Edit Profile (opens in new tab) Xiu, Dongbin Compute Distance To: Compute Author ID: xiu.dongbin Published as: Xiu, Dongbin; Xiu, D. External Links: MGP Documents Indexed: 85 Publications since 2001, including 1 Book Co-Authors: 65 Co-Authors with 79 Joint Publications 2,292 Co-Co-Authors all top 5 Co-Authors 4 single-authored 13 Wu, Kailiang 12 Karniadakis, George Em 8 Narayan, Akil C. 7 Shin, Yeonjong 5 Jakeman, John Davis 5 Li, Jing 4 Chen, Zhen 4 Qin, Tong 4 Zhu, Xueyu 3 Jin, Shi 3 Tartakovsky, Daniel M. 2 Chang, Lo-Bin 2 Chen, Xiaoxiao 2 Chou, Ching-Shan 2 Gittelson, Claude Jeffrey 2 He, Yanyan 2 Kevrekidis, Ioannis George 2 Li, Jinglai 2 Lucor, Didier 2 Marzouk, Youssef M. 2 Shen, Jie 2 Sherwin, Spencer J. 2 Su, Chau-Hsing 2 Wang, Shuyi 2 Yan, Liang 1 Alexeenko, Alina A. 1 Archibald, Richard 1 Archibald, Rick 1 Buzzard, Gregery T. 1 Canuto, Claudio 1 Chen, Yi 1 Churchill, Victor 1 Dong, Suchuan 1 Eldred, Michael S. 1 Gelb, Anne 1 Geneser, Sarah E. 1 Gottlieb, David I. 1 Guo, Ling 1 Guo, Xiaohui 1 Han, Xiaoying 1 Hesthaven, Jan S. 1 Hou, Jun 1 Hu, Jingwei 1 Li, Yukun 1 Linebarger, Erin M. 1 Park, Eun-Jae 1 Pieraccini, Sandra 1 Preusser, Tobias 1 Pulch, Roland 1 Qi, Xin 1 Sachse, Frank B. 1 Saxena, Rishu 1 Sirisup, Sirod 1 Su, Wei-Hung 1 Sun, Zheng 1 Tang, Huazhong 1 Tiesler, Hanne 1 Tsuji, Paul 1 Wan, Xiaoliang 1 Xing, Yulong 1 Xu, Jin 1 Ying, Lexing 1 Zhong, Xinghui 1 Zhou, Tao 1 Zhou, Zixu all top 5 Serials 30 Journal of Computational Physics 20 SIAM Journal on Scientific Computing 9 Communications in Computational Physics 6 Journal of Scientific Computing 2 Computer Methods in Applied Mechanics and Engineering 2 International Journal for Numerical Methods in Engineering 2 Multiscale Modeling & Simulation 2 International Journal for Uncertainty Quantification 2 Communications on Applied Mathematics and Computation 1 International Journal of Heat and Mass Transfer 1 International Journal for Numerical Methods in Fluids 1 Bulletin of Mathematical Biology 1 SIAM Journal on Control and Optimization 1 Applied Numerical Mathematics 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Theoretical Biology 1 SIAM/ASA Journal on Uncertainty Quantification all top 5 Fields 64 Numerical analysis (65-XX) 30 Probability theory and stochastic processes (60-XX) 24 Partial differential equations (35-XX) 14 Approximations and expansions (41-XX) 12 Statistics (62-XX) 11 Fluid mechanics (76-XX) 8 Dynamical systems and ergodic theory (37-XX) 8 Computer science (68-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 3 Ordinary differential equations (34-XX) 3 Biology and other natural sciences (92-XX) 2 Systems theory; control (93-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 76 Publications have been cited 3,304 times in 1,721 Documents Cited by ▼ Year ▼ The Wiener–Askey polynomial chaos for stochastic differential equations. Zbl 1014.65004Xiu, Dongbin; Karniadakis, George Em 802 2002 High-order collocation methods for differential equations with random inputs. Zbl 1091.65006Xiu, Dongbin; Hesthaven, Jan S. 407 2005 Numerical methods for stochastic computations. A spectral method approach. Zbl 1210.65002Xiu, Dongbin 292 2010 Modeling uncertainty in flow simulations via generalized polynomial chaos. Zbl 1047.76111Xiu, Dongbin; Karniadakis, George Em 267 2003 Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos. Zbl 1016.65001Xiu, Dongbin; Karniadakis, George Em 140 2002 Fast numerical methods for stochastic computations: a review. Zbl 1364.65019Xiu, Dongbin 112 2009 Efficient collocational approach for parametric uncertainty analysis. Zbl 1164.65302Xiu, Dongbin 103 2007 A semi-Lagrangian high-order method for Navier-Stokes equations. Zbl 1028.76026Xiu, Dongbin; Karniadakis, George Em 88 2001 A stochastic collocation approach to Bayesian inference in inverse problems. Zbl 1364.62064Marzouk, Youssef; Xiu, Dongbin 71 2009 Numerical methods for differential equations in random domains. Zbl 1114.60056Xiu, Dongbin; Tartakovsky, Daniel M. 68 2006 Galerkin method for wave equations with uncertain coefficients. Zbl 1195.65009Gottlieb, David; Xiu, Dongbin 58 2008 Stochastic collocation algorithms using \(\ell_1\)-minimization. Zbl 1291.65024Yan, Liang; Guo, Ling; Xiu, Dongbin 53 2012 A new stochastic approach to transient heat conduction modeling with uncertainty. Zbl 1038.80003Xiu, Dongbin; Karniadakis, George Em 43 2003 Stochastic collocation for optimal control problems with stochastic PDE constraints. Zbl 1260.60125Tiesler, Hanne; Kirby, Robert M.; Xiu, Dongbin; Preusser, Tobias 39 2012 Stochastic analysis of transport in tubes with rough walls. Zbl 1146.76651Tartakovsky, Daniel M.; Xiu, Dongbin 37 2006 Efficient stochastic Galerkin methods for random diffusion equations. Zbl 1161.65008Xiu, Dongbin; Shen, Jie 37 2009 Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings. Zbl 1352.65407Jin, Shi; Xiu, Dongbin; Zhu, Xueyu 31 2015 Evaluation of failure probability via surrogate models. Zbl 1204.65010Li, Jing; Xiu, Dongbin 30 2010 Equation-free/Galerkin-free POD-assisted computation of incompressible flows. Zbl 1213.76146Sirisup, Sirod; Karniadakis, George Em; Xiu, Dongbin; Kevrekidis, Ioannis G. 29 2005 Data driven governing equations approximation using deep neural networks. Zbl 1455.65125Qin, Tong; Wu, Kailiang; Xiu, Dongbin 26 2019 Stochastic collocation methods on unstructured grids in high dimensions via interpolation. Zbl 1246.65029Narayan, Akil; Xiu, Dongbin 25 2012 A generalized polynomial chaos based ensemble Kalman filter with high accuracy. Zbl 1280.93084Li, Jia; Xiu, Dongbin 25 2009 An efficient surrogate-based method for computing rare failure probability. Zbl 1370.65005Li, Jing; Li, Jinglai; Xiu, Dongbin 23 2011 Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids. Zbl 1218.65010Jakeman, John D.; Archibald, Richard; Xiu, Dongbin 23 2011 Computational aspects of stochastic collocation with multifidelity models. Zbl 1306.65010Zhu, Xueyu; Narayan, Akil; Xiu, Dongbin 22 2014 An efficient spectral method for acoustic scattering from rough surfaces. Zbl 1164.65303Xiu, Dongbin; Shen, Jie 22 2007 A stochastic collocation algorithm with multifidelity models. Zbl 1296.65013Narayan, Akil; Gittelson, Claude; Xiu, Dongbin 20 2014 Discontinuity detection in multivariate space for stochastic simulations. Zbl 1161.65307Archibald, Rick; Gelb, Anne; Saxena, Rishu; Xiu, Dongbin 18 2009 Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions. Zbl 1311.65158Jakeman, John D.; Narayan, Akil; Xiu, Dongbin 18 2013 Local polynomial chaos expansion for linear differential equations with high dimensional random inputs. Zbl 1330.65189Chen, Yi; Jakeman, John; Gittelson, Claude; Xiu, Dongbin 18 2015 A well-balanced stochastic Galerkin method for scalar hyperbolic balance laws with random inputs. Zbl 1342.65010Jin, Shi; Xiu, Dongbin; Zhu, Xueyu 17 2016 Numerical approach for quantification of epistemic uncertainty. Zbl 1204.65008Jakeman, John; Eldred, Michael; Xiu, Dongbin 16 2010 Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network. Zbl 1121.92023Xiu, Dongbin; Sherwin, Spencer J. 16 2007 Multi-fidelity stochastic collocation method for computation of statistical moments. Zbl 1378.65040Zhu, Xueyu; Linebarger, Erin M.; Xiu, Dongbin 16 2017 A two-scale nonperturbative approach to uncertainty analysis of diffusion in random composites. Zbl 1067.60057Xiu, Dongbin; Tartakovsky, Daniel M. 16 2004 Strong and auxiliary forms of the semi-Lagrangian method for incompressible flows. Zbl 1203.76122Xiu, D.; Sherwin, S. J.; Dong, S.; Karniadakis, G. E. 15 2005 Supersensitivity due to uncertain boundary conditions. Zbl 1075.76623Xiu, Dongbin; Karniadakis, George Em 15 2004 A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty. Zbl 1380.65315Wu, Kailiang; Tang, Huazhong; Xiu, Dongbin 15 2017 Numerical aspects for approximating governing equations using data. Zbl 1451.65008Wu, Kailiang; Xiu, Dongbin 15 2019 Nonadaptive quasi-optimal points selection for least squares linear regression. Zbl 06548919Shin, Yeonjong; Xiu, Dongbin 14 2016 Stochastic solutions for the two-dimensional advection-diffusion equation. Zbl 1075.65010Wan, Xiaoliang; Xiu, Dongbin; Karniadakis, George Em 14 2004 Weighted discrete least-squares polynomial approximation using randomized quadratures. Zbl 1349.60086Zhou, Tao; Narayan, Akil; Xiu, Dongbin 13 2015 Generalised polynomial chaos for a class of linear conservation laws. Zbl 1258.65008Pulch, Roland; Xiu, Dongbin 12 2012 Numerical integration formulas of degree two. Zbl 1221.65082Xiu, Dongbin 11 2008 Variance-based global sensitivity analysis via sparse-grid interpolation and cubature. Zbl 1364.41003Buzzard, Gregery T.; Xiu, Dongbin 11 2011 A semi-Lagrangian method for turbulence simulations using mixed spectral discretizations. Zbl 1028.76020Xu, Jin; Xiu, Dongbin; Karniadakis, George Em 10 2002 A stochastic Galerkin method for Hamilton-Jacobi equations with uncertainty. Zbl 1330.65179Hu, Jingwei; Jin, Shi; Xiu, Dongbin 10 2015 Predictability and uncertainty in CFD. Zbl 1032.76662Lucor, D.; Xiu, D.; Su, C.-H.; Karniadakis, G. E. 10 2003 A randomized algorithm for multivariate function approximation. Zbl 1366.41018Shin, Yeonjong; Xiu, Dongbin 9 2017 Sparse approximation using \(\ell_1-\ell_2\) minimization and its application to stochastic collocation. Zbl 1381.94029Yan, Liang; Shin, Yeonjong; Xiu, Dongbin 9 2017 On numerical properties of the ensemble Kalman filter for data assimilation. Zbl 1195.93137Li, Jia; Xiu, Dongbin 7 2008 Performance evaluation of generalized polynomial chaos. Zbl 1188.60038Xiu, Dongbin; Lucor, Didier; Su, C.-H.; Karniadakis, George Em 6 2003 On a near optimal sampling strategy for least squares polynomial regression. Zbl 1384.62249Shin, Yeonjong; Xiu, Dongbin 6 2016 Constructing nested nodal sets for multivariate polynomial interpolation. Zbl 1292.65007Narayan, Akil; Xiu, Dongbin 6 2013 A flexible numerical approach for quantification of epistemic uncertainty. Zbl 1305.65013Chen, Xiaoxiao; Park, Eun-Jae; Xiu, Dongbin 6 2013 Numerical strategy for model correction using physical constraints. Zbl 1349.65202He, Yanyan; Xiu, Dongbin 6 2016 A randomized tensor quadrature method for high dimensional polynomial approximation. Zbl 1373.65012Wu, Kailiang; Shin, Yeonjong; Xiu, Dongbin 5 2017 Correcting data corruption errors for multivariate function approximation. Zbl 1348.65052Shin, Yeonjong; Xiu, Dongbin 5 2016 Structure-preserving method for reconstructing unknown Hamiltonian systems from trajectory data. Zbl 1462.65219Wu, Kailiang; Qin, Tong; Xiu, Dongbin 5 2020 Fast method for high-frequency acoustic scattering from random scatterers. Zbl 1465.65160Tsuji, Paul; Xiu, Dongbin; Ying, Lexing 4 2011 On upper and lower bounds for quantity of interest in problems subject to epistemic uncertainty. Zbl 1300.65046Li, Jing; Qi, Xin; Xiu, Dongbin 4 2014 Sequential data assimilation with multiple models. Zbl 1284.62801Narayan, Akil; Marzouk, Youssef; Xiu, Dongbin 4 2012 Sequential function approximation with noisy data. Zbl 1415.65035Shin, Yeonjong; Wu, Kailiang; Xiu, Dongbin 3 2018 Surrogate based method for evaluation of failure probability under multiple constraints. Zbl 1306.65012Li, Jing; Xiu, Dongbin 3 2014 Convolution neural network shock detector for numerical solution of conservation laws. Zbl 07419160Sun, Zheng; Wang, Shuyi; Chang, Lo-Bin; Xing, Yulong; Xiu, Dongbin 3 2020 Energy conserving Galerkin approximation of two dimensional wave equations with random coefficients. Zbl 1451.65143Chou, Ching-Shan; Li, Yukun; Xiu, Dongbin 3 2019 Uncertainty quantification of discontinuous outputs via a non-intrusive bifidelity strategy. Zbl 1453.62796Canuto, Claudio; Pieraccini, Sandra; Xiu, Dongbin 3 2019 Equation-free, multiscale computation for unsteady random diffusion. Zbl 1089.60040Xiu, Dongbin; Kevrekidis, Ioannis G. 2 2005 Sequential function approximation on arbitrarily distributed point sets. Zbl 1380.65034Wu, Kailiang; Xiu, Dongbin 2 2018 Data-driven learning of nonautonomous systems. Zbl 07364312Qin, Tong; Chen, Zhen; Jakeman, John D.; Xiu, Dongbin 2 2021 Data-driven deep learning of partial differential equations in modal space. Zbl 07505629Wu, Kailiang; Xiu, Dongbin 2 2020 A WENO-based stochastic Galerkin scheme for ideal MHD equations with random inputs. Zbl 1473.65217Wu, Kailiang; Xiu, Dongbin; Zhong, Xinghui 2 2021 Error analysis for numerical formulation of particle filter. Zbl 1334.65021Han, Xiaoying; Li, Jinglai; Xiu, Dongbin 1 2015 An efficient method for uncertainty propagation using fuzzy sets. Zbl 1327.65012Chen, Xiaoxiao; He, Yanyan; Xiu, Dongbin 1 2015 Uncertainty quantification models for micro-scale squeeze-film damping. Zbl 1202.76122Guo, Xiaohui; Li, Jia; Xiu, Dongbin; Alexeenko, Alina 1 2010 Distributional sensitivity for uncertainty quantification. Zbl 1364.65009Narayan, Akil; Xiu, Dongbin 1 2011 Data-driven learning of nonautonomous systems. Zbl 07364312Qin, Tong; Chen, Zhen; Jakeman, John D.; Xiu, Dongbin 2 2021 A WENO-based stochastic Galerkin scheme for ideal MHD equations with random inputs. Zbl 1473.65217Wu, Kailiang; Xiu, Dongbin; Zhong, Xinghui 2 2021 Structure-preserving method for reconstructing unknown Hamiltonian systems from trajectory data. Zbl 1462.65219Wu, Kailiang; Qin, Tong; Xiu, Dongbin 5 2020 Convolution neural network shock detector for numerical solution of conservation laws. Zbl 07419160Sun, Zheng; Wang, Shuyi; Chang, Lo-Bin; Xing, Yulong; Xiu, Dongbin 3 2020 Data-driven deep learning of partial differential equations in modal space. Zbl 07505629Wu, Kailiang; Xiu, Dongbin 2 2020 Data driven governing equations approximation using deep neural networks. Zbl 1455.65125Qin, Tong; Wu, Kailiang; Xiu, Dongbin 26 2019 Numerical aspects for approximating governing equations using data. Zbl 1451.65008Wu, Kailiang; Xiu, Dongbin 15 2019 Energy conserving Galerkin approximation of two dimensional wave equations with random coefficients. Zbl 1451.65143Chou, Ching-Shan; Li, Yukun; Xiu, Dongbin 3 2019 Uncertainty quantification of discontinuous outputs via a non-intrusive bifidelity strategy. Zbl 1453.62796Canuto, Claudio; Pieraccini, Sandra; Xiu, Dongbin 3 2019 Sequential function approximation with noisy data. Zbl 1415.65035Shin, Yeonjong; Wu, Kailiang; Xiu, Dongbin 3 2018 Sequential function approximation on arbitrarily distributed point sets. Zbl 1380.65034Wu, Kailiang; Xiu, Dongbin 2 2018 Multi-fidelity stochastic collocation method for computation of statistical moments. Zbl 1378.65040Zhu, Xueyu; Linebarger, Erin M.; Xiu, Dongbin 16 2017 A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty. Zbl 1380.65315Wu, Kailiang; Tang, Huazhong; Xiu, Dongbin 15 2017 A randomized algorithm for multivariate function approximation. Zbl 1366.41018Shin, Yeonjong; Xiu, Dongbin 9 2017 Sparse approximation using \(\ell_1-\ell_2\) minimization and its application to stochastic collocation. Zbl 1381.94029Yan, Liang; Shin, Yeonjong; Xiu, Dongbin 9 2017 A randomized tensor quadrature method for high dimensional polynomial approximation. Zbl 1373.65012Wu, Kailiang; Shin, Yeonjong; Xiu, Dongbin 5 2017 A well-balanced stochastic Galerkin method for scalar hyperbolic balance laws with random inputs. Zbl 1342.65010Jin, Shi; Xiu, Dongbin; Zhu, Xueyu 17 2016 Nonadaptive quasi-optimal points selection for least squares linear regression. Zbl 06548919Shin, Yeonjong; Xiu, Dongbin 14 2016 On a near optimal sampling strategy for least squares polynomial regression. Zbl 1384.62249Shin, Yeonjong; Xiu, Dongbin 6 2016 Numerical strategy for model correction using physical constraints. Zbl 1349.65202He, Yanyan; Xiu, Dongbin 6 2016 Correcting data corruption errors for multivariate function approximation. Zbl 1348.65052Shin, Yeonjong; Xiu, Dongbin 5 2016 Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings. Zbl 1352.65407Jin, Shi; Xiu, Dongbin; Zhu, Xueyu 31 2015 Local polynomial chaos expansion for linear differential equations with high dimensional random inputs. Zbl 1330.65189Chen, Yi; Jakeman, John; Gittelson, Claude; Xiu, Dongbin 18 2015 Weighted discrete least-squares polynomial approximation using randomized quadratures. Zbl 1349.60086Zhou, Tao; Narayan, Akil; Xiu, Dongbin 13 2015 A stochastic Galerkin method for Hamilton-Jacobi equations with uncertainty. Zbl 1330.65179Hu, Jingwei; Jin, Shi; Xiu, Dongbin 10 2015 Error analysis for numerical formulation of particle filter. Zbl 1334.65021Han, Xiaoying; Li, Jinglai; Xiu, Dongbin 1 2015 An efficient method for uncertainty propagation using fuzzy sets. Zbl 1327.65012Chen, Xiaoxiao; He, Yanyan; Xiu, Dongbin 1 2015 Computational aspects of stochastic collocation with multifidelity models. Zbl 1306.65010Zhu, Xueyu; Narayan, Akil; Xiu, Dongbin 22 2014 A stochastic collocation algorithm with multifidelity models. Zbl 1296.65013Narayan, Akil; Gittelson, Claude; Xiu, Dongbin 20 2014 On upper and lower bounds for quantity of interest in problems subject to epistemic uncertainty. Zbl 1300.65046Li, Jing; Qi, Xin; Xiu, Dongbin 4 2014 Surrogate based method for evaluation of failure probability under multiple constraints. Zbl 1306.65012Li, Jing; Xiu, Dongbin 3 2014 Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions. Zbl 1311.65158Jakeman, John D.; Narayan, Akil; Xiu, Dongbin 18 2013 Constructing nested nodal sets for multivariate polynomial interpolation. Zbl 1292.65007Narayan, Akil; Xiu, Dongbin 6 2013 A flexible numerical approach for quantification of epistemic uncertainty. Zbl 1305.65013Chen, Xiaoxiao; Park, Eun-Jae; Xiu, Dongbin 6 2013 Stochastic collocation algorithms using \(\ell_1\)-minimization. Zbl 1291.65024Yan, Liang; Guo, Ling; Xiu, Dongbin 53 2012 Stochastic collocation for optimal control problems with stochastic PDE constraints. Zbl 1260.60125Tiesler, Hanne; Kirby, Robert M.; Xiu, Dongbin; Preusser, Tobias 39 2012 Stochastic collocation methods on unstructured grids in high dimensions via interpolation. Zbl 1246.65029Narayan, Akil; Xiu, Dongbin 25 2012 Generalised polynomial chaos for a class of linear conservation laws. Zbl 1258.65008Pulch, Roland; Xiu, Dongbin 12 2012 Sequential data assimilation with multiple models. Zbl 1284.62801Narayan, Akil; Marzouk, Youssef; Xiu, Dongbin 4 2012 An efficient surrogate-based method for computing rare failure probability. Zbl 1370.65005Li, Jing; Li, Jinglai; Xiu, Dongbin 23 2011 Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids. Zbl 1218.65010Jakeman, John D.; Archibald, Richard; Xiu, Dongbin 23 2011 Variance-based global sensitivity analysis via sparse-grid interpolation and cubature. Zbl 1364.41003Buzzard, Gregery T.; Xiu, Dongbin 11 2011 Fast method for high-frequency acoustic scattering from random scatterers. Zbl 1465.65160Tsuji, Paul; Xiu, Dongbin; Ying, Lexing 4 2011 Distributional sensitivity for uncertainty quantification. Zbl 1364.65009Narayan, Akil; Xiu, Dongbin 1 2011 Numerical methods for stochastic computations. A spectral method approach. Zbl 1210.65002Xiu, Dongbin 292 2010 Evaluation of failure probability via surrogate models. Zbl 1204.65010Li, Jing; Xiu, Dongbin 30 2010 Numerical approach for quantification of epistemic uncertainty. Zbl 1204.65008Jakeman, John; Eldred, Michael; Xiu, Dongbin 16 2010 Uncertainty quantification models for micro-scale squeeze-film damping. Zbl 1202.76122Guo, Xiaohui; Li, Jia; Xiu, Dongbin; Alexeenko, Alina 1 2010 Fast numerical methods for stochastic computations: a review. Zbl 1364.65019Xiu, Dongbin 112 2009 A stochastic collocation approach to Bayesian inference in inverse problems. Zbl 1364.62064Marzouk, Youssef; Xiu, Dongbin 71 2009 Efficient stochastic Galerkin methods for random diffusion equations. Zbl 1161.65008Xiu, Dongbin; Shen, Jie 37 2009 A generalized polynomial chaos based ensemble Kalman filter with high accuracy. Zbl 1280.93084Li, Jia; Xiu, Dongbin 25 2009 Discontinuity detection in multivariate space for stochastic simulations. Zbl 1161.65307Archibald, Rick; Gelb, Anne; Saxena, Rishu; Xiu, Dongbin 18 2009 Galerkin method for wave equations with uncertain coefficients. Zbl 1195.65009Gottlieb, David; Xiu, Dongbin 58 2008 Numerical integration formulas of degree two. Zbl 1221.65082Xiu, Dongbin 11 2008 On numerical properties of the ensemble Kalman filter for data assimilation. Zbl 1195.93137Li, Jia; Xiu, Dongbin 7 2008 Efficient collocational approach for parametric uncertainty analysis. Zbl 1164.65302Xiu, Dongbin 103 2007 An efficient spectral method for acoustic scattering from rough surfaces. Zbl 1164.65303Xiu, Dongbin; Shen, Jie 22 2007 Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network. Zbl 1121.92023Xiu, Dongbin; Sherwin, Spencer J. 16 2007 Numerical methods for differential equations in random domains. Zbl 1114.60056Xiu, Dongbin; Tartakovsky, Daniel M. 68 2006 Stochastic analysis of transport in tubes with rough walls. Zbl 1146.76651Tartakovsky, Daniel M.; Xiu, Dongbin 37 2006 High-order collocation methods for differential equations with random inputs. Zbl 1091.65006Xiu, Dongbin; Hesthaven, Jan S. 407 2005 Equation-free/Galerkin-free POD-assisted computation of incompressible flows. Zbl 1213.76146Sirisup, Sirod; Karniadakis, George Em; Xiu, Dongbin; Kevrekidis, Ioannis G. 29 2005 Strong and auxiliary forms of the semi-Lagrangian method for incompressible flows. Zbl 1203.76122Xiu, D.; Sherwin, S. J.; Dong, S.; Karniadakis, G. E. 15 2005 Equation-free, multiscale computation for unsteady random diffusion. Zbl 1089.60040Xiu, Dongbin; Kevrekidis, Ioannis G. 2 2005 A two-scale nonperturbative approach to uncertainty analysis of diffusion in random composites. Zbl 1067.60057Xiu, Dongbin; Tartakovsky, Daniel M. 16 2004 Supersensitivity due to uncertain boundary conditions. Zbl 1075.76623Xiu, Dongbin; Karniadakis, George Em 15 2004 Stochastic solutions for the two-dimensional advection-diffusion equation. Zbl 1075.65010Wan, Xiaoliang; Xiu, Dongbin; Karniadakis, George Em 14 2004 Modeling uncertainty in flow simulations via generalized polynomial chaos. Zbl 1047.76111Xiu, Dongbin; Karniadakis, George Em 267 2003 A new stochastic approach to transient heat conduction modeling with uncertainty. Zbl 1038.80003Xiu, Dongbin; Karniadakis, George Em 43 2003 Predictability and uncertainty in CFD. Zbl 1032.76662Lucor, D.; Xiu, D.; Su, C.-H.; Karniadakis, G. E. 10 2003 Performance evaluation of generalized polynomial chaos. Zbl 1188.60038Xiu, Dongbin; Lucor, Didier; Su, C.-H.; Karniadakis, George Em 6 2003 The Wiener–Askey polynomial chaos for stochastic differential equations. Zbl 1014.65004Xiu, Dongbin; Karniadakis, George Em 802 2002 Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos. Zbl 1016.65001Xiu, Dongbin; Karniadakis, George Em 140 2002 A semi-Lagrangian method for turbulence simulations using mixed spectral discretizations. Zbl 1028.76020Xu, Jin; Xiu, Dongbin; Karniadakis, George Em 10 2002 A semi-Lagrangian high-order method for Navier-Stokes equations. Zbl 1028.76026Xiu, Dongbin; Karniadakis, George Em 88 2001 all cited Publications top 5 cited Publications all top 5 Cited by 2,529 Authors 43 Karniadakis, George Em 40 Xiu, Dongbin 37 Narayan, Akil C. 35 Lin, Guang 30 Doostan, Alireza 25 Ghanem, Roger G. 25 Le Maître, Olivier P. 24 Zabaras, Nicholas J. 23 Jin, Shi 22 Zhou, Tao 21 Nobile, Fabio 18 Pulch, Roland 17 Marzouk, Youssef M. 17 Matthies, Hermann Georg 16 Cortés López, Juan Carlos 16 Iaccarino, Gianluca 16 Jakeman, John Davis 16 Najm, Habib N. 16 Tempone, Raúl F. 15 Lucor, Didier 15 Nouy, Anthony 15 Willcox, Karen E. 14 Harbrecht, Helmut 14 Knio, Omar M. 14 Tartakovsky, Daniel M. 13 Chen, Peng 12 Congedo, Pietro Marco 12 Guo, Ling 12 Peherstorfer, Benjamin 12 Schwab, Christoph 12 Sudret, Bruno 12 Zhang, Dongxiao 11 Elman, Howard C. 11 Jornet, Marc 11 Liu, Liu 11 Pareschi, Lorenzo 11 Tamellini, Lorenzo 10 Alexanderian, Alen 10 Jiang, Lijian 10 Keshavarzzadeh, Vahid 10 Li, Jinglai 10 Nordström, Jan 10 Phipps, Eric T. 10 Soize, Christian 10 Venturi, Daniele 10 Wang, Chong 10 Witteveen, Jeroen A. S. 10 Yang, Xiu 10 Zhang, Zhiwen 9 Salvetti, Maria Vittoria 9 Tartakovsky, Alexandre M. 9 Vega, José Manuel 9 Wan, Xiaoliang 9 Webster, Clayton G. 9 Zanella, Mattia 9 Zhu, Xueyu 8 Aluru, Narayana R. 8 Calatayud, Julia 8 Chen, Wei 8 Gunzburger, Max D. 8 Hampton, Jerrad 8 Hou, Thomas Yizhao 8 Nair, Prasanth B. 8 Poëtte, Gaël 8 Raisee, Mehrdad 8 Sagaut, Pierre 8 Sapsis, Themistoklis P. 8 Seaïd, Mohammed 8 Wu, Kailiang 8 Yan, Liang 7 Adhikari, Sondipon 7 Arnst, Maarten 7 Bak, Soyoon 7 Bilionis, Ilias 7 Constantine, Paul G. 7 Frank, Martin 7 Geraci, Gianluca 7 Gibou, Frédéric 7 Grigoriu, Mircea D. 7 Hesthaven, Jan S. 7 Kevrekidis, Ioannis George 7 Kim, Philsu 7 Li, Qin 7 Motamed, Mohammad 7 Peters, Michael D. 7 Quarteroni, Alfio M. 7 Sabelfeld, Karl Karlovich 6 Abgrall, Rémi 6 Adcock, Ben 6 Chen-Charpentier, Benito M. 6 El-Amrani, Mofdi 6 Ganapathysubramanian, Baskar 6 Ghattas, Omar N. 6 Krämer, Boris 6 Kusch, Jonas 6 Lermusiaux, Pierre F. J. 6 Li, Jing 6 Mariotti, Alessandro 6 Min, Chohong 6 Oden, John Tinsley ...and 2,429 more Authors all top 5 Cited in 227 Serials 347 Journal of Computational Physics 202 Computer Methods in Applied Mechanics and Engineering 97 SIAM/ASA Journal on Uncertainty Quantification 90 SIAM Journal on Scientific Computing 63 Journal of Scientific Computing 42 International Journal for Numerical Methods in Engineering 41 Computers and Fluids 37 Journal of Computational and Applied Mathematics 31 Applied Mathematical Modelling 26 Applied Mathematics and Computation 26 Computational Geosciences 24 Computers & Mathematics with Applications 20 Computational Mechanics 19 Applied Numerical Mathematics 18 Numerische Mathematik 17 Multiscale Modeling & Simulation 15 International Journal of Computer Mathematics 14 Mathematics and Computers in Simulation 14 SIAM Journal on Numerical Analysis 14 Communications in Computational Physics 13 Engineering Analysis with Boundary Elements 12 Mathematical Problems in Engineering 11 Automatica 10 Advances in Computational Mathematics 10 International Journal of Computational Methods 8 Journal of Engineering Mathematics 8 Structural and Multidisciplinary Optimization 8 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 7 Acta Mechanica 7 Journal of Fluid Mechanics 7 BIT 7 Physica D 7 SIAM Review 7 Nonlinear Dynamics 7 Communications in Nonlinear Science and Numerical Simulation 7 Archives of Computational Methods in Engineering 7 Foundations of Computational Mathematics 6 Inverse Problems 6 Mathematics of Computation 6 Chaos, Solitons and Fractals 6 SIAM Journal on Control and Optimization 6 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 6 Numerical Algorithms 6 SIAM Journal on Applied Dynamical Systems 6 Stochastic and Partial Differential Equations. Analysis and Computations 5 Numerical Methods for Partial Differential Equations 5 European Journal of Mechanics. A. Solids 5 European Journal of Mechanics. B. Fluids 5 Mathematical Modelling of Natural Phenomena 5 Advances in Applied Mathematics and Mechanics 5 Journal of Mathematics in Industry 5 East Asian Journal on Applied Mathematics 5 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 4 Journal of Mathematical Analysis and Applications 4 Journal of Mathematical Biology 4 Journal of Statistical Physics 4 Mathematical Biosciences 4 Theoretical and Computational Fluid Dynamics 4 Journal of Differential Equations 4 European Journal of Applied Mathematics 4 Linear Algebra and its Applications 4 Computational and Applied Mathematics 4 Computing and Visualization in Science 4 Abstract and Applied Analysis 4 Combustion Theory and Modelling 4 Journal of Applied Mathematics 4 Journal of Machine Learning Research (JMLR) 4 Acta Numerica 4 International Journal of Numerical Analysis and Modeling 3 International Journal of Heat and Mass Transfer 3 Bulletin of Mathematical Biology 3 Fuzzy Sets and Systems 3 Journal of the American Statistical Association 3 Constructive Approximation 3 Mathematical and Computer Modelling 3 SIAM Journal on Optimization 3 Computational Optimization and Applications 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Multibody System Dynamics 3 Vietnam Journal of Mathematics 3 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 3 Stochastic Environmental Research and Risk Assessment 3 Optimization and Engineering 3 Discrete and Continuous Dynamical Systems. Series B 3 Journal of Computational Acoustics 3 Stochastics 3 Acta Mechanica Sinica 3 Kinetic and Related Models 3 GEM - International Journal on Geomathematics 3 The Journal of Mathematical Neuroscience 3 Statistics and Computing 3 Research in the Mathematical Sciences 3 Communications on Applied Mathematics and Computation 2 Computer Physics Communications 2 International Journal of Control 2 Journal of the Franklin Institute 2 Mathematical Methods in the Applied Sciences 2 Physica A 2 Physics Reports 2 Journal of Optimization Theory and Applications ...and 127 more Serials all top 5 Cited in 43 Fields 1,130 Numerical analysis (65-XX) 469 Partial differential equations (35-XX) 442 Probability theory and stochastic processes (60-XX) 366 Fluid mechanics (76-XX) 284 Statistics (62-XX) 207 Mechanics of deformable solids (74-XX) 97 Biology and other natural sciences (92-XX) 86 Systems theory; control (93-XX) 85 Computer science (68-XX) 71 Dynamical systems and ergodic theory (37-XX) 71 Calculus of variations and optimal control; optimization (49-XX) 67 Approximations and expansions (41-XX) 61 Ordinary differential equations (34-XX) 60 Operations research, mathematical programming (90-XX) 51 Geophysics (86-XX) 46 Optics, electromagnetic theory (78-XX) 40 Statistical mechanics, structure of matter (82-XX) 30 Classical thermodynamics, heat transfer (80-XX) 29 Mechanics of particles and systems (70-XX) 28 Information and communication theory, circuits (94-XX) 20 Special functions (33-XX) 20 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 17 Linear and multilinear algebra; matrix theory (15-XX) 17 Harmonic analysis on Euclidean spaces (42-XX) 8 Functional analysis (46-XX) 8 Operator theory (47-XX) 8 Quantum theory (81-XX) 7 Integral equations (45-XX) 5 Combinatorics (05-XX) 5 Global analysis, analysis on manifolds (58-XX) 3 General and overarching topics; collections (00-XX) 3 Mathematical logic and foundations (03-XX) 3 Real functions (26-XX) 2 Measure and integration (28-XX) 2 Functions of a complex variable (30-XX) 2 Difference and functional equations (39-XX) 2 Differential geometry (53-XX) 1 Number theory (11-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year