# zbMATH — the first resource for mathematics

Compute Distance To:
 Documents Indexed: 287 Publications since 1986, including 10 Books
all top 5

#### Co-Authors

 6 single-authored 16 Wan, Xiaoliang 15 Venturi, Daniele 14 Sherwin, Spencer J. 14 Zayernouri, Mohsen 14 Zhang, Zhongqiang 12 Perdikaris, Paris G. 12 Xiu, Dongbin 11 Mao, Zhiping 11 Zeng, Fanhai 10 Triantafyllou, Michael S. 9 Kirby, Robert M. II 9 Li, Zhen 9 Lucor, Didier 9 Raissi, Maziar 9 Song, Fangying 9 Su, Chau-Hsing 8 Caswell, Bruce 8 Dong, Suchuan 8 Lin, Guang 7 Evangelinos, Constantinos 7 Grinberg, Leopold 7 Lomtev, Igor 7 Maxey, Martin R. 7 Orszag, Steven Alan 7 Rozovskii, Boris L. 6 Cho, Heyrim 6 Choi, Minseok 6 Fedosov, Dmitry A. 6 Giannakouros, John G. 6 Pang, Guofei 6 Sirisup, Sirod 6 Wang, Zhi Cheng 6 Yu, Yue 6 Zhang, Dongkun 5 Cai, Wei 5 Constantinides, Yiannis 5 Deng, Mingge 5 Henderson, Ronald D. 5 Ma, Xia 5 Sidilkover, David 5 Warburton, Timothy C. E. 4 Babaee, Hessam 4 Baek, Hyoungsu 4 Bian, Xin 4 Bittencourt, Marco Lúcio 4 Cao, Wanrong 4 Kharazmi, Ehsan 4 Lei, Huan 4 Sapsis, Themistoklis P. 4 Symeonidis, Vasileios 4 Tang, Yuhang 4 Xu, Jin 4 Yang, Xiu 3 Ainsworth, Mark 3 Beskok, Ali 3 Foo, Jasmine 3 Guo, Ling 3 Jagtap, Ameya D. 3 Kevrekidis, Ioannis George 3 Kim, Changho 3 Lu, Lu 3 Meng, Xuhui 3 Patera, Anthony T. 3 Rockwell, Donald 3 Shu, Chi-Wang 3 Tretyakov, Michael V. 3 Triantafyllou, George S. 3 Zheng, Mengdi 3 Zheng, Xiaoning 2 Batcho, Paul F. 2 Bourguet, Rémi 2 Burrage, Kevin 2 Chryssostomidis, C. 2 Cockburn, Bernardo 2 Du, Yiqing 2 Gulian, Mamikon 2 Kaiktsis, Lambros 2 Karamanos, G.-S. 2 Li, Xuejin 2 Lischke, Anna 2 Liu, Wing Kam 2 Luo, Xian 2 Newman, David J. 2 Pivkin, Igor V. 2 Rønquist, Einar M. 2 Tang, Shaoqiang 2 Tartakovsky, Daniel M. 2 Turner, Ian William 2 Wang, Hong 2 Wang, Nan 2 Xie, Fangfang 2 Xu, Chuanju 2 Yazdani, Alireza 2 Yin, Minglang 2 Yosibash, Zohar 2 Yvonnet, Julien 2 Zhao, Xuan 1 Bangia, Anil K. 1 Bargos, Fabiano F. 1 Barouch, Eytan ...and 77 more Co-Authors
all top 5

#### Serials

 83 Journal of Computational Physics 37 SIAM Journal on Scientific Computing 34 Computer Methods in Applied Mechanics and Engineering 29 Journal of Fluid Mechanics 7 International Journal for Numerical Methods in Engineering 7 Journal of Scientific Computing 6 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 4 SIAM Journal on Numerical Analysis 3 International Journal for Numerical Methods in Fluids 3 Applied Numerical Mathematics 3 Computational Mechanics 3 Communications in Computational Physics 3 Numerical Mathematics and Scientific Computation 2 Computers and Fluids 2 International Journal of Heat and Mass Transfer 2 Proceedings of the National Academy of Sciences of the United States of America 2 European Journal of Mechanics. B. Fluids 2 Multiscale Modeling & Simulation 1 Computers & Mathematics with Applications 1 Computers and Structures 1 Journal of Engineering Mathematics 1 Journal of Statistical Physics 1 Physics of Fluids, A 1 Fluid Dynamics Research 1 Theoretical and Computational Fluid Dynamics 1 Chaos, Solitons and Fractals 1 Bulletin of the Polish Academy of Sciences. Technical Sciences 1 Numerische Mathematik 1 Physica D 1 Journal of Non-Newtonian Fluid Mechanics 1 SIAM Review 1 Physics of Fluids 1 Electronic Journal of Differential Equations (EJDE) 1 Parallel Algorithms and Applications 1 Fractional Calculus & Applied Analysis 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Flow, Turbulence and Combustion 1 HERMIS-$$\mu\pi$$. Hellenic European Research on Mathematics and Informatics Science 1 Applied Mathematical Sciences 1 Interdisciplinary Applied Mathematics 1 Lecture Notes in Computational Science and Engineering 1 Journal of Theoretical Biology 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Handbook of Fractional Calculus with Applications 1 Communications on Applied Mathematics and Computation
all top 5

#### Fields

 159 Fluid mechanics (76-XX) 132 Numerical analysis (65-XX) 70 Partial differential equations (35-XX) 52 Probability theory and stochastic processes (60-XX) 34 Mechanics of deformable solids (74-XX) 23 Ordinary differential equations (34-XX) 20 Computer science (68-XX) 18 Biology and other natural sciences (92-XX) 13 Statistics (62-XX) 10 Statistical mechanics, structure of matter (82-XX) 8 Dynamical systems and ergodic theory (37-XX) 7 Approximations and expansions (41-XX) 6 Classical thermodynamics, heat transfer (80-XX) 6 Geophysics (86-XX) 5 General and overarching topics; collections (00-XX) 4 Optics, electromagnetic theory (78-XX) 3 Real functions (26-XX) 2 Mechanics of particles and systems (70-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Special functions (33-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Convex and discrete geometry (52-XX) 1 Quantum theory (81-XX)

#### Citations contained in zbMATH Open

254 Publications have been cited 7,145 times in 4,263 Documents Cited by Year
The Wiener–Askey polynomial chaos for stochastic differential equations. Zbl 1014.65004
2002
High-order splitting methods for the incompressible Navier-Stokes equations. Zbl 0738.76050
Karniadakis, George Em; Israeli, Moshe; Orszag, Steven A.
1991
Spectral/$$hp$$ element methods for computational fluid dynamics. 2nd ed. Zbl 1116.76002
Karniadakis, George Em; Sherwin, Spencer J.
2005
The development of discontinuous Galerkin methods. Zbl 0989.76045
Cockburn, Bernardo; Karniadakis, George E.; Shu, Chi-Wang
2000
Spectral/hp element methods for CFD. Zbl 0954.76001
Karniadakis, George Em; Sherwin, Spencer J.
1999
Modeling uncertainty in flow simulations via generalized polynomial chaos. Zbl 1047.76111
2003
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations. Zbl 1078.65008
2005
Microflows and nanoflows. Fundamentals and simulation. Foreword by Chih-Ming Ho. Zbl 1115.76003
Karniadakis, George; Beskok, Ali; Narayan, Aluru
2005
Multi-element generalized polynomial chaos for arbitrary probability measures. Zbl 1128.65009
2006
Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos. Zbl 1016.65001
2002
Low-dimensional models for complex geometry flows: Application to grooved channels and circular cylinders. Zbl 0746.76021
Deane, A. E.; Kevrekidis, I. G.; Karniadakis, G. E.; Orszag, S. A.
1991
Fractional spectral collocation method. Zbl 1294.65097
2014
Fractional Sturm-Liouville eigen-problems: theory and numerical approximation. Zbl 1349.34095
2013
Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Zbl 1415.68175
Raissi, M.; Perdikaris, P.; Karniadakis, G. E.
2019
Spectral/$$hp$$ element methods for computational fluid dynamics. Reprint of the 2nd hardback ed. (2005). Zbl 1256.76003
Karniadakis, George Em; Sherwin, Spencer J.
2013
A spectral vanishing viscosity method for large eddy simulations. Zbl 0984.76036
Karamanos, G. S.; Karniadakis, G. E.
2000
Exponentially accurate spectral and spectral element methods for fractional ODEs. Zbl 1349.65257
2014
A semi-Lagrangian high-order method for Navier-Stokes equations. Zbl 1028.76026
2001
Fractional spectral collocation methods for linear and nonlinear variable order FPDEs. Zbl 1349.65531
2015
A spectral viscosity method for correcting the long-term behavior of POD models. Zbl 1136.76412
2004
The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications. Zbl 1153.65008
Foo, Jasmine; Wan, Xiaoliang; Karniadakis, George Em
2008
Second-order approximations for variable order fractional derivatives: algorithms and applications. Zbl 1349.65092
Zhao, Xuan; Sun, Zhi-zhong; Karniadakis, George Em
2015
A triangular spectral element method; applications to the incompressible Navier-Stokes equations. Zbl 1075.76621
Sherwin, S. J.; Karniadakis, G. E.
1995
Multi-element probabilistic collocation method in high dimensions. Zbl 1181.65014
2010
Hidden physics models: machine learning of nonlinear partial differential equations. Zbl 1381.68248
2018
Three-dimensional dynamics and transition to turbulence in the wake of bluff objects. Zbl 0754.76043
Karniadakis, George Em; Triantafyllou, George S.
1992
A low-dimensional model for simulating three-dimensional cylinder flow. Zbl 1001.76043
2002
A new triangular and tetrahedral basis for high-order $$(hp)$$ finite element methods. Zbl 0837.73075
Sherwin, Spencer J.; Karniadakis, George Em.
1995
Long-term behavior of polynomial chaos in stochastic flow simulations. Zbl 1123.76058
2006
Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24–26, 1999. Zbl 0935.00043
Cockburn, Bernardo (ed.); Karniadakis, George E. (ed.); Shu, Chi-Wang (ed.)
2000
A unified Petrov-Galerkin spectral method for fractional PDEs. Zbl 1425.65127
Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em.
2015
De-aliasing on non-uniform grids: algorithms and applications. Zbl 1161.76534
Kirby, Robert M.; Karniadakis, George Em
2003
Discontinuous spectral element methods for time- and space-fractional advection equations. Zbl 1304.35757
2014
Frequency selection and asymptotic states in laminar wakes. Zbl 0659.76043
Karniadakis, George Em; Triantafyllou, George S.
1989
Inferring solutions of differential equations using noisy multi-fidelity data. Zbl 1382.65229
Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em
2017
Machine learning of linear differential equations using Gaussian processes. Zbl 1380.68339
Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em
2017
Reweighted $$\ell_1$$ minimization method for stochastic elliptic differential equations. Zbl 1349.60113
2013
Onset of three-dimensionality, equilibria, and early transition in flow over a backward-facing step. Zbl 0728.76057
Kaiktsis, Lambros; Karniadakis, George Em; Orszag, Steven A.
1991
A generalized spectral collocation method with tunable accuracy for variable-order fractional differential equations. Zbl 1339.65197
Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em
2015
Dynamics and low-dimensionality of a turbulent near wake. Zbl 0987.76041
Ma, X.; Karamanos, G.-S.; Karniadakis, G. E.
2000
Micro flows. Fundamentals and simulation. Zbl 0998.76002
2002
Adaptive ANOVA decomposition of stochastic incompressible and compressible flows. Zbl 1408.76428
Yang, Xiu; Choi, Minseok; Lin, Guang; Karniadakis, George Em
2012
A new stochastic approach to transient heat conduction modeling with uncertainty. Zbl 1038.80003
2003
Time-dependent generalized polynomial chaos. Zbl 1201.65216
Gerritsma, Marc; van der Steen, Jan-Bart; Vos, Peter; Karniadakis, George
2010
Tetrahedral spectral elements for CFD. Zbl 0857.76044
Sherwin, S. J.; Karniadakis, G. E.
1995
A discontinuous Galerkin ALE method for compressible viscous flows in moving domains. Zbl 0956.76046
Lomtev, I.; Kirby, R. M.; Karniadakis, G. E.
1999
A combined direct numerical simulation–particle image velocimetry study of the turbulent near wake. Zbl 1177.76156
Dong, S.; Karniadakis, G. E.; Ekmekci, A.; Rockwell, D.
2006
Spectral polynomial chaos solutions of the stochastic advection equation. Zbl 1001.76084
Jardak, M.; Su, C.-H.; Karniadakis, G. E.
2002
Beyond Wiener-Askey expansions: handling arbitrary PDFs. Zbl 1102.65006
2006
A spectral method (of exponential convergence) for singular solutions of the diffusion equation with general two-sided fractional derivative. Zbl 1422.65428
2018
A discontinuous Galerkin method for the viscous MHD equations. Zbl 0954.76051
Warburton, T. C.; Karniadakis, G. E.
1999
Mechanisms of transverse motions in turbulent wall flows. Zbl 1039.76028
2003
Spectral element-Fourier methods for incompressible turbulent flows. Zbl 0722.76053
1990
Unstructured spectral element methods for simulation of turbulent flows. Zbl 0840.76070
Henderson, Ronald D.; Karniadakis, George Em
1995
A direct numerical simulation study of flow past a freely vibrating cable. Zbl 0901.76062
Newman, David J.; Karniadakis, George Em
1997
Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations. Zbl 1352.65278
Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em
2016
Tempered fractional Sturm-Liouville eigenproblems. Zbl 1323.34012
Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em
2015
A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains. Zbl 1349.76569
Dong, S.; Karniadakis, G. E.; Chryssostomidis, C.
2014
Unsteadiness and convective instabilities in two-dimensional flow over a backward-facing step. Zbl 0875.76111
Kaiktsis, Lambros; Karniadakis, George Em; Orszag, Steven A.
1996
Implicit-explicit difference schemes for nonlinear fractional differential equations with nonsmooth solutions. Zbl 1355.65104
Cao, Wanrong; Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em
2016
A fractional phase-field model for two-phase flows with tunable sharpness: algorithms and simulations. Zbl 1423.76102
Song, Fangying; Xu, Chuanju; Karniadakis, George Em
2016
A generalized spectral collocation method with tunable accuracy for fractional differential equations with end-point singularities. Zbl 1431.65193
Zeng, Fanhai; Mao, Zhiping; Karniadakis, George Em
2017
Drag reduction in wall-bounded turbulence via a transverse travelling wave. Zbl 1112.76373
Du, Yiqing; Symeonidis, V.; Karniadakis, G. E.
2002
Spectral and discontinuous spectral element methods for fractional delay equations. Zbl 1314.34159
Zayernouri, Mohsen; Cao, Wanrong; Zhang, Zhongqiang; Karniadakis, George Em
2014
Tetrahedral $$hp$$ finite elements: Algorithms and flow simulations. Zbl 0847.76038
Sherwin, S. J.; Karniadakis, G. E.
1996
Spectral/hp methods for viscous compressible flows on unstructured 2D meshes. Zbl 0929.76095
Lomtev, I.; Quillen, C. B.; Karniadakis, G. E.
1998
Numerical Gaussian processes for time-dependent and nonlinear partial differential equations. Zbl 1386.65030
Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em
2018
Equation-free/Galerkin-free POD-assisted computation of incompressible flows. Zbl 1213.76146
Sirisup, Sirod; Karniadakis, George Em; Xiu, Dongbin; Kevrekidis, Ioannis G.
2005
Petrov-Galerkin and spectral collocation methods for distributed order differential equations. Zbl 1367.65113
Kharazmi, Ehsan; Zayernouri, Mohsen; Karniadakis, George Em
2017
Dynamics and flow structures in the turbulent wake of rigid and flexible cylinders subject to vortex-induced vibrations. Zbl 0983.76029
1999
A new method to impose no-slip boundary conditions in dissipative particle dynamics. Zbl 1177.76325
Pivkin, Igor V.; Karniadakis, George Em
2005
Basis functions for triangular and quadrilateral high-order elements. Zbl 0930.35016
Warburton, T. C.; Sherwin, S. J.; Karniadakis, G. E.
1999
A discontinuous Galerkin method for the Navier-Stokes equations. Zbl 0951.76041
1999
Systematic coarse-graining of spectrin-level red blood cell models. Zbl 1231.74311
Fedosov, Dmitry A.; Caswell, Bruce; Karniadakis, George Em
2010
Spectral element simulations of laminar and turbulent flows in complex geometries. Zbl 0678.76050
1989
Generalized polynomial chaos and random oscillators. Zbl 1060.70515
Lucor, D.; Su, C.-H.; Karniadakis, G. E.
2004
A convergence study of a new partitioned fluid-structure interaction algorithm based on fictitious mass and damping. Zbl 1426.76496
2012
Exact PDF equations and closure approximations for advective-reactive transport. Zbl 1349.35068
Venturi, D.; Tartakovsky, D. M.; Tartakovsky, A. M.; Karniadakis, G. E.
2013
Stability and accuracy of periodic flow solutions obtained by a POD-penalty method. Zbl 1070.35024
2005
Optimal error estimates of spectral Petrov-Galerkin and collocation methods for initial value problems of fractional differential equations. Zbl 1326.65100
Zhang, Zhongqiang; Zeng, Fanhai; Karniadakis, George Em
2015
Galerkin and discontinuous Galerkin spectral/$$hp$$ methods. Zbl 0924.76078
Warburton, T. C.; Lomtev, I.; Du, Y.; Sherwin, S. J.; Karniadakis, G. E.
1999
What is the fractional Laplacian? A comparative review with new results. Zbl 1453.35179
Lischke, Anna; Pang, Guofei; Gulian, Mamikon; Song, Fangying; Glusa, Christian; Zheng, Xiaoning; Mao, Zhiping; Cai, Wei; Meerschaert, Mark M.; Ainsworth, Mark; Karniadakis, George Em
2020
Generalized fictitious methods for fluid-structure interactions: analysis and simulations. Zbl 1349.76577
Yu, Yue; Baek, Hyoungsu; Karniadakis, George Em
2013
Spectral element methods for elliptic problems in nonsmooth domains. Zbl 0844.65082
1995
Stochastic low-dimensional modelling of a random laminar wake past a circular cylinder. Zbl 1146.76018
Venturi, Daniele; Wan, Xiaoliang; Karniadakis, George Em
2008
Numerical methods for stochastic partial differential equations with white noise. Zbl 1380.65021
2017
Gappy data and reconstruction procedures for flow past a cylinder. Zbl 1065.76159
2004
Three-dimensionality effects in flow around two tandem cylinders. Zbl 1156.76370
Papaioannou, Georgios V.; Yue, Dick K. P.; Triantafyllou, Michael S.; Karniadakis, George E.
2006
Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions. Zbl 1439.65081
Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em
2017
Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems. Zbl 1371.60119
2014
The stochastic piston problem. Zbl 1135.76334
Lin, Guang; Su, Chau-Hsing; Karniadakis, G. E.
2004
DPIV-driven flow simulation: a new computational paradigm. Zbl 1116.76413
Ma, X.; Karniadakis, G. E.; Park, H.; Gharib, M.
2003
Spectral distributed Lagrange multiplier method: algorithm and benchmark tests. Zbl 1115.76349
Dong, Suchuan; Liu, Dong; Maxey, Martin R.; Karniadakis, George Em
2004
Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling. Zbl 1407.62252
Perdikaris, P.; Raissi, M.; Damianou, A.; Lawrence, N. D.; Karniadakis, G. E.
2017
A Petrov-Galerkin spectral method of linear complexity for fractional multiterm ODEs on the half line. Zbl 1367.65108
Lischke, Anna; Zayernouri, Mohsen; Karniadakis, George Em
2017
Computing fractional Laplacians on complex-geometry domains: algorithms and simulations. Zbl 1380.65357
Song, Fangying; Xu, Chuanju; Karniadakis, George Em
2017
A computable evolution equation for the joint response-excitation probability density function of stochastic dynamical systems. Zbl 1365.92023
Venturi, D.; Sapsis, T. P.; Cho, H.; Karniadakis, G. E.
2012
Stochastic bifurcation analysis of Rayleigh-Bénard convection. Zbl 1189.76213
Venturi, Daniele; Wan, Xiaoliang; Karniadakis, George Em
2010
Supersensitivity due to uncertain boundary conditions. Zbl 1075.76623
2004
Adaptive generalized polynomial chaos for nonlinear random oscillators. Zbl 1075.65008
2004
DeepXDE: a deep learning library for solving differential equations. Zbl 1459.65002
Lu, Lu; Meng, Xuhui; Mao, Zhiping; Karniadakis, George Em
2021
Two-point stress-strain-rate correlation structure and non-local eddy viscosity in turbulent flows. Zbl 1461.76181
Clark Di Leoni, Patricio; Zaki, Tamer A.; Karniadakis, George; Meneveau, Charles
2021
What is the fractional Laplacian? A comparative review with new results. Zbl 1453.35179
Lischke, Anna; Pang, Guofei; Gulian, Mamikon; Song, Fangying; Glusa, Christian; Zheng, Xiaoning; Mao, Zhiping; Cai, Wei; Meerschaert, Mark M.; Ainsworth, Mark; Karniadakis, George Em
2020
Physics-informed neural networks for high-speed flows. Zbl 1442.76092
Mao, Zhiping; Jagtap, Ameya D.; Karniadakis, George Em
2020
Physics-informed generative adversarial networks for stochastic differential equations. Zbl 1440.60065
Yang, Liu; Zhang, Dongkun; Karniadakis, George Em
2020
Learning in modal space: solving time-dependent stochastic PDEs using physics-informed neural networks. Zbl 1440.60067
Zhang, Dongkun; Guo, Ling; Karniadakis, George Em
2020
Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems. Zbl 1442.92002
Jagtap, Ameya D.; Kharazmi, Ehsan; Karniadakis, George Em
2020
Adaptive activation functions accelerate convergence in deep and physics-informed neural networks. Zbl 1453.68165
Jagtap, Ameya D.; Kawaguchi, Kenji; Karniadakis, George Em
2020
A stabilized semi-implicit Fourier spectral method for nonlinear space-fractional reaction-diffusion equations. Zbl 1453.65370
Zhang, Hui; Jiang, Xiaoyun; Zeng, Fanhai; Karniadakis, George Em
2020
A fast solver for spectral elements applied to fractional differential equations using hierarchical matrix approximation. Zbl 1442.65144
Li, Xianjuan; Mao, Zhiping; Wang, Nan; Song, Fangying; Wang, Hong; Karniadakis, George Em
2020
A composite neural network that learns from multi-fidelity data: application to function approximation and inverse PDE problems. Zbl 1454.76006
2020
Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Zbl 1415.68175
Raissi, M.; Perdikaris, P.; Karniadakis, G. E.
2019
FPINNs: fractional physics-informed neural networks. Zbl 1420.35459
Pang, Guofei; Lu, Lu; Karniadakis, George Em
2019
Deep learning of vortex-induced vibrations. Zbl 1415.76177
Raissi, Maziar; Wang, Zhicheng; Triantafyllou, Michael S.; Karniadakis, George Em
2019
Efficient multistep methods for tempered fractional calculus: algorithms and simulations. Zbl 07099350
Guo, Ling; Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em
2019
Multi-domain spectral collocation method for variable-order nonlinear fractional differential equations. Zbl 1440.65258
Zhao, Tinggang; Mao, Zhiping; Karniadakis, George Em
2019
Fractional Gray-Scott model: well-posedness, discretization, and simulations. Zbl 1440.35344
Wang, Tingting; Song, Fangying; Wang, Hong; Karniadakis, George Em
2019
An entropy-viscosity large eddy simulation study of turbulent flow in a flexible pipe. Zbl 1415.76369
Wang, Zhicheng; Triantafyllou, Michael S.; Constantinides, Yiannis; Karniadakis, George Em
2019
Machine learning of space-fractional differential equations. Zbl 1419.35209
Gulian, Mamikon; Raissi, Maziar; Perdikaris, Paris; Karniadakis, George
2019
Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network. Zbl 1434.76053
Mehta, Pavan Pranjivan; Pang, Guofei; Song, Fangying; Karniadakis, George Em
2019
Numerical methods. Zbl 1410.65001
2019
Mapping the properties of the vortex-induced vibrations of flexible cylinders in uniform oncoming flow. Zbl 1430.76091
Fan, Dixia; Wang, Zhicheng; Triantafyllou, Michael S.; Karniadakis, George Em
2019
Fractional magneto-hydrodynamics: algorithms and applications. Zbl 1416.76127
2019
A computational mechanics special issue on: data-driven modeling and simulation – theory, methods, and applications. Zbl 07095663
Liu, Wing Kam; Karniadakis, George; Tang, Shaoqiang; Yvonnet, Julien
2019
A spectral penalty method for two-sided fractional differential equations with General boundary conditions. Zbl 07099316
Wang, Nan; Mao, Zhiping; Huang, Chengming; Karniadakis, George Em
2019
Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems. Zbl 1454.65008
Zhang, Dongkun; Lu, Lu; Guo, Ling; Karniadakis, George Em
2019
Hidden physics models: machine learning of nonlinear partial differential equations. Zbl 1381.68248
2018
A spectral method (of exponential convergence) for singular solutions of the diffusion equation with general two-sided fractional derivative. Zbl 1422.65428
2018
Numerical Gaussian processes for time-dependent and nonlinear partial differential equations. Zbl 1386.65030
Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em
2018
A Riesz basis Galerkin method for the tempered fractional Laplacian. Zbl 1402.65120
Zhang, Zhijiang; Deng, Weihua; Karniadakis, George Em
2018
A partitioned coupling framework for peridynamics and classical theory: analysis and simulations. Zbl 1440.74045
Yu, Yue; Bargos, Fabiano F.; You, Huaiqian; Parks, Michael L.; Bittencourt, Marco L.; Karniadakis, George E.
2018
A new class of semi-implicit methods with linear complexity for nonlinear fractional differential equations. Zbl 1404.65105
Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em
2018
A dissipative particle dynamics method for arbitrarily complex geometries. Zbl 1380.76123
Li, Zhen; Bian, Xin; Tang, Yu-Hang; Karniadakis, George Em
2018
A computational stochastic methodology for the design of random meta-materials under geometric constraints. Zbl 1398.60073
Tsantili, Ivi C.; Cho, Min Hyung; Cai, Wei; Karniadakis, George Em
2018
Multi-fidelity optimization of super-cavitating hydrofoils. Zbl 1439.74256
Bonfiglio, L.; Perdikaris, P.; Brizzolara, S.; Karniadakis, G. E.
2018
Stochastic domain decomposition via moment minimization. Zbl 1391.60167
Zhang, Dongkun; Babaee, Hessam; Karniadakis, George Em
2018
A spectral-element/Fourier smoothed profile method for large-eddy simulations of complex VIV problems. Zbl 1410.76320
Wang, Zhicheng; Triantafyllou, Michael S.; Constantinides, Yiannis; Karniadakis, George Em
2018
Active learning of constitutive relation from mesoscopic dynamics for macroscopic modeling of non-Newtonian flows. Zbl 1392.76058
Zhao, Lifei; Li, Zhen; Caswell, Bruce; Ouyang, Jie; Karniadakis, George Em
2018
Inferring solutions of differential equations using noisy multi-fidelity data. Zbl 1382.65229
Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em
2017
Machine learning of linear differential equations using Gaussian processes. Zbl 1380.68339
Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em
2017
A generalized spectral collocation method with tunable accuracy for fractional differential equations with end-point singularities. Zbl 1431.65193
Zeng, Fanhai; Mao, Zhiping; Karniadakis, George Em
2017
Petrov-Galerkin and spectral collocation methods for distributed order differential equations. Zbl 1367.65113
Kharazmi, Ehsan; Zayernouri, Mohsen; Karniadakis, George Em
2017
Numerical methods for stochastic partial differential equations with white noise. Zbl 1380.65021
2017
Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions. Zbl 1439.65081
Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em
2017
Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling. Zbl 1407.62252
Perdikaris, P.; Raissi, M.; Damianou, A.; Lawrence, N. D.; Karniadakis, G. E.
2017
A Petrov-Galerkin spectral method of linear complexity for fractional multiterm ODEs on the half line. Zbl 1367.65108
Lischke, Anna; Zayernouri, Mohsen; Karniadakis, George Em
2017
Computing fractional Laplacians on complex-geometry domains: algorithms and simulations. Zbl 1380.65357
Song, Fangying; Xu, Chuanju; Karniadakis, George Em
2017
Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization. Zbl 1419.62499
Pang, Guofei; Perdikaris, Paris; Cai, Wei; Karniadakis, George Em
2017
Multi-fidelity Gaussian process regression for prediction of random fields. Zbl 1419.62272
Parussini, L.; Venturi, D.; Perdikaris, P.; Karniadakis, G. E.
2017
Adaptive finite element method for fractional differential equations using hierarchical matrices. Zbl 1439.65091
Zhao, Xuan; Hu, Xiaozhe; Cai, Wei; Karniadakis, George Em
2017
A tunable finite difference method for fractional differential equations with non-smooth solutions. Zbl 1439.65082
Chen, Xuejuan; Zeng, Fanhai; Karniadakis, George Em
2017
Fractional Burgers equation with nonlinear non-locality: spectral vanishing viscosity and local discontinuous Galerkin methods. Zbl 1380.65280
2017
A robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problems. Zbl 1380.76093
Babaee, Hessam; Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em
2017
A Petrov-Galerkin spectral element method for fractional elliptic problems. Zbl 1439.65205
Kharazmi, Ehsan; Zayernouri, Mohsen; Karniadakis, George Em
2017
Dissipative particle dynamics: foundation, evolution, implementation, and applications. Zbl 1387.35496
Li, Z.; Bian, X.; Li, X.; Deng, M.; Tang, Y.-H.; Caswell, B.; Karniadakis, George E.
2017
Numerical methods for high-dimensional kinetic equations. Zbl 1404.65117
Cho, Heyrim; Venturi, Daniele; Karniadakis, George Em
2017
Efficient two-dimensional simulations of the fractional Szabo equation with different time-stepping schemes. Zbl 1412.65091
Song, Fangying; Zeng, Fanhai; Cai, Wei; Chen, Wen; Karniadakis, George Em
2017
Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations. Zbl 1352.65278
Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em
2016
Implicit-explicit difference schemes for nonlinear fractional differential equations with nonsmooth solutions. Zbl 1355.65104
Cao, Wanrong; Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em
2016
A fractional phase-field model for two-phase flows with tunable sharpness: algorithms and simulations. Zbl 1423.76102
Song, Fangying; Xu, Chuanju; Karniadakis, George Em
2016
Multifidelity information fusion algorithms for high-dimensional systems and massive data sets. Zbl 1342.62110
Perdikaris, Paris; Venturi, Daniele; Karniadakis, George Em
2016
Numerical methods for high-dimensional probability density function equations. Zbl 1349.65046
Cho, H.; Venturi, D.; Karniadakis, G. E.
2016
Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms. Zbl 1415.74049
Yu, Yue; Perdikaris, Paris; Karniadakis, George Em
2016
Strong and weak convergence order of finite element methods for stochastic PDEs with spatial white noise. Zbl 1357.65013
Zhang, Zhongqiang; Rozovskii, Boris; Karniadakis, George Em.
2016
Multi-fidelity modelling of mixed convection based on experimental correlations and numerical simulations. Zbl 1383.76438
Babaee, H.; Perdikaris, P.; Chryssostomidis, C.; Karniadakis, G. E.
2016
Fractional-order uniaxial visco-elasto-plastic models for structural analysis. Zbl 1439.74077
Suzuki, J. L.; Zayernouri, M.; Bittencourt, M. L.; Karniadakis, G. E.
2016
Flow in complex domains simulated by dissipative particle dynamics driven by geometry-specific body-forces. Zbl 1349.76069
Yazdani, Alireza; Deng, Mingge; Caswell, Bruce; Karniadakis, George Em
2016
Fractional spectral collocation methods for linear and nonlinear variable order FPDEs. Zbl 1349.65531
2015
Second-order approximations for variable order fractional derivatives: algorithms and applications. Zbl 1349.65092
Zhao, Xuan; Sun, Zhi-zhong; Karniadakis, George Em
2015
A unified Petrov-Galerkin spectral method for fractional PDEs. Zbl 1425.65127
Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em.
2015
A generalized spectral collocation method with tunable accuracy for variable-order fractional differential equations. Zbl 1339.65197
Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em
2015
Tempered fractional Sturm-Liouville eigenproblems. Zbl 1323.34012
Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em
2015
Optimal error estimates of spectral Petrov-Galerkin and collocation methods for initial value problems of fractional differential equations. Zbl 1326.65100
Zhang, Zhongqiang; Zeng, Fanhai; Karniadakis, George Em
2015
Time-splitting schemes for fractional differential equations I: Smooth solutions. Zbl 1320.65106
Cao, Wanrong; Zhang, Zhongqiang; Karniadakis, George Em
2015
Special issue on “Fractional PDEs: theory, numerics, and applications”. Zbl 1349.35004
2015
Numerical methods for stochastic delay differential equations via the Wong-Zakai approximation. Zbl 1329.60233
Cao, Wanrong; Zhang, Zhongqiang; Karniadakis, George Em
2015
Multi-resolution flow simulations by smoothed particle hydrodynamics via domain decomposition. Zbl 1349.76663
Bian, Xin; Li, Zhen; Karniadakis, George Em
2015
Numerical methods for SPDEs with tempered stable processes. Zbl 1320.65020
2015
Algorithms for propagating uncertainty across heterogeneous domains. Zbl 1347.60093
Cho, H.; Yang, X.; Venturi, D.; Karniadakis, G. E.
2015
Adaptive multi-element polynomial chaos with discrete measure: algorithms and application to SPDEs. Zbl 1326.65140
Zheng, Mengdi; Wan, Xiaoliang; Karniadakis, George Em
2015
Multiscale universal interface: a concurrent framework for coupling heterogeneous solvers. Zbl 1349.76738
Tang, Yu-Hang; Kudo, Shuhei; Bian, Xin; Li, Zhen; Karniadakis, George Em
2015
Wiener chaos versus stochastic collocation methods for linear advection-diffusion-reaction equations with multiplicative white noise. Zbl 1327.60133
Zhang, Zhongqiang; Tretyakov, Michael V.; Rozovskii, Boris; Karniadakis, George E.
2015
Adaptive Wick-Malliavin approximation to nonlinear SPDEs with discrete random variables. Zbl 1326.60099
Zheng, Mengdi; Rozovsky, Boris; Karniadakis, George E.
2015
U-shaped fairings suppress vortex-induced vibrations for cylinders in cross-flow. Zbl 1381.76141
Xie, Fangfang; Yu, Yue; Constantinides, Yiannis; Triantafyllou, Michael S.; Karniadakis, George Em
2015
Brownian motion of a Rayleigh particle confined in a channel: a generalized Langevin equation approach. Zbl 1317.82043
2015
Quantification of sampling uncertainty for molecular dynamics simulation: time-dependent diffusion coefficient in simple fluids. Zbl 1349.76762
Kim, Changho; Borodin, Oleg; Karniadakis, George Em
2015
Fractional spectral collocation method. Zbl 1294.65097
2014
Exponentially accurate spectral and spectral element methods for fractional ODEs. Zbl 1349.65257
2014
Discontinuous spectral element methods for time- and space-fractional advection equations. Zbl 1304.35757
2014
A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains. Zbl 1349.76569
Dong, S.; Karniadakis, G. E.; Chryssostomidis, C.
2014
Spectral and discontinuous spectral element methods for fractional delay equations. Zbl 1314.34159
Zayernouri, Mohsen; Cao, Wanrong; Zhang, Zhongqiang; Karniadakis, George Em
2014
Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems. Zbl 1371.60119
2014
Energy-conserving dissipative particle dynamics with temperature-dependent properties. Zbl 1349.76709
Li, Zhen; Tang, Yu-Hang; Lei, Huan; Caswell, Bruce; Karniadakis, George Em
2014
On the equivalence of dynamically orthogonal and bi-orthogonal methods: theory and numerical simulations. Zbl 1349.65535
Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em
2014
Statistical analysis and simulation of random shocks in stochastic Burgers equation. Zbl 1371.76081
Cho, Heyrim; Venturi, Daniele; Karniadakis, George E.
2014
Probing red blood cell mechanics, rheology and dynamics with a two-component multi-scale model. Zbl 1353.92037
Li, Xuejin; Peng, Zhangli; Lei, Huan; Dao, Ming; Karniadakis, George Em
2014
A recursive sparse grid collocation method for differential equations with white noise. Zbl 1332.65015
Zhang, Z.; Tretyakov, M. V.; Rozovskii, B.; Karniadakis, G. E.
2014
Time correlation functions of Brownian motion and evaluation of friction coefficient in the near-Brownian-limit regime. Zbl 1327.82067
2014
A semi-local spectral/hp element solver for linear elasticity problems. Zbl 1352.74476
Yu, Yue; Bittencourt, Marco L.; Karniadakis, George Em.
2014
Fractional Sturm-Liouville eigen-problems: theory and numerical approximation. Zbl 1349.34095
2013
...and 154 more Documents
all top 5

#### Cited by 6,148 Authors

 167 Karniadakis, George Em 67 Sherwin, Spencer J. 39 Lin, Guang 36 Xiu, Dongbin 35 Wang, Hong 31 Thompson, Mark Christopher 27 Doostan, Alireza 25 Shen, Jie 24 Dehghan Takht Fooladi, Mehdi 23 Le Maître, Olivier P. 22 Narayan, Akil C. 21 Ghanem, Roger G. 21 Hourigan, Kerry 21 Venturi, Daniele 21 Zheng, Xiangcheng 20 Blackburn, Hugh M. 20 Schwab, Christoph 20 Zabaras, Nicholas J. 19 Kopriva, David Alan 18 Dumbser, Michael 18 Nobile, Fabio 18 Perdikaris, Paris G. 18 Rozza, Gianluigi 18 Shu, Chi-Wang 17 Jin, Shi 17 Lucor, Didier 17 Sagaut, Pierre 17 Zaky, Mahmoud A. 17 Zhou, Tao 16 Guo, Ben-Yu 16 Hesthaven, Jan S. 16 Noack, Bernd R. 16 Wang, Lilian 15 Abbaszadeh, Mostafa 15 Giraldo, Francis X. 15 Iaccarino, Gianluca 15 Mao, Zhiping 15 Wan, Xiaoliang 15 Warburton, Timothy 14 Baccouch, Mahboub 14 Jakeman, John Davis 14 Knio, Omar M. 14 Najm, Habib N. 14 Pasquetti, Richard 14 Quarteroni, Alfio M. 14 Tartakovsky, Daniel M. 14 Zeng, Fanhai 13 Ainsworth, Mark 13 Bourguet, Rémi 13 Dong, Suchuan 13 Elman, Howard C. 13 Jiang, Xiaoyun 13 Liu, Fawang 13 Machado, José António Tenreiro 13 Nordström, Jan 13 Pulch, Roland 13 Sheard, Gregory John 13 Xing, Yulong 13 Zayernouri, Mohsen 12 Boscheri, Walter 12 Congedo, Pietro Marco 12 Gerritsma, Marc I. 12 Matthies, Hermann Georg 12 Nouy, Anthony 12 Reddy, Junuthula Narasimha 12 Tartakovsky, Alexandre M. 12 Triantafyllou, Michael S. 12 Turner, Ian William 12 Zhang, Zhongqiang 11 Cheng, Liang 11 Dawson, Clint N. 11 Fischer, Paul F. 11 Gunzburger, Max D. 11 Guo, Ling 11 Leweke, Thomas 11 Li, Zhen 11 Luo, Hong 11 Maxey, Martin R. 11 Mishra, Siddhartha 11 Pavarino, Luca Franco 11 Soize, Christian 11 Stiller, Jörg 11 Xu, Chuanju 11 Yang, Xiu 11 Zhang, Dongxiao 11 Zhang, Zhimin 11 Zhang, Zhiwen 10 Bhrawy, Ali Hassan 10 Chan, Jesse 10 Deville, Michel O. 10 Ferrer, Esteban 10 Grigoriu, Mircea D. 10 Kronbichler, Martin 10 Li, Hong 10 Liu, Jianguo 10 Lo Jacono, David 10 Marzouk, Youssef M. 10 Peiró, Joaquim 10 Qiu, Jingmei 10 Raissi, Maziar ...and 6,048 more Authors
all top 5

#### Cited in 299 Serials

 834 Journal of Computational Physics 351 Computer Methods in Applied Mechanics and Engineering 260 Journal of Fluid Mechanics 260 Journal of Scientific Computing 241 Computers and Fluids 136 SIAM Journal on Scientific Computing 127 Physics of Fluids 110 Applied Numerical Mathematics 101 Computers & Mathematics with Applications 95 Journal of Computational and Applied Mathematics 76 International Journal for Numerical Methods in Engineering 71 Applied Mathematics and Computation 65 International Journal for Numerical Methods in Fluids 65 SIAM/ASA Journal on Uncertainty Quantification 59 Applied Mathematical Modelling 51 Mathematics of Computation 46 European Journal of Mechanics. B. Fluids 34 Numerical Algorithms 33 Mathematics and Computers in Simulation 33 Computational Mechanics 31 SIAM Journal on Numerical Analysis 28 Numerische Mathematik 27 Advances in Computational Mathematics 27 Computational Geosciences 26 International Journal of Heat and Mass Transfer 26 Communications in Nonlinear Science and Numerical Simulation 25 Computational and Applied Mathematics 25 Mathematical Problems in Engineering 22 Fractional Calculus & Applied Analysis 21 Engineering Analysis with Boundary Elements 20 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 19 Nonlinear Dynamics 18 Journal of Mathematical Analysis and Applications 18 International Journal of Computer Mathematics 17 Journal of Engineering Mathematics 17 Archives of Computational Methods in Engineering 16 Multiscale Modeling & Simulation 15 Physica D 15 Advances in Difference Equations 13 Journal of Statistical Physics 13 International Journal of Computational Methods 12 Chaos, Solitons and Fractals 12 Numerical Methods for Partial Differential Equations 12 Applied Mathematics Letters 12 International Journal of Computational Fluid Dynamics 11 Theoretical and Computational Fluid Dynamics 11 Mathematical and Computer Modelling 10 Computer Physics Communications 10 BIT 9 Acta Mechanica 9 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 9 Mathematical Modelling of Natural Phenomena 8 Automatica 8 Chaos 8 European Journal of Mechanics. A. Solids 8 Journal of Turbulence 8 Journal of Computational Acoustics 8 Acta Mechanica Sinica 8 Advances in Applied Mathematics and Mechanics 8 Journal of Theoretical Biology 8 AMM. Applied Mathematics and Mechanics. (English Edition) 7 Meccanica 7 International Journal of Numerical Methods for Heat & Fluid Flow 7 Communications on Applied Mathematics and Computation 6 Journal of Mathematical Physics 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 SIAM Review 6 Continuum Mechanics and Thermodynamics 6 Abstract and Applied Analysis 6 Computational Methods in Applied Mathematics 6 SIAM Journal on Applied Dynamical Systems 6 Acta Numerica 6 Communications in Applied and Industrial Mathematics 6 Stochastic and Partial Differential Equations. Analysis and Computations 6 East Asian Journal on Applied Mathematics 6 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 6 Results in Applied Mathematics 5 Mathematical Methods in the Applied Sciences 5 SIAM Journal on Control and Optimization 5 Applied Mathematics and Mechanics. (English Edition) 5 Journal of Non-Newtonian Fluid Mechanics 5 Archive of Applied Mechanics 5 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 5 Flow, Turbulence and Combustion 5 Foundations of Computational Mathematics 5 Discrete and Continuous Dynamical Systems. Series B 5 Journal of Numerical Mathematics 5 Journal of Applied Mathematics and Computing 5 Structural and Multidisciplinary Optimization 5 Research in the Mathematical Sciences 5 International Journal of Applied and Computational Mathematics 4 Inverse Problems 4 Journal of Mathematical Biology 4 Calcolo 4 Computing 4 Chinese Annals of Mathematics. Series B 4 SIAM Journal on Matrix Analysis and Applications 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Communications in Numerical Methods in Engineering 4 Computing and Visualization in Science ...and 199 more Serials
all top 5

#### Cited in 45 Fields

 2,485 Numerical analysis (65-XX) 1,966 Fluid mechanics (76-XX) 1,196 Partial differential equations (35-XX) 423 Mechanics of deformable solids (74-XX) 408 Probability theory and stochastic processes (60-XX) 208 Ordinary differential equations (34-XX) 193 Statistics (62-XX) 174 Biology and other natural sciences (92-XX) 145 Real functions (26-XX) 131 Computer science (68-XX) 119 Statistical mechanics, structure of matter (82-XX) 111 Classical thermodynamics, heat transfer (80-XX) 99 Dynamical systems and ergodic theory (37-XX) 99 Approximations and expansions (41-XX) 91 Optics, electromagnetic theory (78-XX) 90 Systems theory; control (93-XX) 84 Geophysics (86-XX) 60 Calculus of variations and optimal control; optimization (49-XX) 51 Special functions (33-XX) 49 Integral equations (45-XX) 45 Operations research, mathematical programming (90-XX) 33 Mechanics of particles and systems (70-XX) 29 Information and communication theory, circuits (94-XX) 24 Linear and multilinear algebra; matrix theory (15-XX) 24 Harmonic analysis on Euclidean spaces (42-XX) 24 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 19 Operator theory (47-XX) 12 Functional analysis (46-XX) 12 Quantum theory (81-XX) 11 Global analysis, analysis on manifolds (58-XX) 9 General and overarching topics; collections (00-XX) 9 Integral transforms, operational calculus (44-XX) 8 Difference and functional equations (39-XX) 5 Functions of a complex variable (30-XX) 4 Number theory (11-XX) 4 Astronomy and astrophysics (85-XX) 3 Differential geometry (53-XX) 2 History and biography (01-XX) 2 Combinatorics (05-XX) 2 Measure and integration (28-XX) 2 Relativity and gravitational theory (83-XX) 1 Mathematical logic and foundations (03-XX) 1 Potential theory (31-XX) 1 Convex and discrete geometry (52-XX) 1 Mathematics education (97-XX)

#### Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.