## Du, Qiang

Compute Distance To:
 Author ID: du.qiang Published as: Du, Qiang; Du, Q.; Du, Qiand more...less Homepage: http://www.columbia.edu/~qd2125/ External Links: MGP · Wikidata · dblp · IdRef
 Documents Indexed: 258 Publications since 1988, including 1 Book 1 Contribution as Editor Co-Authors: 151 Co-Authors with 234 Joint Publications 5,574 Co-Co-Authors
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### Co-Authors

 16 single-authored 36 Gunzburger, Max D. 24 Ju, Lili 21 Tian, Xiaochuan 12 Liu, Chun 11 Wang, Xiaoqiang 10 Wang, Desheng 8 Lehoucq, Richard B. 8 Mengesha, Tadele 8 Yang, Jiang 8 Zhang, Lei 8 Zhu, Liyong 7 Chen, Longqing 7 Peterson, Janet S. 7 Yu, Peng 6 Tao, Yunzhe 6 Zhang, Jingyan 6 Zhang, Jiwei 6 Zhou, Kun 5 Li, Tien-Yien 5 Sun, Qi 5 Tian, Li 5 Zheng, Chunxiong 4 Bao, Weizhu 4 Chapman, Stephen Jonathan 4 Dai, Shibin 4 Emelianenko, Maria 4 Ryham, Rolf J. 4 Zhou, Zhi 3 Ding, Shijin 3 Huang, Zhan 3 Li, Manlin 3 Li, Xiao 3 Lu, Jianfang 3 Montanelli, Hadrien 3 Qiao, Zhonghua 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 Gu, Ran 2 Huang, Kuang 2 Hyon, Yunkyong 2 Jin, Ming 2 Lee, Hwi-Young 2 Lee, Jeehyun 2 Li, Changpin 2 Li, Ruotai 2 Lin, Fang Hua 2 Liu, ZiKui 2 Ma, Yanping 2 Ming, Ju 2 Nicolaides, Roy A. 2 Parks, Michael L. 2 Sun, WaiChing 2 Tian, Hao 2 Toniazzi, Lorenzo 2 Wang, Chang-Yi 2 Wang, Jiakou 2 Wang, Kun 2 Wu, Xiaonan 2 Xu, Zirui 2 Yang, Haizhao 2 Yin, Xiaobo 2 Yuan, Guangwei 2 Zeng, Zhonggang 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 Chiu, Chichia 1 Chung, Tsz Shun Eric 1 Das, Sovan Lal 1 Defterli, Ozlem 1 Di, Xuan 1 Dong, Cheng 1 Dupont, Todd F. 1 Engquist, Bjorn E. 1 Faber, Vance 1 Feng, Xiaobing 1 Gu, Yiqi 1 Guo, Ben-Yu 1 Han, Houde 1 Hesthaven, Jan S. 1 Hintermüller, Michael 1 Hoskins, Meghan Henty 1 Hou, L. Steven 1 Hou, Lisheng ...and 53 more Co-Authors
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### Serials

 34 SIAM Journal on Numerical Analysis 16 Journal of Computational Physics 14 SIAM Journal on Applied Mathematics 10 Computer Methods in Applied Mechanics and Engineering 10 SIAM Journal on Scientific Computing 9 Mathematics of Computation 9 Communications in Computational Physics 8 Journal of Scientific Computing 7 Discrete and Continuous Dynamical Systems. Series B 6 SIAM Journal on Mathematical Analysis 6 Multiscale Modeling & Simulation 6 Communications in Mathematical Sciences 5 Computers & Mathematics with Applications 5 Journal of Computational and Applied Mathematics 5 SIAM Review 4 IMA Journal of Numerical Analysis 4 Journal of Mathematical Analysis and Applications 3 Archive for Rational Mechanics and Analysis 3 Nonlinearity 3 Applied Mathematics and Computation 3 Journal of Computational Mathematics 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 Numerical Methods for Partial Differential Equations 2 Discrete and Continuous Dynamical Systems 2 Fractional Calculus & Applied Analysis 2 Communications on Pure and Applied Analysis 2 Numerical Mathematics: Theory, Methods and Applications 2 Science China. Mathematics 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 Journal of Functional Analysis 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Quarterly of Applied Mathematics 1 Mathematica Numerica Sinica 1 Acta Mathematica Hungarica 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 Journal of Mathematical Imaging and Vision 1 Journal of Nonlinear Science 1 Numerical Linear Algebra with Applications 1 Advances in Computational Mathematics 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Interfaces and Free Boundaries 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 Analysis and Applications (Singapore) 1 Mathematical Biosciences and Engineering 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 Kinetic and Related Models 1 Scientia Sinica. Mathematica 1 Journal of Mathematical Research with Applications 1 Nonlinear Analysis. Theory, Methods & Applications 1 SIAM Journal on Mathematics of Data Science
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### Fields

 156 Numerical analysis (65-XX) 115 Partial differential equations (35-XX) 64 Statistical mechanics, structure of matter (82-XX) 58 Mechanics of deformable solids (74-XX) 41 Integral equations (45-XX) 33 Fluid mechanics (76-XX) 22 Calculus of variations and optimal control; optimization (49-XX) 20 Functional analysis (46-XX) 17 Operator theory (47-XX) 13 Computer science (68-XX) 10 Optics, electromagnetic theory (78-XX) 9 Dynamical systems and ergodic theory (37-XX) 9 Biology and other natural sciences (92-XX) 8 Probability theory and stochastic processes (60-XX) 7 Classical thermodynamics, heat transfer (80-XX) 6 Real functions (26-XX) 6 Ordinary differential equations (34-XX) 6 Global analysis, analysis on manifolds (58-XX) 6 Statistics (62-XX) 4 Convex and discrete geometry (52-XX) 3 Manifolds and cell complexes (57-XX) 3 Operations research, mathematical programming (90-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Systems theory; control (93-XX) 2 General and overarching topics; collections (00-XX) 2 Combinatorics (05-XX) 2 Approximations and expansions (41-XX) 2 Geometry (51-XX) 2 Mechanics of particles and systems (70-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Field theory and polynomials (12-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Differential geometry (53-XX)

### Citations contained in zbMATH Open

231 Publications have been cited 5,018 times in 2,614 Documents Cited by Year
Centroidal Voronoi tessellations: Applications and algorithms. Zbl 0983.65021
Du, Qiang; Faber, Vance; Gunzburger, Max
1999
Analysis and approximation of nonlocal diffusion problems with volume constraints. Zbl 1422.76168
Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun
2012
A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws. Zbl 1266.26020
Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun
2013
Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow. Zbl 1061.82025
Bao, Weizhu; Du, Qiang
2004
Analysis and approximation of the Ginzburg-Landau model of superconductivity. Zbl 0787.65091
Du, Qiang; Gunzburger, Max D.; Peterson, Janet S.
1992
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
2004
Numerical analysis of a continuum model of phase transition. Zbl 0744.65089
Du, Qiang; Nicolaides, R. A.
1991
Mathematical and numerical analysis of linear peridynamic models with nonlocal boundary conditions. Zbl 1220.82074
Zhou, Kun; Du, Qiang
2010
Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions. Zbl 1086.74024
Du, Qiang; Liu, Chun; Wang, Xiaoqiang
2006
A finite difference domain decomposition algorithm for numerical solution of the heat equation. Zbl 0732.65091
Dawson, Clint N.; Du, Qiang; Dupont, Todd F.
1991
Analysis and comparison of different approximations to nonlocal diffusion and linear peridynamic equations. Zbl 1295.82021
Tian, Xiaochuan; Du, Qiand
2013
Finite element methods with matching and nonmatching meshes for Maxwell equations with discontinuous coefficients. Zbl 0964.78017
Chen, Zhiming; Du, Qiang; Zou, Jun
2000
Asymptotically compatible schemes and applications to robust discretization of nonlocal models. Zbl 1303.65098
Tian, Xiaochuan; Du, Qiang
2014
Analysis of a linear fluid-structure interaction problem. Zbl 1039.35076
Du, Qiang; Gunzburger, M. D.; Hou, L. S.; Lee, J.
2003
Maximum principle preserving exponential time differencing schemes for the nonlocal Allen-Cahn equation. Zbl 1419.65018
Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua
2019
Global existence and uniqueness of solutions on the time-dependent Ginzburg- Landau model for superconductivity. Zbl 0843.35019
Du, Qiang
1994
Modelling and simulations of multi-component lipid membranes and open membranes via diffuse interface approaches. Zbl 1143.92001
Wang, Xiaoqiang; Du, Qiang
2008
Numerical approximation of some linear stochastic partial differential equations driven by special additive noises. Zbl 1030.65002
Du, Qiang; Zhang, Tianyu
2002
Analysis and applications of the exponential time differencing schemes and their contour integration modifications. Zbl 1080.65074
Du, Qiang; Zhu, Wenxiang
2005
A phase field formulation of the Willmore problem. Zbl 1125.35366
Du, Qiang; Liu, Chun; Ryham, Rolf; Wang, Xiaoqiang
2005
Mathematical analysis for the peridynamic nonlocal continuum theory. Zbl 1269.45005
Du, Qiang; Zhou, Kun
2011
Numerical studies of discrete approximations to the Allen-Cahn equation in the sharp interface limit. Zbl 1198.82045
Zhang, Jian; Du, Qiang
2009
Dynamics of rotating Bose-Einstein condensates and its efficient and accurate numerical computation. Zbl 1141.35052
Bao, Weizhu; Du, Qiang; Zhang, Yanzhi
2006
Nonlocal constrained value problems for a linear peridynamic Navier equation. Zbl 1297.74051
2014
Fractional diffusion on bounded domains. Zbl 1488.35557
Defterli, Ozlem; D’Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Rich; Meerschaert, Mark M.
2015
Constrained centroidal Voronoi tessellations for surfaces. Zbl 1036.65101
Du, Qiang; Gunzburger, Max D.; Ju, Lili
2003
Fast explicit integration factor methods for semilinear parabolic equations. Zbl 1317.65172
Ju, Lili; Zhang, Jian; Zhu, Liyong; Du, Qiang
2015
Analysis of a phase field Navier-Stokes vesicle-fluid interaction model. Zbl 1172.74016
Du, Qiang; Li, Manlin; Liu, Chun
2007
The bond-based peridynamic system with Dirichlet-type volume constraint. Zbl 1381.35177
2014
On the variational limit of a class of nonlocal functionals related to peridynamics. Zbl 1330.45011
2015
Adaptive finite element method for a phase field bending elasticity model of vesicle membrane deformations. Zbl 1162.74042
Du, Qiang; Zhang, Jian
2008
Energetic variational approaches in modeling vesicle and fluid interactions. Zbl 1183.74056
Du, Qiang; Liu, Chun; Ryham, Rolf; Wang, Xiaoqiang
2009
Analysis of a Ladyzhenskaya model for incompressible viscous flow. Zbl 0712.76039
Du, Qiang; Gunzburger, Max D.
1991
Maximum bound principles for a class of semilinear parabolic equations and exponential time-differencing schemes. Zbl 1465.35081
Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua
2021
Analysis of a scalar nonlocal peridynamic model with a sign changing kernel. Zbl 1278.45014
2013
Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation. Zbl 1395.65099
Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua
2018
Grid generation and optimization based on centroidal Voronoi tessellations. Zbl 1024.65118
Du, Qiang; Gunzburger, Max
2002
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
2013
Efficient parallel algorithms for parabolic problems. Zbl 1013.65090
Du, Q.; Mu, M.; Wu, Z. N.
2001
Analysis of the volume-constrained peridynamic Navier equation of linear elasticity. Zbl 1277.35007
Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun
2013
Convergence of the Lloyd algorithm for computing centroidal Voronoi tessellations. Zbl 1115.65017
Du, Qiang; Emelianenko, Maria; Ju, Lili
2006
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
2016
A new approach for a nonlocal, nonlinear conservation law. Zbl 1248.35121
Du, Qiang; Kamm, James R.; Lehoucq, R. B.; Parks, Michael L.
2012
Stability analysis and application of the exponential time differencing schemes. Zbl 1052.65081
Du, Qiang; Zhu, Wenxiang
2004
Nonlocal modeling, analysis, and computation. Zbl 1423.00007
Du, Qiang
2019
Ginzburg-Landau vortices: dynamics, pinning, and hysteresis. Zbl 0888.35054
Lin, Fang-Hua; Du, Qiang
1997
Asymptotically compatible Fourier spectral approximations of nonlocal Allen-Cahn equations. Zbl 1342.65198
Du, Qiang; Yang, Jiang
2016
Spectral viscosity approximations to multidimensional scalar conservation laws. Zbl 0799.35148
Chen, Gui-Qiang; Du, Qiang; Tadmor, Eitan
1993
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.
2005
Weak solutions for the Cahn-Hilliard equation with degenerate mobility. Zbl 1333.35188
Dai, Shibin; Du, Qiang
2016
Finite element approximation of the Cahn-Hilliard equation on surfaces. Zbl 1230.80010
Du, Qiang; Ju, Lili; Tian, Li
2011
Retrieving topological information for phase field models. Zbl 1114.74044
Du, Qiang; Liu, Chun; Wang, Xiaoqiang
2005
Nonlocal convection-diffusion volume-constrained problems and jump processes. Zbl 1284.35223
Du, Qiang; Huang, Zhan; Lehoucq, Richard B.
2014
Finite element methods for the time-dependent Ginzburg-Landau model of superconductivity. Zbl 0802.65128
Du, Q.
1994
Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations. Zbl 1106.74431
Du, Qiang; Wang, Desheng
2003
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.
2006
Error estimates of the Markov finite approximation of the Frobenius- Perron operator. Zbl 0788.28009
Chiu, C.; Du, Q.; Li, T. Y.
1992
A Ginzburg-Landau type model of superconducting normal junctions including Josephson junctions. Zbl 0843.35120
Chapman, S. Jonathan; Du, Qiang; Gunzburger, Max D.
1995
Probabilistic methods for centroidal Voronoi tessellations and their parallel implementations. Zbl 1014.68202
Ju, Lili; Du, Qiang; Gunzburger, Max
2002
Existence of weak solutions to some vortex density models. Zbl 1044.35085
Du, Qiang; Zhang, Ping
2003
Anisotropic centroidal Voronoi tessellations and their applications. Zbl 1121.65306
Du, Qiang; Wang, Desheng
2005
Numerical approximations of the Ginzburg-Landau models for superconductivity. Zbl 1111.82067
Du, Qiang
2005
High order approximation of the Frobenius-Perron operator. Zbl 0769.65025
Ding, J.; Du, Q.; Li, T. Y.
1993
Finite-element approximations of a Ladyzhenskaya model for stationary incompressible viscous flow. Zbl 0697.76046
Du, Qiang; Gunzburger, Max D.
1990
A convergent adaptive finite element algorithm for nonlocal diffusion and peridynamic models. Zbl 1271.82011
Du, Qiang; Tian, Li; Zhao, Xuying
2013
Shrinking dimer dynamics and its applications to saddle point search. Zbl 1254.37060
Zhang, Jingyan; Du, Qiang
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
2003
FENE dumbbell model and its several linear and nonlinear closure approximations. Zbl 1108.76006
Du, Qiang; Liu, Chun; Yu, Peng
2005
Characterization of function spaces of vector fields and an application in nonlinear peridynamics. Zbl 1353.46027
2016
Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations. Zbl 1411.74058
Tao, Yunzhe; Tian, Xiaochuan; Du, Qiang
2017
Voronoi-based finite volume methods, optimal Voronoi meshes, and PDEs on the sphere. Zbl 1046.65094
Du, Qiang; Gunzburger, Max D.; Ju, Lili
2003
Advances in studies and applications of centroidal Voronoi tessellations. Zbl 1224.52032
Du, Qiang; Gunzburger, Max; Ju, Lili
2010
A model for variable thickness superconducting thin films. Zbl 0862.35119
Chapman, S. J.; Du, Qiang; Gunzburger, M. D.
1996
The optimal centroidal Voronoi tessellations and the Gersho’s conjecture in the three-dimensional space. Zbl 1077.65019
Du, Qiang; Wang, Desheng
2005
Computational studies of coarsening rates for the Cahn-Hilliard equation with phase-dependent diffusion mobility. Zbl 1349.80043
Dai, Shibin; Du, Qiang
2016
The phase field method for geometric moving interfaces and their numerical approximations. Zbl 1455.35276
Du, Qiang; Feng, Xiaobing
2020
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.
2009
Approximations of a Ginzburg-Landau model for superconducting hollow spheres based on spherical centroidal Voronoi tessellations. Zbl 1221.65293
Du, Qiang; Ju, Lili
2005
Motion of interfaces governed by the Cahn-Hilliard equation with highly disparate diffusion mobility. Zbl 1276.35033
Dai, Shibin; Du, Qiang
2012
Nonconforming discontinuous Galerkin methods for nonlocal variational problems. Zbl 1322.65109
Tian, Xiaochuan; Du, Qiang
2015
Analysis of a nonlocal-in-time parabolic equation. Zbl 1362.45015
Du, Qiang; Yang, Jiang; Zhou, Zhi
2017
Adaptive finite element methods for elliptic equations over hierarchical T-meshes. Zbl 1231.65222
Tian, Li; Chen, Falai; Du, Qiang
2011
Nonlocal convection-diffusion problems and finite element approximations. Zbl 1423.74925
Tian, Hao; Ju, Lili; Du, Qiang
2015
Cascadic multigrid methods for parabolic problems. Zbl 1178.65114
Du, Qiang; Ming, PingBing
2008
On mesh geometry and stiffness matrix conditioning for general finite element spaces. Zbl 1191.65152
Du, Qiang; Wang, Desheng; Zhu, Liyong
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
2006
Recent progress in robust and quality Delaunay mesh generation. Zbl 1096.65016
Du, Qiang; Wang, Desheng
2006
Time-fractional Allen-Cahn equations: analysis and numerical methods. Zbl 1456.65062
Du, Qiang; Yang, Jiang; Zhou, Zhi
2020
High-kappa limits of the time-dependent Ginzburg-Landau model. Zbl 0865.35119
Du, Qiang; Gray, Paul
1996
Semidiscrete finite element approximations of a linear fluid-structure interaction problem. Zbl 1159.74343
Du, Qiang; Gunzburger, M. D.; Hou, Lisheng; Lee, Jeehyun
2004
Discrete gauge invariant approximations of a time dependent Ginzburg-Landau model of superconductivity. Zbl 0907.65086
Du, Qiang
1998
Coarsening mechanism for systems governed by the Cahn-Hilliard equation with degenerate diffusion mobility. Zbl 1327.35150
Dai, Shibin; Du, Qiang
2014
A constrained string method and its numerical analysis. Zbl 1186.65079
Du, Qiang; Zhang, Lei
2009
Trace theorems for some nonlocal function spaces with heterogeneous localization. Zbl 1373.46030
Tian, Xiaochuan; Du, Qiang
2017
Meshfree, probabilistic determination of point sets and support regions for meshless computing. Zbl 0993.65009
Du, Qiang; Gunzburger, Max; Ju, Lili
2002
Fourier spectral approximation to a dissipative system modeling the flow of liquid crystals. Zbl 1007.76057
Du, Qiang; Guo, Benyu; Shen, Jie
2001
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
2009
Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrödinger equation. Zbl 1202.35311
Zhang, Yanzhi; Bao, Weizhu; Du, Qiang
2007
Artificial boundary conditions for nonlocal heat equations on unbounded domain. Zbl 1373.45011
Zhang, Wei; Yang, Jiang; Zhang, Jiwei; Du, Qiang
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
2017
Nonlocal trace spaces and extension results for nonlocal calculus. Zbl 07505259
Du, Qiang; Tian, Xiaochuan; Wright, Cory; Yu, Yue
2022
Stability of a nonlocal traffic flow model for connected vehicles. Zbl 1486.35293
Huang, Kuang; Du, Qiang
2022
Maximum bound principles for a class of semilinear parabolic equations and exponential time-differencing schemes. Zbl 1465.35081
Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua
2021
Discovery of dynamics using linear multistep methods. Zbl 1466.65050
Keller, Rachael T.; Du, Qiang
2021
Deep ReLU networks overcome the curse of dimensionality for generalized bandlimited functions. Zbl 07533079
Montanelli, Hadrien; Yang, Haizhao; Du, Qiang
2021
A non-cooperative meta-modeling game for automated third-party calibrating, validating and falsifying constitutive laws with parallelized adversarial attacks. Zbl 07337795
Wang, Kun; Sun, WaiChing; Du, Qiang
2021
The graph limit of the minimizer of the Onsager-Machlup functional and its computation. Zbl 1462.35007
Du, Qiang; Li, Tiejun; Li, Xiaoguang; Ren, Weiqing
2021
The phase field method for geometric moving interfaces and their numerical approximations. Zbl 1455.35276
Du, Qiang; Feng, Xiaobing
2020
Time-fractional Allen-Cahn equations: analysis and numerical methods. Zbl 1456.65062
Du, Qiang; Yang, Jiang; Zhou, Zhi
2020
Asymptotically compatible schemes for robust discretization of parametrized problems with applications to nonlocal models. Zbl 1485.65058
Tian, Xiaochuan; Du, Qiang
2020
Stochastic representation of solution to nonlocal-in-time diffusion. Zbl 1441.60060
Du, Qiang; Toniazzi, Lorenzo; Zhou, Zhi
2020
Nonlocal gradient operators with a nonspherical interaction neighborhood and their applications. Zbl 1450.76031
Lee, Hwi; Du, Qiang
2020
Stability and error analysis for a second-order fast approximation of the local and nonlocal diffusion equations on the real line. Zbl 1446.82045
Zheng, Chunxiong; Du, Qiang; Ma, Xiang; Zhang, Jiwei
2020
Mathematics of smoothed particle hydrodynamics: a study via nonlocal Stokes equations. Zbl 1448.76112
Du, Qiang; Tian, Xiaochuan
2020
Multiscale modeling, homogenization and nonlocal effects: mathematical and computational issues. Zbl 1481.65263
Du, Qiang; Engquist, Bjorn; Tian, Xiaochuan
2020
A discontinuous Galerkin method with penalty for one-dimensional nonlocal diffusion problems. Zbl 1449.65242
Du, Qiang; Ju, Lili; Lu, Jianfang; Tian, Xiaochuan
2020
Variational phase field formulations of polarization and phase transition in ferroelectric thin films. Zbl 1447.78019
Du, Qiang; Li, Ruotai; Zhang, Lei
2020
Stochastic training of residual networks in deep learning. Zbl 1463.68074
Sun, Qi; Tao, Yunzhe; Du, Qiang
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
2019
Nonlocal modeling, analysis, and computation. Zbl 1423.00007
Du, Qiang
2019
A discontinuous Galerkin method for one-dimensional time-dependent nonlocal diffusion problems. Zbl 1405.65118
Du, Qiang; Ju, Lili; Lu, Jianfang
2019
A conforming DG method for linear nonlocal models with integrable kernels. Zbl 1428.82037
Du, Qiang; Yin, Xiaobo
2019
On uniform second order nonlocal approximations to linear two-point boundary value problems. Zbl 1426.47013
Du, Qiang; Zhang, Jiwei; Zheng, Chunxiong
2019
Asymptotically compatible discretization of multidimensional nonlocal diffusion models and approximation of nonlocal Green’s functions. Zbl 1466.65222
Du, Qiang; Tao, Yunzhe; Tian, Xiaochuan; Yang, Jiang
2019
A cooperative game for automated learning of elasto-plasticity knowledge graphs and models with AI-guided experimentation. Zbl 1464.74034
Wang, Kun; Sun, WaiChing; Du, Qiang
2019
Nonlocal models with heterogeneous localization and their application to seamless local-nonlocal coupling. Zbl 1447.45001
Tao, Yunzhe; Tian, Xiaochuan; Du, Qiang
2019
Asymptotically compatible SPH-like particle discretizations of one dimensional linear advection models. Zbl 1409.76114
Lee, Hwi; Du, Qiang
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
2019
New error bounds for deep ReLU networks using sparse grids. Zbl 07468821
2019
Preface to the focused issue on fractional derivatives and general nonlocal models. Zbl 1449.00002
2019
Heterogeneously localized nonlocal operators, boundary traces and variational problems. Zbl 1442.46024
Du, Qiang; Tian, Xiaochuan
2019
Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation. Zbl 1395.65099
Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua
2018
A quasi-nonlocal coupling method for nonlocal and local diffusion models. Zbl 06880667
Du, Qiang; Li, Xingjie Helen; Lu, Jianfeng; Tian, Xiaochuan
2018
Uniform $$L^p$$-bound of the Allen-Cahn equation and its numerical discretization. Zbl 1408.65076
Yang, Jiang; Du, Qiang; Zhang, Wei
2018
Numerical solution of a two-dimensional nonlocal wave equation on unbounded domains. Zbl 1392.82036
Du, Qiang; Han, Houde; Zhang, Jiwei; Zheng, Chunxiong
2018
A peridynamic model of fracture mechanics with bond-breaking. Zbl 1395.74041
Du, Qiang; Tao, Yunzhe; Tian, Xiaochuan
2018
Stability of nonlocal Dirichlet integrals and implications for peridynamic correspondence material modeling. Zbl 1394.45002
Du, Qiang; Tian, Xiaochuan
2018
Nonlocal wave propagation in unbounded multi-scale media. Zbl 1475.65156
Du, Qiang; Zhang, Jiwei; Zheng, Chunxiong
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
2018
A spectral method for nonlocal diffusion operators on the sphere. Zbl 1415.65238
Slevinsky, Richard Mikaël; Montanelli, Hadrien; Du, Qiang
2018
Asymptotically compatible schemes for stochastic homogenization. Zbl 1452.35022
Sun, Qi; Du, Qiang; Ming, Ju
2018
Data-driven compressive sensing and applications in uncertainty quantification. Zbl 1416.65389
Liang, Hong; Sun, Qi; Du, Qiang
2018
An invitation to nonlocal modeling, analysis and computation. Zbl 1462.45019
Du, Qiang
2018
Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations. Zbl 1411.74058
Tao, Yunzhe; Tian, Xiaochuan; Du, Qiang
2017
Analysis of a nonlocal-in-time parabolic equation. Zbl 1362.45015
Du, Qiang; Yang, Jiang; Zhou, Zhi
2017
Trace theorems for some nonlocal function spaces with heterogeneous localization. Zbl 1373.46030
Tian, Xiaochuan; Du, Qiang
2017
Artificial boundary conditions for nonlocal heat equations on unbounded domain. Zbl 1373.45011
Zhang, Wei; Yang, Jiang; Zhang, Jiwei; Du, Qiang
2017
Nonlocal convection-diffusion problems on bounded domains and finite-range jump processes. Zbl 1436.35307
D&rsquo;Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Richard
2017
A conservative nonlocal convection-diffusion model and asymptotically compatible finite difference discretization. Zbl 1439.65134
Tian, Hao; Ju, Lili; Du, Qiang
2017
Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications. Zbl 1380.65435
Du, Qiang; Yang, Jiang
2017
Nonlocal conservation laws. A new class of monotonicity-preserving models. Zbl 1377.35196
Du, Qiang; Huang, Zhan; LeFloch, Philippe G.
2017
Numerical solution of the nonlocal diffusion equation on the real line. Zbl 1376.82053
Zheng, Chunxiong; Hu, Jiashun; Du, Qiang; Zhang, Jiwei
2017
Numerical solution of a scalar one-dimensional monotonicity-preserving nonlocal nonlinear conservation law. Zbl 1389.35223
Du, Qiang; Huang, Zhan
2017
Asymptotically compatible schemes for space-time nonlocal diffusion equations. Zbl 1422.65279
Chen, An; Du, Qiang; Li, Changpin; Zhou, Zhi
2017
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
2016
Asymptotically compatible Fourier spectral approximations of nonlocal Allen-Cahn equations. Zbl 1342.65198
Du, Qiang; Yang, Jiang
2016
Weak solutions for the Cahn-Hilliard equation with degenerate mobility. Zbl 1333.35188
Dai, Shibin; Du, Qiang
2016
Characterization of function spaces of vector fields and an application in nonlinear peridynamics. Zbl 1353.46027
2016
Computational studies of coarsening rates for the Cahn-Hilliard equation with phase-dependent diffusion mobility. Zbl 1349.80043
Dai, Shibin; Du, Qiang
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
2016
Optimization-based shrinking dimer method for finding transition states. Zbl 1332.37062
Zhang, Lei; Du, Qiang; Zheng, Zhenzhen
2016
On the consistency between nearest-neighbor peridynamic discretizations and discretized classical elasticity models. Zbl 1439.74044
Seleson, Pablo; Du, Qiang; Parks, Michael L.
2016
Multiscale analysis of linear evolution equations with applications to nonlocal models for heterogeneous media. Zbl 1348.74287
Du, Qiang; Lipton, Robert; Mengesha, Tadele
2016
A class of high order nonlocal operators. Zbl 1362.46042
Tian, Xiaochuan; Du, Qiang
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
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
2016
Generalized local and nonlocal master equations for some stochastic processes. Zbl 1443.60052
Zhao, Yanxiang; Wang, Jiakou; Ma, Yanping; Du, Qiang
2016
Fractional diffusion on bounded domains. Zbl 1488.35557
Defterli, Ozlem; D&rsquo;Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Rich; Meerschaert, Mark M.
2015
Fast explicit integration factor methods for semilinear parabolic equations. Zbl 1317.65172
Ju, Lili; Zhang, Jian; Zhu, Liyong; Du, Qiang
2015
On the variational limit of a class of nonlocal functionals related to peridynamics. Zbl 1330.45011
2015
Nonconforming discontinuous Galerkin methods for nonlocal variational problems. Zbl 1322.65109
Tian, Xiaochuan; Du, Qiang
2015
Nonlocal convection-diffusion problems and finite element approximations. Zbl 1423.74925
Tian, Hao; Ju, Lili; Du, Qiang
2015
Integral approximations to classical diffusion and smoothed particle hydrodynamics. Zbl 1423.76363
Du, Qiang; Lehoucq, R. B.; Tartakovsky, A. M.
2015
Multiscale analysis of linearized peridynamics. Zbl 1327.74129
2015
Robust discretization of nonlocal models related to peridynamics. Zbl 1342.74178
Du, Qiang; Tian, Xiaochuan
2015
Asymptotically compatible schemes and applications to robust discretization of nonlocal models. Zbl 1303.65098
Tian, Xiaochuan; Du, Qiang
2014
Nonlocal constrained value problems for a linear peridynamic Navier equation. Zbl 1297.74051
2014
The bond-based peridynamic system with Dirichlet-type volume constraint. Zbl 1381.35177
2014
Nonlocal convection-diffusion volume-constrained problems and jump processes. Zbl 1284.35223
Du, Qiang; Huang, Zhan; Lehoucq, Richard B.
2014
Coarsening mechanism for systems governed by the Cahn-Hilliard equation with degenerate diffusion mobility. Zbl 1327.35150
Dai, Shibin; Du, Qiang
2014
Linear finite element superconvergence on simplicial meshes. Zbl 1312.65187
Chen, Jie; Wang, Desheng; Du, Qiang
2014
Mesh dependent stability and condition number estimates for finite element approximations of parabolic problems. Zbl 1279.65119
Zhu, Liyong; Du, Qiang
2014
Finding critical nuclei in phase transformations by shrinking dimer dynamics and its variants. Zbl 1373.82033
Zhang, Lei; Zhang, Jingyan; Du, Qiang
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
2014
Zhao, Xuying; Shi, Zhong-Ci; Du, Qiang
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
2013
Analysis and comparison of different approximations to nonlocal diffusion and linear peridynamic equations. Zbl 1295.82021
Tian, Xiaochuan; Du, Qiand
2013
Analysis of a scalar nonlocal peridynamic model with a sign changing kernel. Zbl 1278.45014
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
2013
Analysis of the volume-constrained peridynamic Navier equation of linear elasticity. Zbl 1277.35007
Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun
2013
A convergent adaptive finite element algorithm for nonlocal diffusion and peridynamic models. Zbl 1271.82011
Du, Qiang; Tian, Li; Zhao, Xuying
2013
Abstract principal component analysis. Zbl 1305.62223
Li, Tianjiang; Du, Qiang
2013
Analysis and approximation of nonlocal diffusion problems with volume constraints. Zbl 1422.76168
Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun
2012
A new approach for a nonlocal, nonlinear conservation law. Zbl 1248.35121
Du, Qiang; Kamm, James R.; Lehoucq, R. B.; Parks, Michael L.
2012
Shrinking dimer dynamics and its applications to saddle point search. Zbl 1254.37060
Zhang, Jingyan; Du, Qiang
2012
Motion of interfaces governed by the Cahn-Hilliard equation with highly disparate diffusion mobility. Zbl 1276.35033
Dai, Shibin; Du, Qiang
2012
Constrained shrinking dimer dynamics for saddle point search with constraints. Zbl 1248.65069
Zhang, Jingyan; Du, Qiang
2012
Periodic centroidal Voronoi tessellations. Zbl 1267.65029
Zhang, Jingyan; Emelianenk, Maria; Du, Qiang
2012
A hybrid implicit-explicit adaptive multirate numerical scheme for time-dependent equations. Zbl 1244.65100
Chabaud, Brandon; Du, Q.
2012
Mathematical analysis for the peridynamic nonlocal continuum theory. Zbl 1269.45005
Du, Qiang; Zhou, Kun
2011
...and 131 more Documents
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### Cited by 3,412 Authors

 119 Du, Qiang 57 Gunzburger, Max D. 54 Ju, Lili 30 Yang, Xiaofeng 28 Li, Jichun 26 Liu, Chun 26 Wang, Cheng 25 Huang, Yunqing 25 Shen, Jie 22 Bao, Weizhu 22 Tian, Xiaochuan 21 Ding, Jiu 19 Fan, Jishan 18 Kim, Junseok 18 Pan, Xingbin 17 D’Elia, Marta 17 Feng, Xinlong 17 Wang, Qi 16 Antoine, Xavier 15 Qiao, Zhonghua 15 Wise, Steven M. 15 Zhang, Yanzhi 14 Lowengrub, John Samuel 14 Yang, Jiang 13 Cai, Yongyong 13 Li, Xiao 13 Mengesha, Tadele 13 Wang, Desheng 13 Wang, Hong 13 Yang, Wei 13 Zhao, Jia 12 Dehghan Takht Fooladi, Mehdi 12 Lin, Ping 12 Pan, Kejia 12 Wang, Xiaoqiang 12 Yu, Yue 11 Chen, Wenbin 11 Li, Buyang 11 Li, Yibao 11 Liu, Zuhan 11 Promislow, Keith Steven 11 Warma, Mahamadi 10 Dassi, Franco 10 Gong, Yuezheng 10 Huang, Chengming 10 Lee, Hyun Geun 10 Lipton, Robert P. 10 Rabczuk, Timon 10 Rossi, Julio Daniel 10 Wang, Hanquan 10 Zhou, Zhi 9 Bellido, José Carlos 9 Chien, Cheng-Sheng 9 Chung, Tsz Shun Eric 9 Elliott, Charles M. 9 Guillén González, Francisco M. 9 Guo, Boling 9 Liang, Dong 9 Liu, Zhengguang 9 Muha, Boris 9 Nie, Yufeng 9 Owolabi, Kolade Matthew 9 Serfaty, Sylvia 9 Trask, Nathaniel A. 9 Triggiani, Roberto 9 Wang, Zhu 9 Xiao, Xufeng 9 You, Huaiqian 9 Yuan, Guangwei 9 Zhang, Jiwei 9 Zhang, Zhimin 9 Zhou, Aihui 9 Zhu, Liyong 8 Avalos, George 8 Barrett, John William 8 Boglaev, Igor P. 8 Bronsard, Lia 8 Čanić, Sunčica 8 Cheng, Kelong 8 Foster, John T. jun. 8 Helffer, Bernard 8 Huang, Ting-Zhu 8 Karniadakis, George Em 8 Lasiecka, Irena 8 Lehoucq, Richard B. 8 Li, Shaofan 8 Li, Xiaoli 8 Lin, Wen-Wei 8 Roychowdhury, Mrinal Kanti 8 Shi, Dongyang 8 Shieh, Shih-Feng 8 Tang, Qinglin 8 Voigt, Axel 8 Wang, Tingchun 8 Wang, Yushun 8 Zhou, Zhongguo 7 Aksoylu, Burak 7 Alama, Stan 7 Almog, Yaniv 7 Cai, Wenjun ...and 3,312 more Authors
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### Cited in 346 Serials

 266 Journal of Computational Physics 149 Computer Methods in Applied Mechanics and Engineering 117 Journal of Scientific Computing 109 Journal of Computational and Applied Mathematics 91 Computers & Mathematics with Applications 90 Applied Mathematics and Computation 62 SIAM Journal on Numerical Analysis 57 SIAM Journal on Scientific Computing 55 Applied Numerical Mathematics 51 Mathematics of Computation 48 Journal of Mathematical Analysis and Applications 42 Communications in Computational Physics 37 Numerische Mathematik 37 Physica D 31 Applied Mathematics Letters 30 Numerical Methods for Partial Differential Equations 28 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 26 Journal of Differential Equations 24 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 24 Numerical Algorithms 24 Communications in Nonlinear Science and Numerical Simulation 23 Journal of Mathematical Physics 22 Multiscale Modeling & Simulation 21 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 21 SIAM Journal on Mathematical Analysis 21 Advances in Computational Mathematics 20 Applicable Analysis 20 Archive for Rational Mechanics and Analysis 20 International Journal of Computer Mathematics 19 ZAMP. Zeitschrift für angewandte Mathematik und Physik 19 SIAM Journal on Applied Mathematics 19 Calculus of Variations and Partial Differential Equations 18 Computational Mechanics 18 Discrete and Continuous Dynamical Systems. Series B 17 Science China. Mathematics 16 Computer Physics Communications 15 International Journal for Numerical Methods in Engineering 15 Computer Aided Geometric Design 15 Advances in Difference Equations 14 Mathematics and Computers in Simulation 13 Applied Mathematical Modelling 13 Computational and Applied Mathematics 13 Nonlinear Analysis. Theory, Methods & Applications 12 Communications in Mathematical Physics 12 Mathematical Methods in the Applied Sciences 12 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 12 Journal of Elasticity 12 Engineering Analysis with Boundary Elements 12 Discrete and Continuous Dynamical Systems 11 BIT 11 Advances in Applied Mathematics and Mechanics 10 Fractional Calculus & Applied Analysis 10 Communications on Pure and Applied Analysis 10 International Journal of Numerical Analysis and Modeling 9 Journal of Fluid Mechanics 9 Transactions of the American Mathematical Society 8 International Journal of Control 8 Journal of Functional Analysis 8 European Journal of Applied Mathematics 8 Mathematics and Mechanics of Solids 8 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 8 Evolution Equations and Control Theory 8 East Asian Journal on Applied Mathematics 8 Communications on Applied Mathematics and Computation 7 Journal of Mathematical Biology 7 Chaos, Solitons and Fractals 7 Science in China. Series A 7 Mathematical Problems in Engineering 7 Nonlinear Analysis. Real World Applications 6 Computers and Fluids 6 Communications on Pure and Applied Mathematics 6 Nonlinearity 6 Automatica 6 Numerical Functional Analysis and Optimization 6 SIAM Journal on Matrix Analysis and Applications 6 Journal of Mathematical Imaging and Vision 6 Journal of Nonlinear Science 6 NoDEA. Nonlinear Differential Equations and Applications 6 Computational Geosciences 6 Communications in Contemporary Mathematics 6 SIAM Journal on Applied Dynamical Systems 6 International Journal of Computational Methods 6 Discrete and Continuous Dynamical Systems. Series S 6 Journal of Theoretical Biology 6 Results in Applied Mathematics 5 Inverse Problems 5 Journal of Statistical Physics 5 Applied Mathematics and Optimization 5 Calcolo 5 Mathematical and Computer Modelling 5 SIAM Review 5 Chaos 5 Acta Mathematica Sinica. English Series 5 Computational Methods in Applied Mathematics 5 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 5 AIMS Mathematics 4 Physica A 4 Bulletin of Mathematical Biology 4 Advances in Mathematics 4 Journal of Optimization Theory and Applications ...and 246 more Serials
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### Cited in 50 Fields

 1,570 Numerical analysis (65-XX) 1,355 Partial differential equations (35-XX) 504 Fluid mechanics (76-XX) 373 Statistical mechanics, structure of matter (82-XX) 343 Mechanics of deformable solids (74-XX) 173 Calculus of variations and optimal control; optimization (49-XX) 128 Biology and other natural sciences (92-XX) 118 Optics, electromagnetic theory (78-XX) 115 Probability theory and stochastic processes (60-XX) 100 Integral equations (45-XX) 75 Computer science (68-XX) 73 Dynamical systems and ergodic theory (37-XX) 68 Real functions (26-XX) 67 Operator theory (47-XX) 63 Quantum theory (81-XX) 58 Ordinary differential equations (34-XX) 58 Systems theory; control (93-XX) 49 Operations research, mathematical programming (90-XX) 44 Functional analysis (46-XX) 44 Global analysis, analysis on manifolds (58-XX) 41 Approximations and expansions (41-XX) 32 Statistics (62-XX) 30 Differential geometry (53-XX) 29 Classical thermodynamics, heat transfer (80-XX) 25 Information and communication theory, circuits (94-XX) 24 Geophysics (86-XX) 21 Measure and integration (28-XX) 18 Linear and multilinear algebra; matrix theory (15-XX) 16 Combinatorics (05-XX) 16 Convex and discrete geometry (52-XX) 12 Mechanics of particles and systems (70-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Potential theory (31-XX) 7 Special functions (33-XX) 7 Difference and functional equations (39-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 4 Geometry (51-XX) 3 General and overarching topics; collections (00-XX) 3 Integral transforms, operational calculus (44-XX) 3 Astronomy and astrophysics (85-XX) 2 History and biography (01-XX) 2 Mathematical logic and foundations (03-XX) 2 Algebraic geometry (14-XX) 2 Algebraic topology (55-XX) 2 Relativity and gravitational theory (83-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Group theory and generalizations (20-XX) 1 Functions of a complex variable (30-XX) 1 Abstract harmonic analysis (43-XX) 1 Mathematics education (97-XX)

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