## Cai, Wei

Compute Distance To:
 Author ID: cai.wei Published as: Cai, Wei; Cai, W. External Links: ORCID
 Documents Indexed: 127 Publications since 1986, including 6 Books Co-Authors: 122 Co-Authors with 113 Joint Publications 3,294 Co-Co-Authors
all top 5

### Co-Authors

 9 single-authored 11 Cho, Minhyung 8 Deng, Shaozhong 7 Xu, Zhenli 6 Chen, Duan 6 Ji, Xia 6 Lu, Tiao 6 Xin, Jianguo 5 Karniadakis, George Em 5 Shao, Sihong 5 Wang, Bo 5 Zhang, Pingwen 5 Zhang, Wenzhong 4 Jiang, Haiyan 4 Weinberger, Christopher R. 3 Barnett, David M. 3 Bulatov, Vasily V. 3 Chen, Wen 3 Gottlieb, David I. 3 Jacobs, Donald J. 3 Shu, Chi-Wang 3 Tang, Huazhong 3 Zeng, Xuan 3 Zhang, Wu 3 Zinser, Brian F. 2 Fan, Kai 2 Guo, Nailong 2 Lax, Melvin J. 2 Lin, Huimin 2 Pang, Guofei 2 Song, Fangying 2 Tadi, Mohsen 2 Wang, Fajie 2 Xu, Min 2 Zheng, Bin 2 Zhou, Dian 2 Zhou, Yijing 1 Ainsworth, Mark 1 Arsenlis, Athanasios 1 Baker, Katherine 1 Baumketner, Andrij 1 Cash, William D. 1 Chai, Chunhong 1 Chen, Dangxing 1 Chen, Zhenzhu 1 Cheng, Xiaolin 1 Deo, C. S. 1 Elsen, Erich 1 Fan, Jiajie 1 Fan, Ying 1 Fong, William 1 Galli, Giulia A. 1 Glusa, Christian 1 Guan, Guoyu 1 Gulian, Mamikon 1 Guo, Xiaofeng 1 Guo, Yinglong 1 Harten, Ami 1 He, Liping 1 Her, Tsing-Hua 1 Hsu, Elton P. 1 Hu, Jun 1 Hu, Xiaozhe 1 Huang, Jingfang 1 Jia, Wei 1 Jin, Chengming 1 Klibanov, Michael V. 1 Kuykendall, William P. 1 Lee, Eunseok 1 Lee, Hyung-Chun 1 Lee, Youngpak 1 Li, Keqiang 1 Li, Shanqing 1 Li, Xiaoguang 1 Li, Zhilin 1 Liang, Yingjie 1 Lin, Huiqiu 1 Lischke, Anna 1 Liu, Hailong 1 Liu, Lizuo 1 Liu, Zhengxing 1 Liu, Ziqi 1 Lu, Yuehui 1 Mao, Zhiping 1 Meerschaert, Mark Marvin 1 Nix, William D. 1 Oh, Wonho 1 Pan, Rui 1 Patten, William Neff 1 Perdikaris, Paris G. 1 Qin, Peihua 1 Retz, Caylah 1 Sills, R. B. 1 Singham, Dashi I. 1 Srolovitz, David J. 1 Su, Yangfeng 1 Sun, Jiguang 1 Tan, Zheng 1 Tsantili, Ivi C. 1 Tsu, Raphael 1 Wang, Hansheng ...and 26 more Co-Authors
all top 5

### Serials

 29 Journal of Computational Physics 16 Communications in Computational Physics 7 Journal of Scientific Computing 6 Journal of the Mechanics and Physics of Solids 6 SIAM Journal on Scientific Computing 3 Computers & Mathematics with Applications 3 Computer Physics Communications 3 SIAM Journal on Numerical Analysis 3 Journal of Computational Mathematics 2 International Journal for Numerical Methods in Engineering 2 Mathematica Numerica Sinica 2 Mathematics in Practice and Theory 2 Journal of Beijing Normal University. Natural Science 2 IEEE Transactions on Circuits and Systems. I: Fundamental Theory and Applications 2 Mathematics and Mechanics of Solids 1 AIAA Journal 1 Computer Methods in Applied Mechanics and Engineering 1 Inverse Problems 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Mathematics of Computation 1 Ars Combinatoria 1 International Journal of Circuit Theory and Applications 1 Journal of Computational and Applied Mathematics 1 Journal of Shanghai Jiaotong University (Chinese Edition) 1 Journal of Xinjiang University. Natural Science 1 Applied Mathematical Modelling 1 European Journal of Operational Research 1 Journal of Dynamic Systems, Measurement and Control 1 SIAM Review 1 Computational Statistics and Data Analysis 1 Fractals 1 Advances in Computational Mathematics 1 Engineering Analysis with Boundary Elements 1 European Journal of Mechanics. A. Solids 1 Discrete and Continuous Dynamical Systems. Series B 1 Communications in Mathematical Sciences 1 ANACM. Applied Numerical Analysis and Computational Mathematics 1 International Journal of Numerical Analysis and Modeling 1 Pure and Applied Mathematics Quarterly 1 Numerical Mathematics: Theory, Methods and Applications 1 Advances in Mathematical Physics 1 Science China. Mathematics 1 Communications in Mathematics and Statistics 1 Fractional Calculus in Applied Sciences and Engineering 1 Oxford Finance Series
all top 5

### Fields

 67 Numerical analysis (65-XX) 43 Optics, electromagnetic theory (78-XX) 34 Partial differential equations (35-XX) 18 Mechanics of deformable solids (74-XX) 13 Quantum theory (81-XX) 11 Fluid mechanics (76-XX) 11 Statistical mechanics, structure of matter (82-XX) 11 Biology and other natural sciences (92-XX) 7 Probability theory and stochastic processes (60-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Computer science (68-XX) 4 Information and communication theory, circuits (94-XX) 3 Real functions (26-XX) 3 Ordinary differential equations (34-XX) 3 Integral equations (45-XX) 3 Statistics (62-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Operations research, mathematical programming (90-XX) 2 Systems theory; control (93-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Operator theory (47-XX) 1 Convex and discrete geometry (52-XX) 1 Mechanics of particles and systems (70-XX) 1 Geophysics (86-XX)

### Citations contained in zbMATH Open

98 Publications have been cited 706 times in 549 Documents Cited by Year
Discontinuous Galerkin methods for dispersive and lossy Maxwell’s equations and PML boundary conditions. Zbl 1115.78330
Lu, Tiao; Zhang, Pingwen; Cai, Wei
2004
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
Adaptive multiresolution collocation methods for initial boundary value problems of nonlinear PDEs. Zbl 0856.65115
Cai, Wei; Wang, Jianzhong
1996
Essentially nonoscillatory spectral Fourier methods for shock wave calculations. Zbl 0666.65067
Cai, Wei; Gottlieb, David; Shu, Chi-Wang
1989
A non-singular continuum theory of dislocations. Zbl 1120.74329
Cai, Wei; Arsenlis, Athanasios; Weinberger, Christopher R.; Bulatov, Vasily V.
2006
An upwinding embedded boundary method for Maxwell’s equations in media with material interfaces: 2D case. Zbl 1031.78005
Cai, Wei; Deng, Shaozhong
2003
Computational methods for electromagnetic phenomena. Electrostatics in solvation, scattering, and electron transport. Zbl 06136469
Cai, Wei
2013
Computer simulations of dislocations. Zbl 1119.74001
Bulatov, Vasily V.; Cai, Wei
2006
Adaptive conservative cell average spectral element methods for transient Wigner equation in quantum transport. Zbl 1364.65211
Shao, Sihong; Lu, Tiao; Cai, Wei
2011
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
An inversion method for parabolic equations based on quasireversibility. Zbl 1050.65089
Tadi, M.; Klibanov, M. V.; Cai, Wei
2002
Adaptive finite element method for fractional differential equations using hierarchical matrices. Zbl 1439.65091
Zhao, Xuan; Hu, Xiaozhe; Cai, Wei; Karniadakis, George Em
2017
Extending the fast multipole method to charges inside or outside a dielectric sphere. Zbl 1183.78038
Cai, Wei; Deng, Shaozhong; Jacobs, Donald
2007
Fast calculations of dyadic Green’s functions for electromagnetic scattering in a multilayered medium. Zbl 1040.78015
Cai, Wei; Yu, Tiejun
2000
A parallel fast algorithm for computing the Helmholtz integral operator in 3-D layered media. Zbl 1277.35143
Cho, Min Hyung; Cai, Wei
2012
High-order DGTD methods for dispersive Maxwell’s equations and modelling of silver nanowire coupling. Zbl 1194.78055
Ji, Xia; Cai, Wei; Zhang, Pingwen
2007
Non-Euclidean distance fundamental solution of Hausdorff derivative partial differential equations. Zbl 1403.65252
Chen, Wen; Wang, Fajie; Zheng, Bin; Cai, Wei
2017
Algorithmic issues for electromagnetic scattering in layered media: Green’s functions, current basis, and fast solver. Zbl 0992.78035
Cai, Wei
2002
Cai, Wei; Zhang, Wu
1998
A Fourier spectral-discontinuous Galerkin method for time-dependent 3-D Schrödinger-Poisson equations with discontinuous potentials. Zbl 1146.65072
Lu, Tiao; Cai, Wei
2008
On one-sided filters for spectral Fourier approximations of discontinuous functions. Zbl 0755.65140
Cai, Wei; Gottlieb, David; Shu, Chi-Wang
1992
Conservative local discontinuous Galerkin methods for time dependent Schrödinger equation. Zbl 1070.65096
Lu, Tiao; Cai, Wei; Zhang, Pingwen
2005
Fast analytical methods for macroscopic electrostatic models in biomolecular simulations. Zbl 1228.92008
Xu, Zhenli; Cai, Wei
2011
Boundary treatments in non-equilibrium Green’s function (NEGF) methods for quantum transport in nano-MOSFETs. Zbl 1151.82395
Jiang, Haiyan; Shao, Sihong; Cai, Wei; Zhang, Pingwen
2008
Divergence-free $$\mathbf{\mathcal{H}}(\mathbf{div})$$-conforming hierarchical bases for magnetohydrodynamics (MHD). Zbl 1311.76048
Cai, Wei; Wu, Jian; Xin, Jianguo
2013
Coupling of spectral methods and the $$p$$-version of the finite element method for elliptic boundary value problems containing singularities. Zbl 0790.65093
Cai, W.; Lee, H. C.; Oh, H.-S.
1993
Analysis and application of an orthogonal nodal basis on triangles for discontinuous spectral element methods. Zbl 1114.78018
Deng, Shaozhong; Cai, Wei
2005
Torsion and bending periodic boundary conditions for modeling the intrinsic strength of nanowires. Zbl 1176.74020
Cai, Wei; Fong, William; Elsen, Erich; Weinberger, Christopher R.
2008
An adaptive wavelet method for nonlinear circuit simulation. Zbl 0963.94056
Zhou, Dian; Cai, Wei; Zhang, Wu
1999
Accurate and efficient Nyström volume integral equation method for the Maxwell equations for multiple 3-D scatterers. Zbl 1349.78110
Chen, Duan; Cai, Wei; Zinser, Brian; Cho, Min Hyung
2016
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
A wideband fast multipole method for the two-dimensional complex Helmholtz equation. Zbl 1219.65140
Cho, Min Hyung; Cai, Wei
2010
A heterogeneous FMM for layered media Helmholtz equation. I: Two layers in $$\mathbb{R}^2$$. Zbl 1392.78018
Cho, Min Hyung; Huang, Jingfang; Chen, Dangxing; Cai, Wei
2018
A phase shift deep neural network for high frequency approximation and wave problems. Zbl 1455.35246
Cai, Wei; Li, Xiaoguang; Liu, Lizuo
2020
Image charge method for reaction fields in a hybrid ion-channel model. Zbl 1365.92015
Xu, Zhenli; Cai, Wei; Cheng, Xiaolin
2011
A parallel method for solving Laplace equations with Dirichlet data using local boundary integral equations and random walks. Zbl 1362.65008
Yan, Chanhao; Cai, Wei; Zeng, Xuan
2013
Uniform high-order spectral methods for one- and two-dimensional Euler equations. Zbl 0766.76069
Cai, Wei; Shu, Chi-Wang
1993
High-order hybrid numerical simulations of two-dimensional detonation waves. Zbl 0844.76070
Cai, Wei
1995
Effect of boundary treatments on quantum transport current in the Green’s function and Wigner distribution methods for a nano-scale DG-MOSFET. Zbl 1191.82042
Jiang, Haiyan; Cai, Wei
2010
Extending the fast multipole method for charges inside a dielectric sphere in an ionic solvent: high-order image approximations for reaction fields. Zbl 1143.78011
Deng, Shaozhong; Cai, Wei
2007
Cell averaging Chebyshev methods for hyperbolic problems. Zbl 0764.65056
Cai, Wei; Gottlieb, David; Harten, Ami
1992
A generalized discontinuous Galerkin (GDG) method for Schrödinger equations with nonsmooth solutions. Zbl 1135.65374
Fan, Kai; Cai, Wei; Ji, Xia
2008
On the construction of well-conditioned hierarchical bases for $$\mathcal H(\mathrm{div})$$-conforming $$\mathbb R^n$$ simplicial elements. Zbl 1388.65161
Xin, Jianguo; Cai, Wei; Guo, Nailong
2013
Accurate and efficient Nyström volume integral equation method for electromagnetic scattering of 3-D metamaterials in layered media. Zbl 1387.78012
Chen, Duan; Cho, Min Hyung; Cai, Wei
2018
Accuracy of the Frensley inflow boundary condition for Wigner equations in simulating resonant tunneling diodes. Zbl 1210.82067
Jiang, Haiyan; Cai, Wei; Tsu, Raphael
2011
Multi-scale deep neural network (MscaleDNN) for solving Poisson-Boltzmann equation in complex domains. Zbl 1473.65348
Liu, Ziqi; Cai, Wei; Xu, Zhi-Qin John
2020
Efficient and accurate computation of electric field dyadic Green’s function in layered media. Zbl 1372.78024
Cho, Min Hyung; Cai, Wei
2017
Singularity treatment and high-order RWG basis functions for integral equations of electromagnetic scattering. Zbl 1112.78316
Cai, W.; Yu, Yijun; Yuan, X. C.
2002
Computing image stress in an elastic cylinder. Zbl 1170.74010
Weinberger, Christopher R.; Cai, Wei
2007
Accurate calculation of Green’s function of the Schrödinger equation in a block layered potential. Zbl 1101.81055
Shao, Sihong; Cai, Wei; Tang, Huazhong
2006
A fast wavelet collocation method for high-speed circuit simulation. Zbl 0963.94055
Zhou, Dian; Cai, Wei
1999
A device adaptive inflow boundary condition for Wigner equations of quantum transport. Zbl 1349.81061
Jiang, Haiyan; Lu, Tiao; Cai, Wei
2014
Image charge methods for a three-dielectric-layer hybrid solvation model of biomolecules. Zbl 1365.92005
Qin, Peihua; Xu, Zhenli; Cai, Wei; Jacobs, Donald
2009
Energy of a prismatic dislocation loop in an elastic cylinder. Zbl 1257.74015
Cai, Wei; Weinberger, Christopher R.
2009
Image approximations to electrostatic potentials in layered electrolytes/dielectrics and an ion-channel model. Zbl 1282.78034
Lin, Huimin; Xu, Zhenli; Tang, Huazhong; Cai, Wei
2012
A full vectorial generalized discontinuous Galerkin beam propagation method (GDG-BPM) for nonsmooth electromagnetic fields in waveguides. Zbl 1154.65093
Fan, Kai; Cai, Wei; Ji, Xia
2008
Interactions of delta shock waves for zero-pressure gas dynamics with energy conservation law. Zbl 1347.35165
Cai, Wei; Zhang, Yanyan
2016
High order hierarchical divergence-free constrained transport $$H\left({div} \right)$$ finite element method for magnetic induction equation. Zbl 1399.65243
Cai, Wei; Hu, Jun; Zhang, Shangyou
2017
A principal-agent problem with heterogeneous demand distributions for a carbon capture and storage system. Zbl 1380.91094
Cai, W.; Singham, D. I.
2018
Multi-scale deep neural network (MscaleDNN) methods for oscillatory Stokes flows in complex domains. Zbl 1473.35541
Wang, Bo; Zhang, Wenzhong; Cai, Wei
2020
A well-conditioned hierarchical basis for triangular $$H(curl)$$-conforming elements. Zbl 1364.65257
Xin, Jianguo; Cai, Wei
2011
A high order efficient numerical method for 4-D Wigner equation of quantum double-slit interferences. Zbl 1452.65270
Chen, Zhenzhu; Shao, Sihong; Cai, Wei
2019
Convergence of two nonconforming membrane finite elements. Zbl 0636.73064
Cai, Wei
1986
Random processes in physics and finance. Zbl 1111.60002
Lax, Melvin; Cai, Wei; Xu, Min
2006
A boundary integral equation method for photonic crystal fibers. Zbl 1158.78306
Cho, Min Hyung; Cai, Wei; Her, Tsing-Hua
2006
Image charge approximations of reaction fields in solvents with arbitrary ionic strength. Zbl 1160.78320
Xu, Zhenli; Deng, Shaozhong; Cai, Wei
2009
High-order mixed current basis functions for electromagnetic scattering of curved surfaces. Zbl 0972.78007
Cai, Wei
1999
Numerical solution of the Robin problem of Laplace equations with a Feynman-Kac formula and reflecting Brownian motions. Zbl 1352.65021
Zhou, Yijing; Cai, Wei
2016
Hausdorff calculus. Applications to fractal systems. Zbl 1414.28002
Liang, Yingjie; Chen, Wen; Cai, Wei
2019
Linear scaling discontinuous Galerkin density matrix minimization method with local orbital enriched finite element basis: 1-D lattice model system. Zbl 1373.81010
Lu, Tiao; Cai, Wei; Xin, Jianguo; Guo, Yinglong
2013
Quadrature weights on tensor-product nodes for accurate integration of hypersingular functions over some simple 3-D geometric shapes. Zbl 1388.65026
Zinser, Brian; Cai, Wei; Chen, Duan
2016
Computation of the local time of reflecting Brownian motion and the probabilistic representation of the Neumann problem. Zbl 1358.65005
Zhou, Yijing; Cai, Wei; Hsu, Elton
2017
Fast integral equation solver for Maxwell’s equations in layered media with FMM for Bessel functions. Zbl 1306.78010
Cho, Min Hyung; Cai, Wei
2013
Network linear discriminant analysis. Zbl 1469.62028
Cai, Wei; Guan, Guoyu; Pan, Rui; Zhu, Xuening; Wang, Hansheng
2018
Vertical impedance of a tapered pile in inhomogeneous saturated soil described by fractional viscoelastic model. Zbl 1481.74548
Wang, Jue; Zhou, Ding; Zhang, Yuquan; Cai, Wei
2019
Exponential convergence for multipole and local expansions and their translations for sources in layered media: two-dimensional acoustic wave. Zbl 1459.76119
Zhang, Wenzhong; Wang, Bo; Cai, Wei
2020
An $$O(N \log N)$$ hierarchical random compression method for kernel matrices by sampling partial matrix entries. Zbl 1453.65089
Chen, Duan; Cai, Wei
2019
Taylor expansion based fast multipole method for 3-d Helmholtz equations in layered media. Zbl 1453.78013
Wang, Bo; Chen, Duan; Zhang, Bo; Zhang, Wenzhong; Cho, Min Hyung; Cai, Wei
2020
Pulse coupled neural network based image fusion. Zbl 1084.68671
Li, Min; Cai, Wei; Tan, Zheng
2005
The limite problems for Zienkiewicz triangle elements. Zbl 0622.73075
Cai, Wei
1986
The temperature-dependent fractional evolutional model for sintered nanoscale silver films. Zbl 1486.74101
Wang, Ping; Cai, Wei; Fan, Jiajie
2021
Electromechanical coupled finite element and dynamic equations. Zbl 0913.73068
Liu, Zhengxing; Yang, Yaowen; Cai, Wei; Li, Shanqing
1997
Well-conditioned orthonormal hierarchical $$\mathcal{L}_{2}$$ bases on $$\mathbb R^{n }$$ simplicial elements. Zbl 1242.65245
Xin, Jianguo; Cai, Wei
2012
On the construction of well-conditioned hierarchical bases for tetrahedral $${\mathcal H}$$(curl)-conforming Nédélec elements. Zbl 1249.65255
Xin, Jianguo; Guo, Nailong; Cai, Wei
2011
Computer simulations of dislocations. Reprint of the 2006 hardback ed. Zbl 1268.74001
Bulatov, Vasily V.; Cai, Wei
2013
FIFA-fast interpolation and filtering algorithm for calculating dyadic Green’s function in the electromagnetic scattering of multi-layered structures. Zbl 1114.78361
Yu, T.; Cai, W.
2006
A comparable study of image approximations to the reaction field. Zbl 1196.78010
Deng, Shaozhong; Cai, Wei; Jacobs, Donald
2007
A Schwarz generalized eigen-oscillation spectral element method (GeSEM) for 2-D high frequency electromagnetic scattering in dispersive inhomogeneous media. Zbl 1155.78003
Cai, Wei; Ji, Xia; Sun, Jiguang; Shao, Sihong
2008
Reflection/transmission characteristics of a discontinuous Galerkin method for Maxwell’s equations in dispersive inhomogeneous media. Zbl 1174.78003
Ji, Xia; Cai, Wei; Zhang, Pingwen
2008
Direct numerical calculations of a neutral stability curve for one-dimensional detonations. Zbl 0855.76029
Cai, Wei; Oh, Wonho; Zhu, Youlan
1996
Fast multipole method for 3-D Helmholtz equation in layered media. Zbl 1433.78027
Wang, Bo; Zhang, Wenzhong; Cai, Wei
2019
Modeling a distribution of point defects as misfitting inclusions in stressed solids. Zbl 1323.82051
Cai, W.; Sills, R. B.; Barnett, D. M.; Nix, W. D.
2014
Accuracy and efficiency in computing electrostatic potential for an ion channel model in layered dielectric/electrolyte media. Zbl 1349.76922
Lin, Huimin; Tang, Huazhong; Cai, Wei
2014
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
Investigating the selectivity of KcsA channel by an image charge solvation method (ICSM) in molecular dynamics simulations. Zbl 1373.94035
Baker, Katherine; Chen, Duan; Cai, Wei
2016
On cyclic edge connectivity of regular graphs with two orbits. Zbl 1349.05196
Yang, Weihua; Lin, Huiqiu; Cai, Wei; Guo, Xiaofeng
2015
Inverse matrix evaluation for linear systems. Zbl 0990.34013
2001
Derivation and numerical validation of the fundamental solutions for constant and variable-order structural derivative advection-dispersion models. Zbl 1462.35447
Wang, Fajie; Cai, Wei; Zheng, Bin; Wang, Chao
2020
The temperature-dependent fractional evolutional model for sintered nanoscale silver films. Zbl 1486.74101
Wang, Ping; Cai, Wei; Fan, Jiajie
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
A phase shift deep neural network for high frequency approximation and wave problems. Zbl 1455.35246
Cai, Wei; Li, Xiaoguang; Liu, Lizuo
2020
Multi-scale deep neural network (MscaleDNN) for solving Poisson-Boltzmann equation in complex domains. Zbl 1473.65348
Liu, Ziqi; Cai, Wei; Xu, Zhi-Qin John
2020
Multi-scale deep neural network (MscaleDNN) methods for oscillatory Stokes flows in complex domains. Zbl 1473.35541
Wang, Bo; Zhang, Wenzhong; Cai, Wei
2020
Exponential convergence for multipole and local expansions and their translations for sources in layered media: two-dimensional acoustic wave. Zbl 1459.76119
Zhang, Wenzhong; Wang, Bo; Cai, Wei
2020
Taylor expansion based fast multipole method for 3-d Helmholtz equations in layered media. Zbl 1453.78013
Wang, Bo; Chen, Duan; Zhang, Bo; Zhang, Wenzhong; Cho, Min Hyung; Cai, Wei
2020
Derivation and numerical validation of the fundamental solutions for constant and variable-order structural derivative advection-dispersion models. Zbl 1462.35447
Wang, Fajie; Cai, Wei; Zheng, Bin; Wang, Chao
2020
A high order efficient numerical method for 4-D Wigner equation of quantum double-slit interferences. Zbl 1452.65270
Chen, Zhenzhu; Shao, Sihong; Cai, Wei
2019
Hausdorff calculus. Applications to fractal systems. Zbl 1414.28002
Liang, Yingjie; Chen, Wen; Cai, Wei
2019
Vertical impedance of a tapered pile in inhomogeneous saturated soil described by fractional viscoelastic model. Zbl 1481.74548
Wang, Jue; Zhou, Ding; Zhang, Yuquan; Cai, Wei
2019
An $$O(N \log N)$$ hierarchical random compression method for kernel matrices by sampling partial matrix entries. Zbl 1453.65089
Chen, Duan; Cai, Wei
2019
Fast multipole method for 3-D Helmholtz equation in layered media. Zbl 1433.78027
Wang, Bo; Zhang, Wenzhong; Cai, Wei
2019
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
A heterogeneous FMM for layered media Helmholtz equation. I: Two layers in $$\mathbb{R}^2$$. Zbl 1392.78018
Cho, Min Hyung; Huang, Jingfang; Chen, Dangxing; Cai, Wei
2018
Accurate and efficient Nyström volume integral equation method for electromagnetic scattering of 3-D metamaterials in layered media. Zbl 1387.78012
Chen, Duan; Cho, Min Hyung; Cai, Wei
2018
A principal-agent problem with heterogeneous demand distributions for a carbon capture and storage system. Zbl 1380.91094
Cai, W.; Singham, D. I.
2018
Network linear discriminant analysis. Zbl 1469.62028
Cai, Wei; Guan, Guoyu; Pan, Rui; Zhu, Xuening; Wang, Hansheng
2018
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
Adaptive finite element method for fractional differential equations using hierarchical matrices. Zbl 1439.65091
Zhao, Xuan; Hu, Xiaozhe; Cai, Wei; Karniadakis, George Em
2017
Non-Euclidean distance fundamental solution of Hausdorff derivative partial differential equations. Zbl 1403.65252
Chen, Wen; Wang, Fajie; Zheng, Bin; Cai, Wei
2017
Efficient and accurate computation of electric field dyadic Green’s function in layered media. Zbl 1372.78024
Cho, Min Hyung; Cai, Wei
2017
High order hierarchical divergence-free constrained transport $$H\left({div} \right)$$ finite element method for magnetic induction equation. Zbl 1399.65243
Cai, Wei; Hu, Jun; Zhang, Shangyou
2017
Computation of the local time of reflecting Brownian motion and the probabilistic representation of the Neumann problem. Zbl 1358.65005
Zhou, Yijing; Cai, Wei; Hsu, Elton
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
Accurate and efficient Nyström volume integral equation method for the Maxwell equations for multiple 3-D scatterers. Zbl 1349.78110
Chen, Duan; Cai, Wei; Zinser, Brian; Cho, Min Hyung
2016
Interactions of delta shock waves for zero-pressure gas dynamics with energy conservation law. Zbl 1347.35165
Cai, Wei; Zhang, Yanyan
2016
Numerical solution of the Robin problem of Laplace equations with a Feynman-Kac formula and reflecting Brownian motions. Zbl 1352.65021
Zhou, Yijing; Cai, Wei
2016
Quadrature weights on tensor-product nodes for accurate integration of hypersingular functions over some simple 3-D geometric shapes. Zbl 1388.65026
Zinser, Brian; Cai, Wei; Chen, Duan
2016
Investigating the selectivity of KcsA channel by an image charge solvation method (ICSM) in molecular dynamics simulations. Zbl 1373.94035
Baker, Katherine; Chen, Duan; Cai, Wei
2016
On cyclic edge connectivity of regular graphs with two orbits. Zbl 1349.05196
Yang, Weihua; Lin, Huiqiu; Cai, Wei; Guo, Xiaofeng
2015
A device adaptive inflow boundary condition for Wigner equations of quantum transport. Zbl 1349.81061
Jiang, Haiyan; Lu, Tiao; Cai, Wei
2014
Modeling a distribution of point defects as misfitting inclusions in stressed solids. Zbl 1323.82051
Cai, W.; Sills, R. B.; Barnett, D. M.; Nix, W. D.
2014
Accuracy and efficiency in computing electrostatic potential for an ion channel model in layered dielectric/electrolyte media. Zbl 1349.76922
Lin, Huimin; Tang, Huazhong; Cai, Wei
2014
Computational methods for electromagnetic phenomena. Electrostatics in solvation, scattering, and electron transport. Zbl 06136469
Cai, Wei
2013
Divergence-free $$\mathbf{\mathcal{H}}(\mathbf{div})$$-conforming hierarchical bases for magnetohydrodynamics (MHD). Zbl 1311.76048
Cai, Wei; Wu, Jian; Xin, Jianguo
2013
A parallel method for solving Laplace equations with Dirichlet data using local boundary integral equations and random walks. Zbl 1362.65008
Yan, Chanhao; Cai, Wei; Zeng, Xuan
2013
On the construction of well-conditioned hierarchical bases for $$\mathcal H(\mathrm{div})$$-conforming $$\mathbb R^n$$ simplicial elements. Zbl 1388.65161
Xin, Jianguo; Cai, Wei; Guo, Nailong
2013
Linear scaling discontinuous Galerkin density matrix minimization method with local orbital enriched finite element basis: 1-D lattice model system. Zbl 1373.81010
Lu, Tiao; Cai, Wei; Xin, Jianguo; Guo, Yinglong
2013
Fast integral equation solver for Maxwell’s equations in layered media with FMM for Bessel functions. Zbl 1306.78010
Cho, Min Hyung; Cai, Wei
2013
Computer simulations of dislocations. Reprint of the 2006 hardback ed. Zbl 1268.74001
Bulatov, Vasily V.; Cai, Wei
2013
A parallel fast algorithm for computing the Helmholtz integral operator in 3-D layered media. Zbl 1277.35143
Cho, Min Hyung; Cai, Wei
2012
Image approximations to electrostatic potentials in layered electrolytes/dielectrics and an ion-channel model. Zbl 1282.78034
Lin, Huimin; Xu, Zhenli; Tang, Huazhong; Cai, Wei
2012
Well-conditioned orthonormal hierarchical $$\mathcal{L}_{2}$$ bases on $$\mathbb R^{n }$$ simplicial elements. Zbl 1242.65245
Xin, Jianguo; Cai, Wei
2012
Adaptive conservative cell average spectral element methods for transient Wigner equation in quantum transport. Zbl 1364.65211
Shao, Sihong; Lu, Tiao; Cai, Wei
2011
Fast analytical methods for macroscopic electrostatic models in biomolecular simulations. Zbl 1228.92008
Xu, Zhenli; Cai, Wei
2011
Image charge method for reaction fields in a hybrid ion-channel model. Zbl 1365.92015
Xu, Zhenli; Cai, Wei; Cheng, Xiaolin
2011
Accuracy of the Frensley inflow boundary condition for Wigner equations in simulating resonant tunneling diodes. Zbl 1210.82067
Jiang, Haiyan; Cai, Wei; Tsu, Raphael
2011
A well-conditioned hierarchical basis for triangular $$H(curl)$$-conforming elements. Zbl 1364.65257
Xin, Jianguo; Cai, Wei
2011
On the construction of well-conditioned hierarchical bases for tetrahedral $${\mathcal H}$$(curl)-conforming Nédélec elements. Zbl 1249.65255
Xin, Jianguo; Guo, Nailong; Cai, Wei
2011
A wideband fast multipole method for the two-dimensional complex Helmholtz equation. Zbl 1219.65140
Cho, Min Hyung; Cai, Wei
2010
Effect of boundary treatments on quantum transport current in the Green’s function and Wigner distribution methods for a nano-scale DG-MOSFET. Zbl 1191.82042
Jiang, Haiyan; Cai, Wei
2010
Image charge methods for a three-dielectric-layer hybrid solvation model of biomolecules. Zbl 1365.92005
Qin, Peihua; Xu, Zhenli; Cai, Wei; Jacobs, Donald
2009
Energy of a prismatic dislocation loop in an elastic cylinder. Zbl 1257.74015
Cai, Wei; Weinberger, Christopher R.
2009
Image charge approximations of reaction fields in solvents with arbitrary ionic strength. Zbl 1160.78320
Xu, Zhenli; Deng, Shaozhong; Cai, Wei
2009
A Fourier spectral-discontinuous Galerkin method for time-dependent 3-D Schrödinger-Poisson equations with discontinuous potentials. Zbl 1146.65072
Lu, Tiao; Cai, Wei
2008
Boundary treatments in non-equilibrium Green’s function (NEGF) methods for quantum transport in nano-MOSFETs. Zbl 1151.82395
Jiang, Haiyan; Shao, Sihong; Cai, Wei; Zhang, Pingwen
2008
Torsion and bending periodic boundary conditions for modeling the intrinsic strength of nanowires. Zbl 1176.74020
Cai, Wei; Fong, William; Elsen, Erich; Weinberger, Christopher R.
2008
A generalized discontinuous Galerkin (GDG) method for Schrödinger equations with nonsmooth solutions. Zbl 1135.65374
Fan, Kai; Cai, Wei; Ji, Xia
2008
A full vectorial generalized discontinuous Galerkin beam propagation method (GDG-BPM) for nonsmooth electromagnetic fields in waveguides. Zbl 1154.65093
Fan, Kai; Cai, Wei; Ji, Xia
2008
A Schwarz generalized eigen-oscillation spectral element method (GeSEM) for 2-D high frequency electromagnetic scattering in dispersive inhomogeneous media. Zbl 1155.78003
Cai, Wei; Ji, Xia; Sun, Jiguang; Shao, Sihong
2008
Reflection/transmission characteristics of a discontinuous Galerkin method for Maxwell’s equations in dispersive inhomogeneous media. Zbl 1174.78003
Ji, Xia; Cai, Wei; Zhang, Pingwen
2008
Extending the fast multipole method to charges inside or outside a dielectric sphere. Zbl 1183.78038
Cai, Wei; Deng, Shaozhong; Jacobs, Donald
2007
High-order DGTD methods for dispersive Maxwell’s equations and modelling of silver nanowire coupling. Zbl 1194.78055
Ji, Xia; Cai, Wei; Zhang, Pingwen
2007
Extending the fast multipole method for charges inside a dielectric sphere in an ionic solvent: high-order image approximations for reaction fields. Zbl 1143.78011
Deng, Shaozhong; Cai, Wei
2007
Computing image stress in an elastic cylinder. Zbl 1170.74010
Weinberger, Christopher R.; Cai, Wei
2007
A comparable study of image approximations to the reaction field. Zbl 1196.78010
Deng, Shaozhong; Cai, Wei; Jacobs, Donald
2007
A non-singular continuum theory of dislocations. Zbl 1120.74329
Cai, Wei; Arsenlis, Athanasios; Weinberger, Christopher R.; Bulatov, Vasily V.
2006
Computer simulations of dislocations. Zbl 1119.74001
Bulatov, Vasily V.; Cai, Wei
2006
Accurate calculation of Green’s function of the Schrödinger equation in a block layered potential. Zbl 1101.81055
Shao, Sihong; Cai, Wei; Tang, Huazhong
2006
Random processes in physics and finance. Zbl 1111.60002
Lax, Melvin; Cai, Wei; Xu, Min
2006
A boundary integral equation method for photonic crystal fibers. Zbl 1158.78306
Cho, Min Hyung; Cai, Wei; Her, Tsing-Hua
2006
FIFA-fast interpolation and filtering algorithm for calculating dyadic Green’s function in the electromagnetic scattering of multi-layered structures. Zbl 1114.78361
Yu, T.; Cai, W.
2006
Conservative local discontinuous Galerkin methods for time dependent Schrödinger equation. Zbl 1070.65096
Lu, Tiao; Cai, Wei; Zhang, Pingwen
2005
Analysis and application of an orthogonal nodal basis on triangles for discontinuous spectral element methods. Zbl 1114.78018
Deng, Shaozhong; Cai, Wei
2005
Pulse coupled neural network based image fusion. Zbl 1084.68671
Li, Min; Cai, Wei; Tan, Zheng
2005
Discontinuous Galerkin methods for dispersive and lossy Maxwell’s equations and PML boundary conditions. Zbl 1115.78330
Lu, Tiao; Zhang, Pingwen; Cai, Wei
2004
An upwinding embedded boundary method for Maxwell’s equations in media with material interfaces: 2D case. Zbl 1031.78005
Cai, Wei; Deng, Shaozhong
2003
An inversion method for parabolic equations based on quasireversibility. Zbl 1050.65089
Tadi, M.; Klibanov, M. V.; Cai, Wei
2002
Algorithmic issues for electromagnetic scattering in layered media: Green’s functions, current basis, and fast solver. Zbl 0992.78035
Cai, Wei
2002
Singularity treatment and high-order RWG basis functions for integral equations of electromagnetic scattering. Zbl 1112.78316
Cai, W.; Yu, Yijun; Yuan, X. C.
2002
Inverse matrix evaluation for linear systems. Zbl 0990.34013
2001
Fast calculations of dyadic Green’s functions for electromagnetic scattering in a multilayered medium. Zbl 1040.78015
Cai, Wei; Yu, Tiejun
2000
An adaptive wavelet method for nonlinear circuit simulation. Zbl 0963.94056
Zhou, Dian; Cai, Wei; Zhang, Wu
1999
A fast wavelet collocation method for high-speed circuit simulation. Zbl 0963.94055
Zhou, Dian; Cai, Wei
1999
High-order mixed current basis functions for electromagnetic scattering of curved surfaces. Zbl 0972.78007
Cai, Wei
1999
Cai, Wei; Zhang, Wu
1998
Electromechanical coupled finite element and dynamic equations. Zbl 0913.73068
Liu, Zhengxing; Yang, Yaowen; Cai, Wei; Li, Shanqing
1997
Adaptive multiresolution collocation methods for initial boundary value problems of nonlinear PDEs. Zbl 0856.65115
Cai, Wei; Wang, Jianzhong
1996
Direct numerical calculations of a neutral stability curve for one-dimensional detonations. Zbl 0855.76029
Cai, Wei; Oh, Wonho; Zhu, Youlan
1996
High-order hybrid numerical simulations of two-dimensional detonation waves. Zbl 0844.76070
Cai, Wei
1995
Coupling of spectral methods and the $$p$$-version of the finite element method for elliptic boundary value problems containing singularities. Zbl 0790.65093
Cai, W.; Lee, H. C.; Oh, H.-S.
1993
Uniform high-order spectral methods for one- and two-dimensional Euler equations. Zbl 0766.76069
Cai, Wei; Shu, Chi-Wang
1993
On one-sided filters for spectral Fourier approximations of discontinuous functions. Zbl 0755.65140
Cai, Wei; Gottlieb, David; Shu, Chi-Wang
1992
Cell averaging Chebyshev methods for hyperbolic problems. Zbl 0764.65056
Cai, Wei; Gottlieb, David; Harten, Ami
1992
Essentially nonoscillatory spectral Fourier methods for shock wave calculations. Zbl 0666.65067
Cai, Wei; Gottlieb, David; Shu, Chi-Wang
1989
Convergence of two nonconforming membrane finite elements. Zbl 0636.73064
Cai, Wei
1986
The limite problems for Zienkiewicz triangle elements. Zbl 0622.73075
Cai, Wei
1986
all top 5

### Cited by 956 Authors

 38 Cai, Wei 26 Li, Jichun 16 Huang, Yunqing 13 Karniadakis, George Em 13 Wei, Guowei 12 Deng, Shaozhong 11 Cho, Minhyung 9 Wang, Hong 8 Chen, Duan 8 Shao, Sihong 8 Zhao, Shan 7 Xu, Zhenli 6 Wang, Bo 6 Yang, Wei 6 Zheng, Xiangcheng 5 Bokil, Vrushali A. 5 Jiang, Haiyan 5 Kvernadze, George 5 Lanteri, Stéphane 5 Liang, Yingjie 5 Lu, Tiao 5 Nguyen, Duc Duy 5 Vasilyev, Oleg V. 5 Zhang, Wenzhong 4 Chen, Wen 4 D’Elia, Marta 4 Elnagar, Gamal N. 4 Gan, Zecheng 4 Guo, Ben-Yu 4 Jia, Jinhong 4 Jiang, Xiaoyun 4 Kopriva, David Alan 4 Lazar, Markus 4 Lu, Wangtao 4 Mao, Zhiping 4 Shu, Chi-Wang 4 van Meurs, Patrick 4 Wang, Fajie 4 Weinberger, Christopher R. 4 Xia, Kelin 4 Xue, Changfeng 4 Zhang, Zhimin 3 Antoine, Xavier 3 Chen, Zhenzhu 3 Cheng, Yingda 3 Danczul, Tobias 3 Deng, Zuicha 3 Gottlieb, David I. 3 Gulian, Mamikon 3 Hu, Dongdong 3 Ji, Xia 3 Jiang, Yan 3 Kazemi, Mohammad-Ali Afshar 3 Kolesnikova, Anna L. 3 Kumar, Ajeet 3 Li, Fengyan 3 Li, Huiyuan 3 Li, Lingxiao 3 Li, Ruo 3 Liu, Hailiang 3 Ma, Heping 3 Martín, Maria Teresa 3 Melenk, Jens Markus 3 Muscato, Orazio 3 Oyarzúa, Ricardo 3 Pan, Kejia 3 Pang, Guofei 3 Peletier, Mark Adriaan 3 Pellegrini, Yves-Patrick 3 Rim, Kyung Soo 3 Romanov, Alexey E. 3 Rundell, William 3 Sakkaplangkul, Puttha 3 Shi, Dongyang 3 Solano, Manuel E. 3 Sun, Hongguang 3 Vampa, Victoria 3 Vattré, Aurélien 3 Wang, Lilian 3 Wang, Yushun 3 Wu, Yu Mao 3 Xiong, Yunfeng 3 Xu, Zhi-Qin John 3 Yang, Liu 3 Yu, Jianning 3 Yu, Sining 3 Zhang, Jiwei 3 Zhou, Youhe 3 Zúñiga, Paulo 2 Abgrall, Rémi 2 Acosta Minoli, Cesar A. 2 Alonso Rodríguez, Ana 2 Banks, Jeffrey W. 2 Barrera, Domingo 2 Belytschko, Ted Bohdan 2 Berdichevskiĭ, Viktor L’vovich 2 Blokhin, Aleksandr Mikhaĭlovich 2 Borthagaray, Juan Pablo 2 Bruno, Oscar P. 2 Cai, Wenjun ...and 856 more Authors
all top 5

### Cited in 137 Serials

 106 Journal of Computational Physics 38 Journal of Scientific Computing 26 Journal of Computational and Applied Mathematics 20 Journal of the Mechanics and Physics of Solids 19 Communications in Computational Physics 18 Applied Mathematics and Computation 17 SIAM Journal on Scientific Computing 16 Computers & Mathematics with Applications 14 Computer Methods in Applied Mechanics and Engineering 10 Applied Numerical Mathematics 8 Computational Mechanics 8 Fractional Calculus & Applied Analysis 7 Mathematics of Computation 6 Journal of Mathematical Analysis and Applications 6 International Journal of Computer Mathematics 6 Communications in Nonlinear Science and Numerical Simulation 5 Applicable Analysis 5 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 5 Numerical Algorithms 5 Applied Mathematical Modelling 5 Advances in Computational Mathematics 5 International Journal of Wavelets, Multiresolution and Information Processing 5 International Journal of Numerical Analysis and Modeling 4 Computer Physics Communications 4 Physica A 4 International Journal for Numerical Methods in Engineering 4 Mathematics and Computers in Simulation 4 SIAM Journal on Numerical Analysis 4 Applied Mathematics Letters 4 Applied and Computational Harmonic Analysis 4 Fractals 4 Advances in Applied Mathematics and Mechanics 3 Archive for Rational Mechanics and Analysis 3 International Journal of Engineering Science 3 International Journal of Solids and Structures 3 Journal of Engineering Mathematics 3 Numerische Mathematik 3 Numerical Methods for Partial Differential Equations 3 Mathematical and Computer Modelling 3 European Journal of Mechanics. A. Solids 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Science China. Mathematics 2 Acta Mechanica 2 Computers and Fluids 2 International Journal of Plasticity 2 Wave Motion 2 BIT 2 Journal of Differential Equations 2 Quarterly of Applied Mathematics 2 Acta Mathematicae Applicatae Sinica. English Series 2 COMPEL 2 Journal of Elasticity 2 Pattern Recognition 2 SIAM Journal on Applied Mathematics 2 Engineering Analysis with Boundary Elements 2 Mathematics and Mechanics of Solids 2 Nonlinear Dynamics 2 Combustion Theory and Modelling 2 Journal of Numerical Mathematics 2 Inverse Problems in Science and Engineering 2 Discrete and Continuous Dynamical Systems. Series S 2 Numerical Mathematics: Theory, Methods and Applications 2 Communications in Applied and Industrial Mathematics 2 Results in Applied Mathematics 1 Modern Physics Letters B 1 Indian Journal of Pure & Applied Mathematics 1 Inverse Problems 1 Journal of Mathematical Biology 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Mathematical Biosciences 1 Nonlinearity 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Bulletin of Mathematical Biology 1 Chaos, Solitons and Fractals 1 Advances in Mathematics 1 Calcolo 1 Journal of the American Statistical Association 1 Journal of Optimization Theory and Applications 1 Journal für die Reine und Angewandte Mathematik 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 SIAM Journal on Control and Optimization 1 Applied Mathematics and Mechanics. (English Edition) 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Publicacions Matemàtiques 1 Science in China. Series A 1 European Journal of Applied Mathematics 1 Computational Mathematics and Mathematical Physics 1 SIAM Review 1 The Journal of Analysis 1 Calculus of Variations and Partial Differential Equations 1 Communications in Numerical Methods in Engineering 1 Computational and Applied Mathematics 1 Monte Carlo Methods and Applications 1 Mathematical Problems in Engineering 1 International Journal of Computational Fluid Dynamics 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Abstract and Applied Analysis 1 Journal of Applied Mechanics and Technical Physics 1 Journal of Shanghai University ...and 37 more Serials
all top 5

### Cited in 36 Fields

 361 Numerical analysis (65-XX) 232 Partial differential equations (35-XX) 134 Optics, electromagnetic theory (78-XX) 75 Mechanics of deformable solids (74-XX) 71 Fluid mechanics (76-XX) 42 Statistical mechanics, structure of matter (82-XX) 33 Real functions (26-XX) 25 Ordinary differential equations (34-XX) 25 Harmonic analysis on Euclidean spaces (42-XX) 22 Quantum theory (81-XX) 19 Biology and other natural sciences (92-XX) 16 Computer science (68-XX) 15 Integral equations (45-XX) 15 Calculus of variations and optimal control; optimization (49-XX) 12 Classical thermodynamics, heat transfer (80-XX) 11 Probability theory and stochastic processes (60-XX) 8 Approximations and expansions (41-XX) 8 Operator theory (47-XX) 7 Statistics (62-XX) 6 Systems theory; control (93-XX) 6 Information and communication theory, circuits (94-XX) 5 Measure and integration (28-XX) 5 Functional analysis (46-XX) 5 Mechanics of particles and systems (70-XX) 4 Special functions (33-XX) 4 Geophysics (86-XX) 3 Combinatorics (05-XX) 3 Potential theory (31-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Integral transforms, operational calculus (44-XX) 2 Operations research, mathematical programming (90-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Difference and functional equations (39-XX) 1 Differential geometry (53-XX)