Edit Profile Hou, Thomas Yizhao Compute Distance To: Compute Author ID: hou.thomas-yizhao Published as: Hou, T.; Hou, T. Y.; Hou, T.-Y.; Hou, Th. Y.; Hou, Thomas; Hou, Thomas Y.; Hou, Thomas Yizhao Homepage: http://users.cms.caltech.edu/~hou/ External Links: MGP · Wikidata · dblp · GND Documents Indexed: 169 Publications since 1988, including 6 Books Biographic References: 1 Publication all top 5 Co-Authors 11 single-authored 18 Shi, Zuoqiang 14 Efendiev, Yalchin R. 14 Lowengrub, John Samuel 7 Liu, Pengfei 7 Yu, Xinwei 6 Ceniceros, Hector D. 6 Deng, Jian 6 Li, Ruo 6 Wu, Xiaohui 6 Zhang, Zhiwen 5 Beale, J. Thomas 5 Li, Congming 5 Luo, Guo 5 Shelley, Michael J. 5 Yang, Danping 5 Zhang, Pengchuan 5 Zhang, Pingwen 4 Goodman, Jonathan B. 4 Lei, Zhen 4 Wang, Shu 4 Zhou, Hao-Min 3 Cheng, Mulin 3 Lam, Ka Chun 3 LeFloch, Philippe Gerard 3 Li, Qin 3 Luo, Wuan 3 Ran, Hongyu 3 Rozovskii, Boris L. 3 Tavallali, Peyman 3 Wetton, Brian T. R. 2 Aarnes, Jørg E. 2 Caflisch, Russel E. 2 Chan, Tony Fan-Cheong 2 Dostert, Paul 2 Engquist, Bjorn E. 2 Ginting, Victor 2 Graham, Ivan G. 2 Hu, Gang 2 Hu, Xin 2 Huang, De 2 Kim, Hongjoong 2 Liu, Chunguang 2 Liu, Wing Kam 2 Osher, Stanley Joel 2 Schaeffer, Hayden 2 Si, Helen 2 Stredie, V. G. 2 Tadmor, Eitan 2 Tang, Shaoqiang 2 Wu, Theodore Yaotsu 2 Yan, Mike 2 Zhao, Hongkai 1 Alber, Mark S. 1 Avellaneda, Marco 1 Cai, Zhiqiang 1 Chacón Rebollo, Tomás 1 Chan, Raymond Hon-Fu 1 Chang, Yancheng 1 Chen, Xinfu 1 Chen, Yifan 1 Chen, Zhiming 1 Choi, Kyudong 1 Chu, Chenchen 1 Chung, Tsz Shun Eric 1 Ci, Maolin 1 Cottet, Georges-Henri 1 Daubechies, Ingrid Chantal 1 E, Weinan 1 Ercolani, Nicholas M. 1 Ewing, Richard Edward 1 Fetecau, Razvan C. 1 Galvis, Juan 1 Glazier, James A. 1 Huang, Norden E. 1 Hussain, Farzana 1 Hwang, Fengnan 1 Jiang, Lijian 1 Jiang, Yi 1 Jin, Tianling 1 Kiselev, Alexander A. 1 Klapper, Isaac 1 Koumoutsakos, Petros D. 1 Krasny, Robert 1 Lakkis, Omar 1 Landis, Yelena 1 Lax, Peter David 1 Li, Zhilin 1 Liang, Dong 1 Lin, Guang 1 Lions, Pierre-Louis 1 Liu, Chun 1 Liu, Jianguo 1 Ma, Dingjiong 1 Merriman, Barry 1 Papanicolaou, George C. 1 Park, Peter J. 1 Rosakis, Phoebus 1 Scheichl, Robert 1 Shelly, M. J. 1 Strinopoulos, T. ...and 17 more Co-Authors all top 5 Serials 26 Journal of Computational Physics 12 Communications on Pure and Applied Mathematics 12 Multiscale Modeling & Simulation 9 SIAM Journal on Numerical Analysis 8 Mathematics of Computation 7 Discrete and Continuous Dynamical Systems 5 Communications in Partial Differential Equations 4 Physics of Fluids 3 Methods and Applications of Analysis 3 Communications in Mathematical Sciences 3 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Archive for Rational Mechanics and Analysis 2 Journal of Computational Mathematics 2 Journal of Nonlinear Science 2 SIAM Journal on Scientific Computing 2 Applied and Computational Harmonic Analysis 2 Discrete and Continuous Dynamical Systems. Series B 2 Communications in Computational Physics 2 Advances in Adaptive Data Analysis 2 Science China. Mathematics 2 Research in the Mathematical Sciences 1 Communications in Mathematical Physics 1 Computer Methods in Applied Mechanics and Engineering 1 International Journal for Numerical Methods in Fluids 1 Journal of Fluid Mechanics 1 Nonlinearity 1 Advances in Mathematics 1 International Journal for Numerical Methods in Engineering 1 Numerische Mathematik 1 SIAM Journal on Scientific and Statistical Computing 1 Physica D 1 Applied Numerical Mathematics 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Acta Mathematicae Applicatae Sinica. English Series 1 Computational Mechanics 1 Mathematical and Computer Modelling 1 Journal of Scientific Computing 1 Proceedings of the National Academy of Sciences of the United States of America 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 SIAM Review 1 Documenta Mathematica 1 The Asian Journal of Mathematics 1 Computational Geosciences 1 HERMIS-\(\mu\pi\). Hellenic European Research on Mathematics and Informatics Science 1 International Journal of Computational Methods 1 Acta Numerica 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 1 Lecture Notes in Computational Science and Engineering 1 Surveys and Tutorials in the Applied Mathematical Sciences 1 Series in Contemporary Applied Mathematics CAM 1 Inverse Problems and Imaging 1 ICCM Notices 1 SIAM/ASA Journal on Uncertainty Quantification 1 Advances in Data Science and Adaptive Analysis all top 5 Fields 109 Fluid mechanics (76-XX) 86 Partial differential equations (35-XX) 80 Numerical analysis (65-XX) 13 Information and communication theory, circuits (94-XX) 11 Mechanics of deformable solids (74-XX) 8 General and overarching topics; collections (00-XX) 8 Probability theory and stochastic processes (60-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Statistics (62-XX) 2 Computer science (68-XX) 2 Biology and other natural sciences (92-XX) 1 History and biography (01-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 145 Publications have been cited 3,976 times in 2,301 Documents Cited by ▼ Year ▼ A multiscale finite element method for elliptic problems in composite materials and porous media. Zbl 0880.73065Hou, Thomas Y.; Wu, Xiao-Hui 499 1997 Multiscale finite element methods. Theory and applications. Zbl 1163.65080Efendiev, Yalchin; Hou, Thomas Y. 248 2009 A level set formulation of Eulerian interface capturing methods for incompressible fluid flows. Zbl 0847.76048Chang, Y. C.; Hou, T. Y.; Merriman, B.; Osher, S. 204 1996 Removing the stiffness from interfacial flows with surface tension. Zbl 0810.76095Hou, Thomas Y.; Lowengrub, John S.; Shelley, Michael J. 179 1994 Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Zbl 0922.65071Hou, Thomas Y.; Wu, Xiao-Hui; Cai, Zhiqiang 169 1999 Generalized multiscale finite element methods (GMsFEM). Zbl 1349.65617Efendiev, Yalchin; Galvis, Juan; Hou, Thomas Y. 164 2013 Global well-posedness of the viscous Boussinesq equations. Zbl 1274.76185Hou, Thomas Y.; Li, Congming 157 2005 A mixed multiscale finite element method for elliptic problems with oscillating coefficients. Zbl 1017.65088Chen, Zhiming; Hou, Thomas Y. 124 2003 Convergence of a nonconforming multiscale finite element method. Zbl 0951.65105Efendiev, Yalchin R.; Hou, Thomas Y.; Wu, Xiao-Hui 95 2000 A hybrid method for moving interface problems with application to the Hele-Shaw flow. Zbl 0888.76067Hou, Thomas Y.; Li, Zhilin; Osher, Stanley; Zhao, Hongkai 94 1997 Accurate multiscale finite element methods for two-phase flow simulations. Zbl 1158.76349Efendiev, Y.; Ginting, V.; Hou, T.; Ewing, R. 81 2006 Why nonconservative schemes converge to wrong solutions: Error analysis. Zbl 0809.65102Hou, Thomas Y.; Le Floch, Philippe G. 79 1994 A new multiscale finite element method for high-contrast elliptic interface problems. Zbl 1202.65154Chu, C.-C.; Graham, I. G.; Hou, T.-Y. 77 2010 Multiscale finite element methods for nonlinear problems and their applications. Zbl 1083.65105Efendiev, Yalchin R.; Hou, Thomas Yizhao; Ginting, Victor 67 2004 Analysis of upscaling absolute permeability. Zbl 1162.65327Wu, X. H.; Efendiev, Y.; Hou, T. Y. 61 2002 Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics. Zbl 1095.76047Hou, Thomas Y.; Luo, Wuan; Rozovskii, Boris; Zhou, Hao-Min 60 2006 An efficient dynamically adaptive mesh for potentially singular solutions. Zbl 0986.65087Ceniceros, Hector D.; Hou, Thomas Y. 58 2001 Growth rates for the linearized motion of fluid interfaces away from equilibrium. Zbl 0796.76041Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John S. 57 1993 The long-time motion of vortex sheets with surface tension. Zbl 1185.76545Hou, T. Y.; Lowengrub, J. S.; Shelly, M. J. 56 1997 Adaptive multiscale model reduction with generalized multiscale finite element methods. Zbl 1349.76191Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y. 54 2016 Computing nearly singular solutions using pseudo-spectral methods. Zbl 1310.76127Hou, Thomas Y.; Li, Ruo 54 2007 Boundary integral methods for multicomponent fluids and multiphase materials. Zbl 1046.76029Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J. 54 2001 Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible Euler equations. Zbl 1370.76015Hou, Thomas Y.; Li, Ruo 45 2006 Removing the cell resonance error in the multiscale finite element method via a Petrov-Galerkin formulation. Zbl 1085.65109Hou, Thomas Y.; Wu, Xiao-Hui; Zhang, Yu 44 2004 Geometric properties and nonblowup of 3D incompressible Euler flow. Zbl 1142.35549Deng, Jian; Hou, Thomas Y.; Yu, Xinwei 41 2005 Convergence of the point vortex method for the 2-D Euler equations. Zbl 0694.76013Goodman, Jonathan; Hou, Thomas Y.; Lowengrub, John 41 1990 Dynamic stability of the three-dimensional axisymmetric Navier-Stokes equations with swirl. Zbl 1138.35077Hou, Thomas Y.; Li, Congming 39 2008 Preconditioning Markov chain Monte Carlo simulations using coarse-scale models. Zbl 1111.65003Efendiev, Yalchin R.; Hou, Thomas Yizhao; Luo, Wu An 39 2006 Multiscale finite element methods for porous media flows and their applications. Zbl 1112.76046Efendiev, Yalchin R.; Hou, Thomas Yizhao 32 2007 Toward the finite-time blowup of the 3D axisymmetric Euler equations: a numerical investigation. Zbl 1316.35235Luo, Guo; Hou, Thomas Y. 31 2014 Multiscale domain decomposition methods for elliptic problems with high aspect ratios. Zbl 1003.65142Aarnes, Jørg; Hou, Thomas Y. 31 2002 Improved geometric conditions for non-blowup of the 3D incompressible Euler equation. Zbl 1158.76305Deng, Jian; Hou, Thomas Y.; Yu, Xinwei 30 2006 Convergence of a boundary integral method for water waves. Zbl 0858.76046Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John 30 1996 A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. I: Derivation and algorithms. Zbl 1297.65008Cheng, Mulin; Hou, Thomas Y.; Zhang, Zhiwen 29 2013 A mathematical framework of the bridging scale method. Zbl 1117.74056Tang, Shaoqiang; Hou, Thomas Y.; Liu, Wing Kam 28 2006 Global regularity of the 3D axi-symmetric Navier-Stokes equations with anisotropic data. Zbl 1146.76010Hou, Thomas Y.; Lei, Zhen; Li, Congming 26 2008 On the finite-time blowup of a one-dimensional model for the three-dimensional axisymmetric Euler equations. Zbl 1377.35218Choi, Kyudong; Hou, Thomas Y.; Kiselev, Alexander; Luo, Guo; Sverak, Vladimir; Yao, Yao 23 2017 A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. II: Adaptivity and generalizations. Zbl 1297.65007Cheng, Mulin; Hou, Thomas Y.; Zhang, Zhiwen 23 2013 Blowup or no blowup? the interplay between theory and numerics. Zbl 1143.76390Hou, Thomas Y.; Li, Ruo 21 2008 Dispersive approximations in fluid dynamics. Zbl 0729.76065Hou, Thomas Y.; Lax, Peter D. 21 1991 Multiscale finite element methods for stochastic porous media flow equations and application to uncertainty quantification. Zbl 1194.76112Dostert, P.; Efendiev, Y.; Hou, T. Y. 20 2008 A pseudo-spectral multiscale method: interfacial conditions and coarse grid equations. Zbl 1089.65110Tang, Shaoqiang; Hou, Thomas Y.; Liu, Wing Kam 20 2006 On the stabilizing effect of convection in three-dimensional incompressible flows. Zbl 1171.35095Hou, Thomas Y.; Lei, Zhen 19 2009 Data-driven time-frequency analysis. Zbl 1336.94019Hou, Thomas Y.; Shi, Zuoqiang 18 2013 Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier-Stokes equations. Zbl 1422.76041Hou, Thomas Y. 18 2009 Adaptive data analysis via sparse time-frequency representation. Zbl 1234.94015Hou, Thomas Y.; Shi, Zuoqiang 17 2011 An efficient semi-implicit immersed boundary method for the Navier-Stokes equations. Zbl 1161.76048Hou, Thomas Y.; Shi, Zuoqiang 17 2008 Coarse-gradient Langevin algorithms for dynamic data integration and uncertainty quantification. Zbl 1146.76637Dostert, P.; Efendiev, Y.; Hou, T. Y.; Luo, W. 16 2006 Multi-valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems. Zbl 0797.35007Caflisch, Russel E.; Ercolani, Nicholas; Hou, Thomas Y.; Landis, Yelena 16 1993 Homogenization of linear transport equations with oscillatory vector fields. Zbl 0759.35008Hou, Thomas Y.; Xin, Xue 15 1992 Numerical study of Hele-Shaw flow with suction. Zbl 1149.76335Ceniceros, Hector D.; Hou, Thomas Y.; Si, Helen 14 1999 Removing the stiffness of curvature in computing 3-D filaments. Zbl 0917.76063Hou, Thomas Y.; Klapper, Isaac; Si, Helen 14 1998 Computational method for propagating phase boundaries. Zbl 0855.73080Zhong, Xiaoguang; Hou, Thomas Y.; LeFloch, Philippe G. 14 1996 Removing the stiffness of elastic force from the immersed boundary method for the 2D Stokes equations. Zbl 1294.76201Hou, Thomas Y.; Shi, Zuoqiang 13 2008 Level set dynamics and the non-blowup of the 2D quasi-geostrophic equation. Zbl 1173.76006Deng, J.; Hou, T. Y.; Li, R.; Yu, X. 13 2006 Convergence of a non-stiff boundary integral method for interfacial flows with surface tension. Zbl 0905.76012Ceniceros, Héctor D.; Hou, Thomas Y. 13 1998 Geometry related convergence results for domain decomposition algorithms. Zbl 0724.65109Chan, Tony F.; Hou, Thomas Y.; Lions, P. L. 13 1991 On the partial regularity of a 3D model of the Navier-Stokes equations. Zbl 1176.35130Hou, Thomas Y.; Lei, Zhen 12 2009 Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations. Zbl 1194.35307Hou, Thomas Y.; Li, Ruo 12 2007 Multiscale numerical methods for singularly perturbed convection-diffusion equations. Zbl 1182.76902Park, Peter J.; Hou, Thomas Y. 12 2004 Convergence of a boundary integral method for 3-D water waves. Zbl 1131.76339Hou, Thomas Y.; Zhang, Pingwen 12 2002 Second-order convergence of a projection scheme for the incompressible Navier-Stokes equations with boundaries. Zbl 0776.76055Hou, Thomas Y.; Wetton, Brian T. R. 12 1993 Convergence of a variable blob vortex method for the Euler and Navier- Stokes equations. Zbl 0727.76034Hou, Thomas Y. 12 1990 Dynamic generation of capillary waves. Zbl 1147.76354Ceniceros, Hector D.; Hou, Thomas Y. 11 1999 Convergence of a finite difference scheme for the Navier-Stokes equations using vorticity boundary conditions. Zbl 0749.76046Hou, Thomas Y.; Wetton, Brian T. R. 11 1992 Convergence of the point vortex method for the 3-D Euler equations. Zbl 0856.76059Hou, Thomas Y.; Lowengrub, John 11 1990 Convergence of a data-driven time-frequency analysis method. Zbl 1336.94020Hou, Thomas Y.; Shi, Zuoqiang; Tavallali, Peyman 10 2014 A data-driven stochastic method for elliptic PDEs with random coefficients. Zbl 1290.60068Cheng, Mulin; Hou, Thomas Y.; Yan, Mike; Zhang, Zhiwen 10 2013 On singularity formation of a 3D model for incompressible Navier-Stokes equations. Zbl 1252.35219Hou, Thomas Y.; Shi, Zuoqiang; Wang, Shu 10 2012 A level-set approach to the computation of twinning and phase-transition dynamics. Zbl 0936.74052Hou, Thomas Y.; Rosakis, Phoebus; LeFloch, Philippe 10 1999 Optimal local multi-scale basis functions for linear elliptic equations with rough coefficients. Zbl 1333.65131Hou, Thomas Y.; Liu, Pengfei 9 2016 Self-similar singularity of a 1D model for the 3D axisymmetric Euler equations. Zbl 1320.35269Hou, Thomas Y.; Liu, Pengfei 9 2015 On finite time singularity and global regularity of an axisymmetric model for the 3D Euler equations. Zbl 1293.35228Hou, Thomas Y.; Lei, Zhen; Luo, Guo; Wang, Shu; Zou, Chen 9 2014 Numerical solutions to free boundary problems. Zbl 0831.65137Hou, Thomas Y. 9 1995 On the stability of the unsmoothed Fourier method for hyperbolic equations. Zbl 0791.65080Goodman, Jonathan; Hou, Thomas; Tadmor, Eitan 9 1994 Sparse operator compression of higher-order elliptic operators with rough coefficients. Zbl 1412.65215Hou, Thomas Y.; Zhang, Pengchuan 8 2017 On global well-posedness of the Lagrangian averaged Euler equations. Zbl 1111.76006Hou, Thomas Y.; Li, Congming 8 2006 Multiscale modelling and computation of fluid flow. Zbl 1134.76386Hou, Thomas Y. 8 2005 Well-posedness of linearized motion for 3-D water waves far from equilibrium. Zbl 0874.76014Hou, Thomas Y.; Teng, Zhenhuan; Zhang, Pingwen 8 1996 A heterogeneous stochastic FEM framework for elliptic PDEs. Zbl 1352.65510Hou, Thomas Y.; Liu, Pengfei 7 2015 The singular perturbation of surface tension in Hele-Shaw flows. Zbl 0991.76020Ceniceros, Hector D.; Hou, Thomas Y. 7 2000 An efficient boundary integral method for the Mullins-Sekerka problem. Zbl 0879.65092Zhu, Jingyi; Chen, Xinfu; Hou, Thomas Y. 7 1996 Spatial and temporal stability issues for interfacial flows with surface tension. Zbl 0816.76050Beale, J. T.; Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J. 7 1994 Convergence of a point vortex method for vortex sheets. Zbl 0799.76062Hou, Thomas Y.; Lowengrub, John; Krasny, Robert 7 1991 Particle method approximation of oscillatory solutions to hyperbolic differential equations. Zbl 0675.65093Engquist, Bjorn; Hou, Thomas Y. 7 1989 Sparse + low-energy decomposition for viscous conservation laws. Zbl 1352.65413Hou, Thomas Y.; Li, Qin; Schaeffer, Hayden 6 2015 On singularity formation of a nonlinear nonlocal system. Zbl 1241.35038Hou, Thomas Y.; Li, Congming; Shi, Zuoqiang; Wang, Shu; Yu, Xinwei 6 2011 Numerical approximations to multiscale solutions in partial differential equations. Zbl 1027.65154Hou, Thomas Y. 6 2003 New stability estimates for the 2-D vortex method. Zbl 0745.76061Goodman, Jonathan; Hou, Thomas Y. 6 1991 Convergence of the grid-free point vortex method for the three-dimensional Euler equations. Zbl 0850.76489Cottet, Georges-Henri; Goodman, Jonathan; Hou, Thomas Y. 6 1991 Exploring the locally low dimensional structure in solving random elliptic PDEs. Zbl 1365.65015Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan 5 2017 A sparse decomposition of low rank symmetric positive semidefinite matrices. Zbl 1386.65127Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan 5 2017 Potentially singular solutions of the 3D axisymmetric Euler equations. Zbl 1431.35115Luo, Guo; Hou, Thomas Y. 5 2014 Finite difference approximations for partial differential equations with rapidly oscillating coefficients. Zbl 0755.65088Avellaneda, M.; Hou, Th. Y.; Papanicolaou, G. C. 5 1991 A Lagrangian finite element method for the 2-D Euler equations. Zbl 0705.76059Chacon-Rebollo, Tomas; Hou, Thomas Y. 5 1990 A model reduction method for multiscale elliptic PDEs with random coefficients using an optimization approach. Zbl 1420.35083Hou, Thomas Y.; Ma, Dingjiong; Zhang, Zhiwen 4 2019 Extracting a shape function for a signal with intra-wave frequency modulation. Zbl 1353.94017Hou, Thomas Y.; Shi, Zuoqiang 4 2016 Extraction of intrawave signals using the sparse time-frequency representation method. Zbl 1380.94062Tavallali, Peyman; Hou, Thomas Y.; Shi, Zuoqiang 4 2014 Stable fourth-order stream-function methods for incompressible flows with boundaries. Zbl 1212.65318Hou, Thomas Y.; Wetton, Brian R. 4 2009 Multiscale analysis and computation for the three-dimensional incompressible Navier-Stokes equations. Zbl 1248.76037Hou, Thomas Y.; Yang, Danping; Ran, Hongyu 4 2008 A model reduction method for multiscale elliptic PDEs with random coefficients using an optimization approach. Zbl 1420.35083Hou, Thomas Y.; Ma, Dingjiong; Zhang, Zhiwen 4 2019 Formation of finite-time singularities in the 3D axisymmetric Euler equations: a numerics guided study. Zbl 1427.35190Luo, Guo; Hou, Thomas Y. 1 2019 A fast hierarchically preconditioned eigensolver based on multiresolution matrix decomposition. Zbl 07033876Hou, Thomas Y.; Huang, De; Lam, Ka Chun; Zhang, Ziyun 1 2019 An adaptive fast solver for a general class of positive definite matrices via energy decomposition. Zbl 1391.65066Hou, Thomas Y.; Huang, De; Lam, Ka Chun; Zhang, PengChuan 2 2018 Global regularity for a family of 3D models of the axi-symmetric Navier-Stokes equations. Zbl 1393.35170Hou, Thomas Y.; Liu, Pengfei; Wang, Fei 1 2018 On the finite-time blowup of a one-dimensional model for the three-dimensional axisymmetric Euler equations. Zbl 1377.35218Choi, Kyudong; Hou, Thomas Y.; Kiselev, Alexander; Luo, Guo; Sverak, Vladimir; Yao, Yao 23 2017 Sparse operator compression of higher-order elliptic operators with rough coefficients. Zbl 1412.65215Hou, Thomas Y.; Zhang, Pengchuan 8 2017 Exploring the locally low dimensional structure in solving random elliptic PDEs. Zbl 1365.65015Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan 5 2017 A sparse decomposition of low rank symmetric positive semidefinite matrices. Zbl 1386.65127Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan 5 2017 An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients. Zbl 1380.65268Hou, Thomas Y.; Hwang, Feng-Nan; Liu, Pengfei; Yao, Chien-Chou 3 2017 Discrete maximum-norm stability of a linearized second-order finite difference scheme for Allen-Cahn equation. Zbl 1399.65211Hou, T.; Wang, K.; Xiong, Y.; Xiao, X.; Zhang, Sh. 1 2017 Sparse time-frequency decomposition for multiple signals with same frequencies. Zbl 1378.94007Hou, Thomas Y.; Shi, Zuoqiang 1 2017 Adaptive multiscale model reduction with generalized multiscale finite element methods. Zbl 1349.76191Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y. 54 2016 Optimal local multi-scale basis functions for linear elliptic equations with rough coefficients. Zbl 1333.65131Hou, Thomas Y.; Liu, Pengfei 9 2016 Extracting a shape function for a signal with intra-wave frequency modulation. Zbl 1353.94017Hou, Thomas Y.; Shi, Zuoqiang 4 2016 An accelerated method for nonlinear elliptic PDE. Zbl 1368.65004Schaeffer, Hayden; Hou, Thomas Y. 3 2016 A model reduction method for elliptic PDEs with random input using the heterogeneous stochastic FEM framework. Zbl 1341.65004Hou, Thomas Y.; Liu, Pengfei; Zhang, Zhiwen 3 2016 Sparse time-frequency decomposition based on dictionary adaptation. Zbl 1353.42016Hou, Thomas Y.; Shi, Zuoqiang 2 2016 Adaptive data analysis: theory and applications. Theme issue. Zbl 1354.00073Huang, Norden E. (ed.); Daubechies, Ingrid (ed.); Hou, Thomas Y. (ed.) 1 2016 Self-similar singularity of a 1D model for the 3D axisymmetric Euler equations. Zbl 1320.35269Hou, Thomas Y.; Liu, Pengfei 9 2015 A heterogeneous stochastic FEM framework for elliptic PDEs. Zbl 1352.65510Hou, Thomas Y.; Liu, Pengfei 7 2015 Sparse + low-energy decomposition for viscous conservation laws. Zbl 1352.65413Hou, Thomas Y.; Li, Qin; Schaeffer, Hayden 6 2015 Sparse time frequency representations and dynamical systems. Zbl 1346.37062Hou, Thomas Y.; Shi, Zuoqiang; Tavallali, Peyman 3 2015 On the uniqueness of sparse time-frequency representation of multiscale data. Zbl 1357.94035Liu, Chunguang; Shi, Zuoqiang; Hou, Thomas Y. 2 2015 Toward the finite-time blowup of the 3D axisymmetric Euler equations: a numerical investigation. Zbl 1316.35235Luo, Guo; Hou, Thomas Y. 31 2014 Convergence of a data-driven time-frequency analysis method. Zbl 1336.94020Hou, Thomas Y.; Shi, Zuoqiang; Tavallali, Peyman 10 2014 On finite time singularity and global regularity of an axisymmetric model for the 3D Euler equations. Zbl 1293.35228Hou, Thomas Y.; Lei, Zhen; Luo, Guo; Wang, Shu; Zou, Chen 9 2014 Potentially singular solutions of the 3D axisymmetric Euler equations. Zbl 1431.35115Luo, Guo; Hou, Thomas Y. 5 2014 Extraction of intrawave signals using the sparse time-frequency representation method. Zbl 1380.94062Tavallali, Peyman; Hou, Thomas Y.; Shi, Zuoqiang 4 2014 An adaptive ANOVA-based data-driven stochastic method for elliptic PDEs with random coefficient. Zbl 1388.65178Zhang, Zhiwen; Hu, Xin; Hou, Thomas Y.; Lin, Guang; Yan, Mike 3 2014 A multiscale model reduction method for partial differential equations. Zbl 1312.65206Ci, Maolin; Hou, Thomas Y.; Shi, Zuoqiang 2 2014 Generalized multiscale finite element methods (GMsFEM). Zbl 1349.65617Efendiev, Yalchin; Galvis, Juan; Hou, Thomas Y. 164 2013 A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. I: Derivation and algorithms. Zbl 1297.65008Cheng, Mulin; Hou, Thomas Y.; Zhang, Zhiwen 29 2013 A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. II: Adaptivity and generalizations. Zbl 1297.65007Cheng, Mulin; Hou, Thomas Y.; Zhang, Zhiwen 23 2013 Data-driven time-frequency analysis. Zbl 1336.94019Hou, Thomas Y.; Shi, Zuoqiang 18 2013 A data-driven stochastic method for elliptic PDEs with random coefficients. Zbl 1290.60068Cheng, Mulin; Hou, Thomas Y.; Yan, Mike; Zhang, Zhiwen 10 2013 Sparse time-frequency representation of nonlinear and nonstationary data. Zbl 1304.65282Hou, Thomas Yizhao; Shi, Zuoqiang 3 2013 Multiscale modeling of incompressible turbulent flows. Zbl 1291.76241Hou, T. Y.; Hu, X.; Hussain, F. 1 2013 On singularity formation of a 3D model for incompressible Navier-Stokes equations. Zbl 1252.35219Hou, Thomas Y.; Shi, Zuoqiang; Wang, Shu 10 2012 Numerical analysis of multiscale problems. Selected papers based on the presentations at the 91st London Mathematical Society symposium, Durham, UK, July 5–15, 2010. Zbl 1234.65007Graham, Ivan G. (ed.); Hou, Thomas Y. (ed.); Lakkis, Omar (ed.); Scheichl, Robert (ed.) 3 2012 Dynamic growth estimates of maximum vorticity for 3D incompressible Euler equations and the SQG model. Zbl 1237.76014Hou, Thomas Y.; Shi, Zuoqiang 1 2012 Adaptive data analysis via sparse time-frequency representation. Zbl 1234.94015Hou, Thomas Y.; Shi, Zuoqiang 17 2011 On singularity formation of a nonlinear nonlocal system. Zbl 1241.35038Hou, Thomas Y.; Li, Congming; Shi, Zuoqiang; Wang, Shu; Yu, Xinwei 6 2011 A new multiscale finite element method for high-contrast elliptic interface problems. Zbl 1202.65154Chu, C.-C.; Graham, I. G.; Hou, T.-Y. 77 2010 Multiscale finite element methods. Theory and applications. Zbl 1163.65080Efendiev, Yalchin; Hou, Thomas Y. 248 2009 On the stabilizing effect of convection in three-dimensional incompressible flows. Zbl 1171.35095Hou, Thomas Y.; Lei, Zhen 19 2009 Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier-Stokes equations. Zbl 1422.76041Hou, Thomas Y. 18 2009 On the partial regularity of a 3D model of the Navier-Stokes equations. Zbl 1176.35130Hou, Thomas Y.; Lei, Zhen 12 2009 Stable fourth-order stream-function methods for incompressible flows with boundaries. Zbl 1212.65318Hou, Thomas Y.; Wetton, Brian R. 4 2009 Multiscale analysis for convection-dominated transport equations. Zbl 1163.76048Hou, Thomas Y.; Liang, Dong 3 2009 Dynamic stability of the three-dimensional axisymmetric Navier-Stokes equations with swirl. Zbl 1138.35077Hou, Thomas Y.; Li, Congming 39 2008 Global regularity of the 3D axi-symmetric Navier-Stokes equations with anisotropic data. Zbl 1146.76010Hou, Thomas Y.; Lei, Zhen; Li, Congming 26 2008 Blowup or no blowup? the interplay between theory and numerics. Zbl 1143.76390Hou, Thomas Y.; Li, Ruo 21 2008 Multiscale finite element methods for stochastic porous media flow equations and application to uncertainty quantification. Zbl 1194.76112Dostert, P.; Efendiev, Y.; Hou, T. Y. 20 2008 An efficient semi-implicit immersed boundary method for the Navier-Stokes equations. Zbl 1161.76048Hou, Thomas Y.; Shi, Zuoqiang 17 2008 Removing the stiffness of elastic force from the immersed boundary method for the 2D Stokes equations. Zbl 1294.76201Hou, Thomas Y.; Shi, Zuoqiang 13 2008 Multiscale analysis and computation for the three-dimensional incompressible Navier-Stokes equations. Zbl 1248.76037Hou, Thomas Y.; Yang, Danping; Ran, Hongyu 4 2008 Multiscale simulations of porous media flows in flow-based coordinate system. Zbl 1155.76050Efendiev, Yalchin R.; Hou, Thomas Yizhao; Strinopoulos, T. 3 2008 Computing nearly singular solutions using pseudo-spectral methods. Zbl 1310.76127Hou, Thomas Y.; Li, Ruo 54 2007 Multiscale finite element methods for porous media flows and their applications. Zbl 1112.76046Efendiev, Yalchin R.; Hou, Thomas Yizhao 32 2007 Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations. Zbl 1194.35307Hou, Thomas Y.; Li, Ruo 12 2007 Mathematical modeling and simulation of aquatic and aerial animal locomotion. Zbl 1343.76074Hou, T. Y.; Stredie, V. G.; Wu, T. Y. 3 2007 Accurate multiscale finite element methods for two-phase flow simulations. Zbl 1158.76349Efendiev, Y.; Ginting, V.; Hou, T.; Ewing, R. 81 2006 Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics. Zbl 1095.76047Hou, Thomas Y.; Luo, Wuan; Rozovskii, Boris; Zhou, Hao-Min 60 2006 Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible Euler equations. Zbl 1370.76015Hou, Thomas Y.; Li, Ruo 45 2006 Preconditioning Markov chain Monte Carlo simulations using coarse-scale models. Zbl 1111.65003Efendiev, Yalchin R.; Hou, Thomas Yizhao; Luo, Wu An 39 2006 Improved geometric conditions for non-blowup of the 3D incompressible Euler equation. Zbl 1158.76305Deng, Jian; Hou, Thomas Y.; Yu, Xinwei 30 2006 A mathematical framework of the bridging scale method. Zbl 1117.74056Tang, Shaoqiang; Hou, Thomas Y.; Liu, Wing Kam 28 2006 A pseudo-spectral multiscale method: interfacial conditions and coarse grid equations. Zbl 1089.65110Tang, Shaoqiang; Hou, Thomas Y.; Liu, Wing Kam 20 2006 Coarse-gradient Langevin algorithms for dynamic data integration and uncertainty quantification. Zbl 1146.76637Dostert, P.; Efendiev, Y.; Hou, T. Y.; Luo, W. 16 2006 Level set dynamics and the non-blowup of the 2D quasi-geostrophic equation. Zbl 1173.76006Deng, J.; Hou, T. Y.; Li, R.; Yu, X. 13 2006 On global well-posedness of the Lagrangian averaged Euler equations. Zbl 1111.76006Hou, Thomas Y.; Li, Congming 8 2006 A 3D numerical method for studying vortex formation behind a moving plate. Zbl 1218.76034Hou, T. Y.; Stredie, V. G.; Wu, T. Y. 4 2006 A framework for modeling subgrid effects for two-phase flows in porous media. Zbl 1127.76064Hou, Thomas Y.; Westhead, Andrew; Yang, Danping 2 2006 Global well-posedness of the viscous Boussinesq equations. Zbl 1274.76185Hou, Thomas Y.; Li, Congming 157 2005 Geometric properties and nonblowup of 3D incompressible Euler flow. Zbl 1142.35549Deng, Jian; Hou, Thomas Y.; Yu, Xinwei 41 2005 Multiscale modelling and computation of fluid flow. Zbl 1134.76386Hou, Thomas Y. 8 2005 A level set formulation for the 3D incompressible Euler equations. Zbl 1107.76011Deng, Jian; Hou, Thomas Y.; Yu, Xinwei 2 2005 Multiscale finite element methods for nonlinear problems and their applications. Zbl 1083.65105Efendiev, Yalchin R.; Hou, Thomas Yizhao; Ginting, Victor 67 2004 Removing the cell resonance error in the multiscale finite element method via a Petrov-Galerkin formulation. Zbl 1085.65109Hou, Thomas Y.; Wu, Xiao-Hui; Zhang, Yu 44 2004 Multiscale numerical methods for singularly perturbed convection-diffusion equations. Zbl 1182.76902Park, Peter J.; Hou, Thomas Y. 12 2004 Multiscale modelling and computation of incompressible flow. Zbl 1181.76096Hou, Thomas Y. 1 2004 Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics. Zbl 1130.76411Hou, Thomas Y.; Kim, Hongjoong; Rozovskii, Boris; Zhou, Hao-Min 1 2004 Homogenization of incompressible Euler equations. Zbl 1104.76054Hou, Thomas Y.; Yang, Danping; Wang, Ke 1 2004 A mixed multiscale finite element method for elliptic problems with oscillating coefficients. Zbl 1017.65088Chen, Zhiming; Hou, Thomas Y. 124 2003 Numerical approximations to multiscale solutions in partial differential equations. Zbl 1027.65154Hou, Thomas Y. 6 2003 Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics. Zbl 1130.76410Hou, Thomas Y.; Kim, Hongjoong; Rozovski, Boris; Zhou, Hao-Min 4 2003 A nearly optimal existence result for slightly perturbed 3-D vortex sheets. Zbl 1094.76014Hou, Thomas Y.; Hu, Gang 3 2003 Analysis of upscaling absolute permeability. Zbl 1162.65327Wu, X. H.; Efendiev, Y.; Hou, T. Y. 61 2002 Multiscale domain decomposition methods for elliptic problems with high aspect ratios. Zbl 1003.65142Aarnes, Jørg; Hou, Thomas Y. 31 2002 Convergence of a boundary integral method for 3-D water waves. Zbl 1131.76339Hou, Thomas Y.; Zhang, Pingwen 12 2002 Singularity formation in three-dimensional vortex sheets. Zbl 1185.76172Hou, Thomas Y.; Hu, Gang; Zhang, Pingwen 4 2002 An efficient dynamically adaptive mesh for potentially singular solutions. Zbl 0986.65087Ceniceros, Hector D.; Hou, Thomas Y. 58 2001 Boundary integral methods for multicomponent fluids and multiphase materials. Zbl 1046.76029Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J. 54 2001 Numerical study of interfacial problems with small surface tension. Zbl 1288.76050Ceniceros, Hector D.; Hou, Thomas Y. 2 2001 Convergence of a nonconforming multiscale finite element method. Zbl 0951.65105Efendiev, Yalchin R.; Hou, Thomas Y.; Wu, Xiao-Hui 95 2000 The singular perturbation of surface tension in Hele-Shaw flows. Zbl 0991.76020Ceniceros, Hector D.; Hou, Thomas Y. 7 2000 Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Zbl 0922.65071Hou, Thomas Y.; Wu, Xiao-Hui; Cai, Zhiqiang 169 1999 Numerical study of Hele-Shaw flow with suction. Zbl 1149.76335Ceniceros, Hector D.; Hou, Thomas Y.; Si, Helen 14 1999 Dynamic generation of capillary waves. Zbl 1147.76354Ceniceros, Hector D.; Hou, Thomas Y. 11 1999 ...and 45 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,358 Authors 71 Hou, Thomas Yizhao 69 Chung, Tsz Shun Eric 53 Efendiev, Yalchin R. 26 Wu, Jiahong 24 Vasilyeva, Maria V. 23 Cui, Junzhi 22 Chae, Dongho 22 Leung, Wingtat 22 Lowengrub, John Samuel 20 Galvis, Juan 20 Hajibeygi, Hadi 19 Abdulle, Assyr 19 Li, Zhilin 18 Gancedo, Francisco 18 Jiang, Lijian 16 Cordoba, Diego 16 Jenny, Patrick 15 Ceniceros, Hector D. 15 Fu, Shubin 15 Shelley, Michael J. 15 Ye, Zhuan 14 Osher, Stanley Joel 14 Tchelepi, Hamdi A. 14 Valentin, Frédéric 13 Cao, Liqun 13 Peterseim, Daniel 12 Shi, Zuoqiang 12 Wheeler, Mary Fanett 12 Xu, Xiaojing 11 Ambrose, David M. 11 Målqvist, Axel 11 Ohlberger, Mario 11 Presho, Michael 11 Zhang, Zhiwen 10 Babuška, Ivo 10 Kim, Junseok 10 Li, Qin 10 Li, Shuwang 10 Lin, Tao 10 Zabaras, Nicholas J. 9 Calo, Victor Manuel 9 Henning, Patrick 9 Hoang, Viet Ha 9 Lei, Zhen 9 Li, Guanglian 9 Lie, Knut-Andreas 9 Liu, Jianguo 9 Nie, Qing 9 Wei, Guowei 9 Zhao, Hongkai 8 Cao, Chongsheng 8 Castro, Ángel 8 Chen, Jinru 8 Constantin, Peter 8 Fedkiw, Ronald P. 8 Ginting, Victor 8 He, Wenming 8 Jabin, Pierre-Emmanuel 8 Kukavica, Igor 8 Le Bris, Claude 8 LeFloch, Philippe Gerard 8 Owhadi, Houman 8 Reusken, Arnold 8 Tang, Shaoqiang 8 Wang, Yating 8 Zhang, Pingwen 7 Beale, J. Thomas 7 Brown, Donald L. 7 Caflisch, Russel E. 7 Cheung, Siu Wun 7 Cottet, Georges-Henri 7 Deng, Weibing 7 Gómez-Serrano, Javier 7 Heinlein, Alexander 7 Karniadakis, George Em 7 Legoll, Frédéric 7 Li, Ruo 7 Liu, Chun 7 Liu, Wing Kam 7 Lu, Jianfeng 7 Ma, Qiang 7 Protas, Bartosz 7 Pun, Saimang 7 Schaeffer, Hayden 7 Scheichl, Robert 7 Sethian, James A. 7 Shu, Chi-Wang 7 Tang, Huazhong 7 Tang, Tao 7 Titi, Edriss Saleh 7 Yang, Zhiqiang 7 Yotov, Ivan 7 Zhao, Kun 6 Campos Pinto, Martin 6 Dong, Hao 6 Du, Qiang 6 Fish, Jacob 6 Ganapathysubramanian, Baskar 6 Harder, Christopher 6 Kang, Myungjoo ...and 3,258 more Authors all top 5 Cited in 250 Serials 470 Journal of Computational Physics 124 Journal of Computational and Applied Mathematics 122 Computer Methods in Applied Mechanics and Engineering 67 Journal of Fluid Mechanics 64 Multiscale Modeling & Simulation 55 Journal of Scientific Computing 55 Computational Geosciences 53 Computers and Fluids 53 Physics of Fluids 41 Journal of Differential Equations 38 Computers & Mathematics with Applications 38 International Journal for Numerical Methods in Engineering 38 SIAM Journal on Scientific Computing 36 Physica D 35 Applied Numerical Mathematics 33 Archive for Rational Mechanics and Analysis 29 Mathematics of Computation 28 Computational Mechanics 26 Journal of Mathematical Analysis and Applications 26 Applied Mathematics and Computation 24 Communications in Mathematical Physics 24 Numerische Mathematik 23 Nonlinear Analysis. 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