbl 1327.65101
Du, Qiang; Ju, Lili; Tian, Li; Zhou, Kun
33
2013
Fast explicit integration factor methods for semilinear parabolic equations. Zbl 1317.65172
Ju, Lili; Zhang, Jian; Zhu, Liyong; Du, Qiang
32
2015
Analysis of the volume-constrained peridynamic Navier equation of linear elasticity. Zbl 1277.35007
Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun
30
2013
Adaptive finite element method for a phase field bending elasticity model of vesicle membrane deformations. Zbl 1162.74042
Du, Qiang; Zhang, Jian
30
2008
Convergence of the Lloyd algorithm for computing centroidal Voronoi tessellations. Zbl 1115.65017
Du, Qiang; Emelianenko, Maria; Ju, Lili
30
2006
On the variational limit of a class of nonlocal functionals related to peridynamics. Zbl 1330.45011
Mengesha, Tadele; Du, Qiang
29
2015
Efficient parallel algorithms for parabolic problems. Zbl 1013.65090
Du, Q.; Mu, M.; Wu, Z. N.
29
2001
Analysis of a scalar nonlocal peridynamic model with a sign changing kernel. Zbl 1278.45014
Mengesha, Tadele; Du, Qiang
27
2013
Spectral viscosity approximations to multidimensional scalar conservation laws. Zbl 0799.35148
Chen, Gui-Qiang; Du, Qiang; Tadmor, Eitan
27
1993
Stability analysis and application of the exponential time differencing schemes. Zbl 1052.65081
Du, Qiang; Zhu, Wenxiang
26
2004
Ginzburg-Landau vortices: dynamics, pinning, and hysteresis. Zbl 0888.35054
Lin, Fang-Hua; Du, Qiang
25
1997
Error estimates of the Markov finite approximation of the Frobenius- Perron operator. Zbl 0788.28009
Chiu, C.; Du, Q.; Li, T. Y.
25
1992
Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations. Zbl 1106.74431
Du, Qiang; Wang, Desheng
24
2003
Finite element approximation of the Cahn-Hilliard equation on surfaces. Zbl 1230.80010
Du, Qiang; Ju, Lili; Tian, Li
23
2011
Spectral implementation of an adaptive moving mesh method for phase-field equations. Zbl 1120.74042
Feng, W. M.; Yu, P.; Hu, S. Y.; Liu, Z. K.; Du, Q.; Chen, L. Q.
23
2006
A Ginzburg-Landau type model of superconducting normal junctions including Josephson junctions. Zbl 0843.35120
Chapman, S. Jonathan; Du, Qiang; Gunzburger, Max D.
23
1995
Finite element methods for the time-dependent Ginzburg-Landau model of superconductivity. Zbl 0802.65128
Du, Q.
23
1994
A new approach for a nonlocal, nonlinear conservation law. Zbl 1248.35121
Du, Qiang; Kamm, James R.; Lehoucq, R. B.; Parks, Michael L.
22
2012
FENE dumbbell model and its several linear and nonlinear closure approximations. Zbl 1108.76006
Du, Qiang; Liu, Chun; Yu, Peng
22
2005
Retrieving topological information for phase field models. Zbl 1114.74044
Du, Qiang; Liu, Chun; Wang, Xiaoqiang
22
2005
Existence of weak solutions to some vortex density models. Zbl 1044.35085
Du, Qiang; Zhang, Ping
22
2003
High order approximation of the Frobenius-Perron operator. Zbl 0769.65025
Ding, J.; Du, Q.; Li, T. Y.
22
1993
Finite-element approximations of a Ladyzhenskaya model for stationary incompressible viscous flow. Zbl 0697.76046
Du, Qiang; Gunzburger, Max D.
22
1990
A convergent adaptive finite element algorithm for nonlocal diffusion and peridynamic models. Zbl 1271.82011
Du, Qiang; Tian, Li; Zhao, Xuying
21
2013
Modeling the spontaneous curvature effects in static cell membrane deformations by a phase field formulation. Zbl 1078.92004
Du, Q.; Liu, C.; Ryham, R.; Wang, X.
21
2005
Anisotropic centroidal Voronoi tessellations and their applications. Zbl 1121.65306
Du, Qiang; Wang, Desheng
21
2005
Probabilistic methods for centroidal Voronoi tessellations and their parallel implementations. Zbl 1014.68202
Ju, Lili; Du, Qiang; Gunzburger, Max
21
2002
Numerical approximations of the Ginzburg-Landau models for superconductivity. Zbl 1111.82067
Du, Qiang
20
2005
A model for variable thickness superconducting thin films. Zbl 0862.35119
Chapman, S. J.; Du, Qiang; Gunzburger, M. D.
20
1996
Shrinking dimer dynamics and its applications to saddle point search. Zbl 1254.37060
Zhang, Jingyan; Du, Qiang
19
2012
Convergence analysis of a finite volume method for Maxwell’s equations in nonhomogeneous media. Zbl 1067.78018
Chung, Eric T.; Du, Qiang; Zou, Jun
19
2003
Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation. Zbl 1395.65099
Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua
18
2018
Asymptotically compatible Fourier spectral approximations of nonlocal Allen-Cahn equations. Zbl 1342.65198
Du, Qiang; Yang, Jiang
18
2016
Nonlocal convection-diffusion volume-constrained problems and jump processes. Zbl 1284.35223
Du, Qiang; Huang, Zhan; Lehoucq, Richard B.
18
2014
Advances in studies and applications of centroidal Voronoi tessellations. Zbl 1224.52032
Du, Qiang; Gunzburger, Max; Ju, Lili
18
2010
Voronoi-based finite volume methods, optimal Voronoi meshes, and PDEs on the sphere. Zbl 1046.65094
Du, Qiang; Gunzburger, Max D.; Ju, Lili
18
2003
Adaptive finite element methods for elliptic equations over hierarchical T-meshes. Zbl 1231.65222
Tian, Li; Chen, Falai; Du, Qiang
17
2011
Approximations of a Ginzburg-Landau model for superconducting hollow spheres based on spherical centroidal Voronoi tessellations. Zbl 1221.65293
Du, Qiang; Ju, Lili
17
2005
Maximum principle preserving exponential time differencing schemes for the nonlocal Allen-Cahn equation. Zbl 1419.65018
Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua
16
2019
Weak solutions for the Cahn-Hilliard equation with degenerate mobility. Zbl 1333.35188
Dai, Shibin; Du, Qiang
16
2016
The optimal centroidal Voronoi tessellations and the Gersho’s conjecture in the three-dimensional space. Zbl 1077.65019
Du, Qiang; Wang, Desheng
16
2005
High-kappa limits of the time-dependent Ginzburg-Landau model. Zbl 0865.35119
Du, Qiang; Gray, Paul
16
1996
Efficient and stable exponential time differencing Runge-Kutta methods for phase field elastic bending energy models. Zbl 1349.92015
Wang, Xiaoqiang; Ju, Lili; Du, Qiang
15
2016
A Fourier spectral moving mesh method for the Cahn-Hilliard equation with elasticity. Zbl 1364.74097
Feng, W. M.; Yu, P.; Hu, S. Y.; Liu, Z. K.; Du, Q.; Chen, L. Q.
15
2009
On mesh geometry and stiffness matrix conditioning for general finite element spaces. Zbl 1191.65152
Du, Qiang; Wang, Desheng; Zhu, Liyong
15
2009
Characterization of function spaces of vector fields and an application in nonlinear peridynamics. Zbl 1353.46027
Mengesha, Tadele; Du, Qiang
14
2016
Motion of interfaces governed by the Cahn-Hilliard equation with highly disparate diffusion mobility. Zbl 1276.35033
Dai, Shibin; Du, Qiang
13
2012
Cascadic multigrid methods for parabolic problems. Zbl 1178.65114
Du, Qiang; Ming, PingBing
13
2008
Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrödinger equation. Zbl 1202.35311
Zhang, Yanzhi; Bao, Weizhu; Du, Qiang
13
2007
Convergence of numerical approximations to a phase field bending elasticity model of membrane deformations. Zbl 1130.74046
Du, Qiang; Wang, Xiaoqiang
13
2007
Recent progress in robust and quality Delaunay mesh generation. Zbl 1096.65016
Du, Qiang; Wang, Desheng
13
2006
Meshfree, probabilistic determination of point sets and support regions for meshless computing. Zbl 0993.65009
Du, Qiang; Gunzburger, Max; Ju, Lili
13
2002
A model for superconducting thin films having variable thickness. Zbl 0794.58049
Du, Qiang; Gunzburger, Max D.
13
1993
Nonconforming discontinuous Galerkin methods for nonlocal variational problems. Zbl 1322.65109
Tian, Xiaochuan; Du, Qiang
12
2015
An explicit-implicit predictor-corrector domain decomposition method for time dependent multi-dimensional convection diffusion equations. Zbl 1212.65369
Zhu, Liyong; Yuan, Guangwei; Du, Qiang
12
2009
Analysis of a mixed finite element method for a phase field bending elasticity model of vesicle membrane deformation. Zbl 1095.74033
Du, Qiang; Zhu, Liyong
12
2006
Semidiscrete finite element approximations of a linear fluid-structure interaction problem. Zbl 1159.74343
Du, Qiang; Gunzburger, M. D.; Hou, Lisheng; Lee, Jeehyun
12
2004
Numerical simulations of the quantized vortices on a thin superconducting hollow sphere. Zbl 1076.82549
Du, Qiang; Ju, Lili
12
2004
Fourier spectral approximation to a dissipative system modeling the flow of liquid crystals. Zbl 1007.76057
Du, Qiang; Guo, Benyu; Shen, Jie
12
2001
Discrete gauge invariant approximations of a time dependent Ginzburg-Landau model of superconductivity. Zbl 0907.65086
Du, Qiang
12
1998
Impulsive stretching of a surface in a viscous fluid. Zbl 0869.76013
Wang, C. Y.; Du, Q.; Miklavčič, M.; Chang, C. C.
12
1997
Computational studies of coarsening rates for the Cahn-Hilliard equation with phase-dependent diffusion mobility. Zbl 1349.80043
Dai, Shibin; Du, Qiang
11
2016
Optimization based nonoverlapping domain decomposition algorithms and their convergence. Zbl 1004.65132
Du, Qiang
11
2001
Nonlocal modeling, analysis, and computation. Zbl 1423.00007
Du, Qiang
10
2019
Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations. Zbl 1411.74058
Tao, Yunzhe; Tian, Xiaochuan; Du, Qiang
10
2017
Analysis of a nonlocal-in-time parabolic equation. Zbl 1362.45015
Du, Qiang; Yang, Jiang; Zhou, Zhi
10
2017
Nonlocal convection-diffusion problems and finite element approximations. Zbl 1423.74925
Tian, Hao; Ju, Lili; Du, Qiang
10
2015
A constrained string method and its numerical analysis. Zbl 1186.65079
Du, Qiang; Zhang, Lei
10
2009
The dynamics and interaction of quantized vortices in the Ginzburg-Landau-Schrödinger equation. Zbl 1220.35165
Zhang, Yanzhi; Bao, Weizhu; Du, Qiang
10
2007
Finite volume methods on spheres and spherical centroidal Voronoi meshes. Zbl 1099.65107
Du, Qiang; Ju, Lili
10
2005
The phase field method for geometric moving interfaces and their numerical approximations. Zbl 1455.35276
Du, Qiang; Feng, Xiaobing
4
2020
Stochastic representation of solution to nonlocal-in-time diffusion. Zbl 1441.60060
Du, Qiang; Toniazzi, Lorenzo; Zhou, Zhi
1
2020
Asymptotically compatible schemes for robust discretization of parametrized problems with applications to nonlocal models. Zbl 07168053
Tian, Xiaochuan; Du, Qiang
1
2020
Maximum principle preserving exponential time differencing schemes for the nonlocal Allen-Cahn equation. Zbl 1419.65018
Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua
16
2019
Nonlocal modeling, analysis, and computation. Zbl 1423.00007
Du, Qiang
10
2019
A discontinuous Galerkin method for one-dimensional time-dependent nonlocal diffusion problems. Zbl 1405.65118
Du, Qiang; Ju, Lili; Lu, Jianfang
5
2019
On uniform second order nonlocal approximations to linear two-point boundary value problems. Zbl 1426.47013
Du, Qiang; Zhang, Jiwei; Zheng, Chunxiong
4
2019
Asymptotically compatible SPH-like particle discretizations of one dimensional linear advection models. Zbl 1409.76114
Lee, Hwi; Du, Qiang
4
2019
A cooperative game for automated learning of elasto-plasticity knowledge graphs and models with AI-guided experimentation. Zbl 07095676
Wang, Kun; Sun, WaiChing; Du, Qiang
2
2019
Analysis of fully discrete approximations for dissipative systems and application to time-dependent nonlocal diffusion problems. Zbl 1419.65058
Du, Qiang; Ju, Lili; Lu, Jianfang
2
2019
Nonlocal models with heterogeneous localization and their application to seamless local-nonlocal coupling. Zbl 1447.45001
Tao, Yunzhe; Tian, Xiaochuan; Du, Qiang
1
2019
Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation. Zbl 1395.65099
Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua
18
2018
A peridynamic model of fracture mechanics with bond-breaking. Zbl 1395.74041
Du, Qiang; Tao, Yunzhe; Tian, Xiaochuan
6
2018
Numerical solution of a two-dimensional nonlocal wave equation on unbounded domains. Zbl 1392.82036
Du, Qiang; Han, Houde; Zhang, Jiwei; Zheng, Chunxiong
6
2018
Uniform \(L^p\)-bound of the Allen-Cahn equation and its numerical discretization. Zbl 1408.65076
Yang, Jiang; Du, Qiang; Zhang, Wei
5
2018
A quasi-nonlocal coupling method for nonlocal and local diffusion models. Zbl 06880667
Du, Qiang; Li, Xingjie Helen; Lu, Jianfeng; Tian, Xiaochuan
5
2018
Stability of nonlocal Dirichlet integrals and implications for peridynamic correspondence material modeling. Zbl 1394.45002
Du, Qiang; Tian, Xiaochuan
4
2018
A new phase-field approach to variational implicit solvation of charged molecules with the Coulomb-field approximation. Zbl 1407.65234
Zhao, Yanxiang; Ma, Yanping; Sun, Hui; Li, Bo; Du, Qiang
2
2018
A spectral method for nonlocal diffusion operators on the sphere. Zbl 1415.65238
Slevinsky, Richard Mikaël; Montanelli, Hadrien; Du, Qiang
1
2018
Asymptotically compatible schemes for stochastic homogenization. Zbl 1452.35022
Sun, Qi; Du, Qiang; Ming, Ju
1
2018
Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations. Zbl 1411.74058
Tao, Yunzhe; Tian, Xiaochuan; Du, Qiang
10
2017
Analysis of a nonlocal-in-time parabolic equation. Zbl 1362.45015
Du, Qiang; Yang, Jiang; Zhou, Zhi
10
2017
Trace theorems for some nonlocal function spaces with heterogeneous localization. Zbl 1373.46030
Tian, Xiaochuan; Du, Qiang
7
2017
Artificial boundary conditions for nonlocal heat equations on unbounded domain. Zbl 1373.45011
Zhang, Wei; Yang, Jiang; Zhang, Jiwei; Du, Qiang
6
2017
Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications. Zbl 1380.65435
Du, Qiang; Yang, Jiang
5
2017
A conservative nonlocal convection-diffusion model and asymptotically compatible finite difference discretization. Zbl 1439.65134
Tian, Hao; Ju, Lili; Du, Qiang
3
2017
Asymptotically compatible schemes for space-time nonlocal diffusion equations. Zbl 1422.65279
Chen, An; Du, Qiang; Li, Changpin; Zhou, Zhi
3
2017
Numerical solution of the nonlocal diffusion equation on the real line. Zbl 1376.82053
Zheng, Chunxiong; Hu, Jiashun; Du, Qiang; Zhang, Jiwei
3
2017
Nonlocal convection-diffusion problems on bounded domains and finite-range jump processes. Zbl 1436.35307
D’Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Richard
2
2017
Nonlocal conservation laws. A new class of monotonicity-preserving models. Zbl 1377.35196
Du, Qiang; Huang, Zhan; LeFloch, Philippe G.
2
2017
Numerical solution of a scalar one-dimensional monotonicity-preserving nonlocal nonlinear conservation law. Zbl 1389.35223
Du, Qiang; Huang, Zhan
2
2017
Asymptotically compatible Fourier spectral approximations of nonlocal Allen-Cahn equations. Zbl 1342.65198
Du, Qiang; Yang, Jiang
18
2016
Weak solutions for the Cahn-Hilliard equation with degenerate mobility. Zbl 1333.35188
Dai, Shibin; Du, Qiang
16
2016
Efficient and stable exponential time differencing Runge-Kutta methods for phase field elastic bending energy models. Zbl 1349.92015
Wang, Xiaoqiang; Ju, Lili; Du, Qiang
15
2016
Characterization of function spaces of vector fields and an application in nonlinear peridynamics. Zbl 1353.46027
Mengesha, Tadele; Du, Qiang
14
2016
Computational studies of coarsening rates for the Cahn-Hilliard equation with phase-dependent diffusion mobility. Zbl 1349.80043
Dai, Shibin; Du, Qiang
11
2016
Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains. Zbl 1356.65239
Tian, Xiaochuan; Du, Qiang; Gunzburger, Max
9
2016
A class of high order nonlocal operators. Zbl 1362.46042
Tian, Xiaochuan; Du, Qiang
5
2016
Multiscale analysis of linear evolution equations with applications to nonlocal models for heterogeneous media. Zbl 1348.74287
Du, Qiang; Lipton, Robert; Mengesha, Tadele
5
2016
Optimization-based shrinking dimer method for finding transition states. Zbl 1332.37062
Zhang, Lei; Du, Qiang; Zheng, Zhenzhen
5
2016
A multiscale implementation based on adaptive mesh refinement for the nonlocal peridynamics model in one dimension. Zbl 1381.74214
Xu, Feifei; Gunzburger, Max; Burkardt, John; Du, Qiang
4
2016
On the consistency between nearest-neighbor peridynamic discretizations and discretized classical elasticity models. Zbl 1439.74044
Seleson, Pablo; Du, Qiang; Parks, Michael L.
3
2016
Robust a posteriori stress analysis for quadrature collocation approximations of nonlocal models via nonlocal gradients. Zbl 1439.74011
Du, Qiang; Tao, Yunzhe; Tian, Xiaochuan; Yang, Jiang
1
2016
Fractional diffusion on bounded domains. Zbl 06418052
Defterli, Ozlem; D’Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Rich; Meerschaert, Mark M.
38
2015
Fast explicit integration factor methods for semilinear parabolic equations. Zbl 1317.65172
Ju, Lili; Zhang, Jian; Zhu, Liyong; Du, Qiang
32
2015
On the variational limit of a class of nonlocal functionals related to peridynamics. Zbl 1330.45011
Mengesha, Tadele; Du, Qiang
29
2015
Nonconforming discontinuous Galerkin methods for nonlocal variational problems. Zbl 1322.65109
Tian, Xiaochuan; Du, Qiang
12
2015
Nonlocal convection-diffusion problems and finite element approximations. Zbl 1423.74925
Tian, Hao; Ju, Lili; Du, Qiang
10
2015
Integral approximations to classical diffusion and smoothed particle hydrodynamics. Zbl 1423.76363
Du, Qiang; Lehoucq, R. B.; Tartakovsky, A. M.
8
2015
Multiscale analysis of linearized peridynamics. Zbl 1327.74129
Mengesha, Tadele; Du, Qiang
2
2015
Asymptotically compatible schemes and applications to robust discretization of nonlocal models. Zbl 1303.65098
Tian, Xiaochuan; Du, Qiang
52
2014
Nonlocal constrained value problems for a linear peridynamic Navier equation. Zbl 1297.74051
Mengesha, Tadele; Du, Qiang
36
2014
The bond-based peridynamic system with Dirichlet-type volume constraint. Zbl 1381.35177
Mengesha, Tadele; Du, Qiang
34
2014
Nonlocal convection-diffusion volume-constrained problems and jump processes. Zbl 1284.35223
Du, Qiang; Huang, Zhan; Lehoucq, Richard B.
18
2014
Coarsening mechanism for systems governed by the Cahn-Hilliard equation with degenerate diffusion mobility. Zbl 1327.35150
Dai, Shibin; Du, Qiang
9
2014
Mesh dependent stability and condition number estimates for finite element approximations of parabolic problems. Zbl 1279.65119
Zhu, Liyong; Du, Qiang
5
2014
Linear finite element superconvergence on simplicial meshes. Zbl 1312.65187
Chen, Jie; Wang, Desheng; Du, Qiang
4
2014
Finding critical nuclei in phase transformations by shrinking dimer dynamics and its variants. Zbl 1373.82033
Zhang, Lei; Zhang, Jingyan; Du, Qiang
2
2014
Error estimates for approximations of a gradient dynamics for phase field elastic bending energy of vesicle membrane deformation. Zbl 1432.74211
Zhu, Liyong; Du, Qiang
2
2014
Constraint-free adaptive FEMs on quadrilateral nonconforming meshes. Zbl 1310.65150
Zhao, Xuying; Shi, Zhong-Ci; Du, Qiang
1
2014
A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws. Zbl 1266.26020
Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun
122
2013
Analysis and comparison of different approximations to nonlocal diffusion and linear peridynamic equations. Zbl 1295.82021
Tian, Xiaochuan; Du, Qiand
62
2013
A posteriori error analysis of finite element method for linear nonlocal diffusion and peridynamic models. Zbl 1327.65101
Du, Qiang; Ju, Lili; Tian, Li; Zhou, Kun
33
2013
Analysis of the volume-constrained peridynamic Navier equation of linear elasticity. Zbl 1277.35007
Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun
30
2013
Analysis of a scalar nonlocal peridynamic model with a sign changing kernel. Zbl 1278.45014
Mengesha, Tadele; Du, Qiang
27
2013
A convergent adaptive finite element algorithm for nonlocal diffusion and peridynamic models. Zbl 1271.82011
Du, Qiang; Tian, Li; Zhao, Xuying
21
2013
Abstract principal component analysis. Zbl 1305.62223
Li, Tianjiang; Du, Qiang
1
2013
Analysis and approximation of nonlocal diffusion problems with volume constraints. Zbl 1422.76168
Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun
172
2012
A new approach for a nonlocal, nonlinear conservation law. Zbl 1248.35121
Du, Qiang; Kamm, James R.; Lehoucq, R. B.; Parks, Michael L.
22
2012
Shrinking dimer dynamics and its applications to saddle point search. Zbl 1254.37060
Zhang, Jingyan; Du, Qiang
19
2012
Motion of interfaces governed by the Cahn-Hilliard equation with highly disparate diffusion mobility. Zbl 1276.35033
Dai, Shibin; Du, Qiang
13
2012
Constrained shrinking dimer dynamics for saddle point search with constraints. Zbl 1248.65069
Zhang, Jingyan; Du, Qiang
6
2012
Periodic centroidal Voronoi tessellations. Zbl 1267.65029
Zhang, Jingyan; Emelianenk, Maria; Du, Qiang
2
2012
A hybrid implicit-explicit adaptive multirate numerical scheme for time-dependent equations. Zbl 1244.65100
Chabaud, Brandon; Du, Q.
1
2012
Mathematical analysis for the peridynamic nonlocal continuum theory. Zbl 1269.45005
Du, Qiang; Zhou, Kun
47
2011
Finite element approximation of the Cahn-Hilliard equation on surfaces. Zbl 1230.80010
Du, Qiang; Ju, Lili; Tian, Li
23
2011
Adaptive finite element methods for elliptic equations over hierarchical T-meshes. Zbl 1231.65222
Tian, Li; Chen, Falai; Du, Qiang
17
2011
Convergent adaptive finite element method based on centroidal Voronoi tessellations and superconvergence. Zbl 1364.65251
Huang, Yunqing; Qin, Hengfeng; Wang, Desheng; Du, Qiang
9
2011
Mesh-dependent stability for finite element approximations of parabolic equations with mass lumping. Zbl 1269.65084
Zhu, Liyong; Du, Qiang
4
2011
Analysis of a stochastic implicit interface model for an immersed elastic surface in a fluctuating fluid. Zbl 1294.35200
Du, Qiang; Li, Manlin
4
2011
Asymptotic analysis of a diffuse interface relaxation to a nonlocal optimal partition problem. Zbl 1211.35093
Du, Qiang; Zhang, Jingyan
1
2011
Mathematical and numerical analysis of linear peridynamic models with nonlocal boundary conditions. Zbl 1220.82074
Zhou, Kun; Du, Qiang
83
2010
Advances in studies and applications of centroidal Voronoi tessellations. Zbl 1224.52032
Du, Qiang; Gunzburger, Max; Ju, Lili
18
2010
Vortex solutions of the high-\(\kappa\) high-field Ginzburg-Landau model with an applied current. Zbl 1223.82069
Du, Qiang; Wei, Juncheng; Zhao, Chunyi
6
2010
An efficient explicit/implicit domain decomposition method for convection-diffusion equations. Zbl 1196.65160
Zhu, Liyong; Yuan, Guangwei; Du, Qiang
6
2010
Simultaneous prediction of morphologies of a critical nucleus and an equilibrium precipitate in solids. Zbl 1364.82017
Zhang, Lei; Chen, Long-Qing; Du, Qiang
5
2010
Diffuse-interface approach to predicting morphologies of critical nucleus and equilibrium structure for cubic to tetragonal transformations. Zbl 1198.82025
Zhang, Lei; Chen, Long-Qing; Du, Qiang
2
2010
Numerical studies of discrete approximations to the Allen-Cahn equation in the sharp interface limit. Zbl 1198.82045
Zhang, Jian; Du, Qiang
35
2009
Energetic variational approaches in modeling vesicle and fluid interactions. Zbl 1183.74056
Du, Qiang; Liu, Chun; Ryham, Rolf; Wang, Xiaoqiang
34
2009
A Fourier spectral moving mesh method for the Cahn-Hilliard equation with elasticity. Zbl 1364.74097
Feng, W. M.; Yu, P.; Hu, S. Y.; Liu, Z. K.; Du, Q.; Chen, L. Q.
15
2009
On mesh geometry and stiffness matrix conditioning for general finite element spaces. Zbl 1191.65152
Du, Qiang; Wang, Desheng; Zhu, Liyong
15
2009
An explicit-implicit predictor-corrector domain decomposition method for time dependent multi-dimensional convection diffusion equations. Zbl 1212.65369
Zhu, Liyong; Yuan, Guangwei; Du, Qiang
12
2009
A constrained string method and its numerical analysis. Zbl 1186.65079
Du, Qiang; Zhang, Lei
10
2009
A phase field model for vesicle-substrate adhesion. Zbl 1173.74028
Zhang, Jian; Das, Sovan; Du, Qiang
9
2009
A finite volume method on general surfaces and its error estimates. Zbl 1160.65340
Ju, Lili; Du, Qiang
7
2009
Numerical approximations of a norm-preserving gradient flow and applications to an optimal partition problem. Zbl 1157.65401
Du, Qiang; Lin, Fanghua
7
2009
Analysis of a mixed finite-volume discretization of fourth-order equations on general surfaces. Zbl 1166.65057
Du, Qiang; Ju, Lili; Tian, Li
6
2009
Modelling and simulations of multi-component lipid membranes and open membranes via diffuse interface approaches. Zbl 1143.92001
Wang, Xiaoqiang; Du, Qiang
46
2008
Adaptive finite element method for a phase field bending elasticity model of vesicle membrane deformations. Zbl 1162.74042
Du, Qiang; Zhang, Jian
30
2008
Cascadic multigrid methods for parabolic problems. Zbl 1178.65114
Du, Qiang; Ming, PingBing
13
2008
...and 104 more Documents
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Cited by 2,898 Authors

103 Du, Qiang
52 Gunzburger, Max D.
41 Ju, Lili
22 Li, Jichun
21 Bao, Weizhu
21 Liu, Chun
21 Wang, Cheng
20 Ding, Jiu
20 Huang, Yunqing
18 Fan, Jishan
17 Pan, Xingbin
17 Shen, Jie
17 Yang, Xiaofeng
15 Tian, Xiaochuan
15 Wang, Qi
14 Zhang, Yanzhi
13 Lowengrub, John Samuel
13 Wang, Desheng
12 Kim, Junseok
12 Mengesha, Tadele
12 Zhao, Jia
11 Antoine, Xavier
11 Wang, Xiaoqiang
11 Wise, Steven M.
10 Dehghan Takht Fooladi, Mehdi
10 Liu, Zuhan
10 Pan, Kejia
10 Qiao, Zhonghua
10 Triggiani, Roberto
10 Wang, Hong
9 Cai, Yongyong
9 Chen, Wenbin
9 Chien, Cheng-Sheng
9 Feng, Xinlong
9 Guo, Boling
9 Lasiecka, Irena
9 Li, Buyang
9 Serfaty, Sylvia
9 Wang, Hanquan
9 Warma, Mahamadi
9 Yang, Wei
9 Zhou, Aihui
8 Bellido, José Carlos
8 Boglaev, Igor P.
8 Bronsard, Lia
8 Elliott, Charles M.
8 Gong, Yuezheng
8 Guillén González, Francisco M.
8 Helffer, Bernard
8 Huang, Chengming
8 Layton, William J.
8 Lee, Hyun Geun
8 Lehoucq, Richard B.
8 Liang, Dong
8 Lin, Wen-Wei
8 Lipton, Robert P.
8 Rabczuk, Timon
8 Shieh, Shih-Feng
8 Voigt, Axel
8 Wang, Tingchun
8 Yang, Jiang
8 Zhou, Zhi
8 Zhu, Liyong
7 Aksoylu, Burak
7 Alama, Stan
7 Almog, Yaniv
7 Avalos, George
7 Barrett, John W.
7 Cheng, Kelong
7 Chung, Tsz Shun Eric
7 Dassi, Franco
7 Duan, Jinqiao
7 Gal, Ciprian Gheorghe Sorin
7 Huang, Ting-Zhu
7 Huang, Weizhang
7 Karniadakis, George Em
7 Li, Yibao
7 Lin, Ping
7 Meerschaert, Mark M.
7 Promislow, Keith Steven
7 Rossi, Julio Daniel
7 Süli, Endre E.
7 Wang, Xiaoming
7 Yoshida, Natsumi
7 Yuan, Guangwei
7 Zhou, Zhongguo
7 Zou, Jun
6 Beirão da Veiga, Lourenço
6 Bertozzi, Andrea Louise
6 Čanić, Sunčica
6 Chen, Long
6 Chen, Zhiming
6 Dai, Shibin
6 D’Elia, Marta
6 Deng, Jiansong
6 Deng, Weihua
6 Fernández Bonder, Julián
6 Fournais, Søren
6 Gómez, Héctor J.
6 He, Dongdong
...and 2,798 more Authors
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Cited in 301 Serials

218 Journal of Computational Physics
99 Journal of Computational and Applied Mathematics
93 Computer Methods in Applied Mechanics and Engineering
82 Journal of Scientific Computing
78 Applied Mathematics and Computation
72 Computers & Mathematics with Applications
54 SIAM Journal on Numerical Analysis
48 Mathematics of Computation
47 Journal of Mathematical Analysis and Applications
41 SIAM Journal on Scientific Computing
37 Applied Numerical Mathematics
35 Physica D
32 Numerische Mathematik
30 Numerical Methods for Partial Differential Equations
25 Applied Mathematics Letters
24 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
22 Journal of Mathematical Physics
22 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
21 Journal of Differential Equations
20 SIAM Journal on Mathematical Analysis
19 ZAMP. Zeitschrift für angewandte Mathematik und Physik
19 Multiscale Modeling & Simulation
18 Archive for Rational Mechanics and Analysis
16 Computer Physics Communications
16 Calculus of Variations and Partial Differential Equations
16 Science China. Mathematics
15 International Journal for Numerical Methods in Engineering
15 Computer Aided Geometric Design
15 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
15 SIAM Journal on Applied Mathematics
15 Advances in Computational Mathematics
15 Discrete and Continuous Dynamical Systems. Series B
14 Computational Mechanics
13 Applicable Analysis
13 Communications in Nonlinear Science and Numerical Simulation
13 Nonlinear Analysis. Theory, Methods & Applications
12 Mathematical Methods in the Applied Sciences
12 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
12 Numerical Algorithms
12 International Journal of Computer Mathematics
12 Journal of Elasticity
11 Communications in Mathematical Physics
11 Applied Mathematical Modelling
11 Discrete and Continuous Dynamical Systems
10 Mathematics and Computers in Simulation
9 BIT
9 Advances in Difference Equations
8 International Journal of Control
8 Transactions of the American Mathematical Society
8 Engineering Analysis with Boundary Elements
7 Journal of Fluid Mechanics
7 Journal of Mathematical Biology
7 Mathematical and Computer Modelling
7 Science in China. Series A
7 Mathematical Problems in Engineering
7 Mathematics and Mechanics of Solids
7 Fractional Calculus & Applied Analysis
7 Nonlinear Analysis. Real World Applications
6 Computers and Fluids
6 Communications on Pure and Applied Mathematics
6 Automatica
6 Journal of Functional Analysis
6 European Journal of Applied Mathematics
6 Communications in Contemporary Mathematics
6 Communications on Pure and Applied Analysis
6 International Journal of Computational Methods
6 Journal of Theoretical Biology
6 Communications on Applied Mathematics and Computation
5 Journal of Statistical Physics
5 Nonlinearity
5 Chaos, Solitons and Fractals
5 Numerical Functional Analysis and Optimization
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5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
5 Acta Mathematica Sinica. English Series
5 Computational Geosciences
5 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
5 Evolution Equations and Control Theory
5 East Asian Journal on Applied Mathematics
4 Bulletin of Mathematical Biology
4 Applied Mathematics and Optimization
4 Calcolo
4 Journal of Optimization Theory and Applications
4 Chinese Annals of Mathematics. Series B
4 Acta Applicandae Mathematicae
4 SIAM Journal on Matrix Analysis and Applications
4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
4 SIAM Review
4 Potential Analysis
4 NoDEA. Nonlinear Differential Equations and Applications
4 Chaos
4 International Journal of Nonlinear Sciences and Numerical Simulation
4 Milan Journal of Mathematics
4 Discrete and Continuous Dynamical Systems. Series S
3 Inverse Problems
3 Journal of the Franklin Institute
3 Reviews in Mathematical Physics
3 Advances in Mathematics
3 Osaka Journal of Mathematics
...and 201 more Serials
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Cited in 49 Fields

1,179 Numerical analysis (65-XX)
1,068 Partial differential equations (35-XX)
395 Fluid mechanics (76-XX)
324 Statistical mechanics, structure of matter (82-XX)
263 Mechanics of deformable solids (74-XX)
136 Calculus of variations and optimal control; optimization (49-XX)
102 Biology and other natural sciences (92-XX)
100 Optics, electromagnetic theory (78-XX)
90 Probability theory and stochastic processes (60-XX)
74 Integral equations (45-XX)
60 Dynamical systems and ergodic theory (37-XX)
53 Operator theory (47-XX)
52 Quantum theory (81-XX)
48 Systems theory; control (93-XX)
47 Ordinary differential equations (34-XX)
45 Computer science (68-XX)
41 Global analysis, analysis on manifolds (58-XX)
40 Real functions (26-XX)
37 Operations research, mathematical programming (90-XX)
35 Functional analysis (46-XX)
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18 Information and communication theory, circuits (94-XX)
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15 Geophysics (86-XX)
13 Combinatorics (05-XX)
12 Linear and multilinear algebra; matrix theory (15-XX)
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9 Difference and functional equations (39-XX)
6 Special functions (33-XX)
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5 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
3 Geometry (51-XX)
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2 General and overarching topics; collections (00-XX)
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2 Algebraic topology (55-XX)
2 Relativity and gravitational theory (83-XX)
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1 Group theory and generalizations (20-XX)
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