Hou, Thomas Y. (2022) Potential Singularity of the 3D Euler Equations in the Interior Domain Foundations of Computational Mathematics; (In Press)

Hou, Thomas Y. (2022) Potentially Singular Behavior of the 3D Navier-Stokes Equations Foundations of Computational Mathematics; (In Press)

Hou, Thomas Y.; Huang, De (2022) A potential two-scale traveling wave singularity for 3D incompressible Euler equations Physica D; Vol. 435;

Chen, Jiajie; Hou, Thomas Y. et al. (2022) Asymptotically self-similar blowup of the Hou-Luo model for the 3D Euler equations Annals of PDE; Vol. 8; No. 2;

Chen, Yifan; Hou, Thomas Y. (2022) Multiscale Elliptic PDE Upscaling and Function Approximation via Subsampled Data Multiscale Modeling and Simulation; Vol. 20; No. 1;

Zhang, Shumao; Zhang, Pengchuan et al. (2021) Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference Proceedings of Machine Learning Research; Vol. 139; 38th International Conference on Machine Learning, 18-24 July 2021 , [Online Only]

Chen, Yifan; Hou, Thomas Y. et al. (2021) Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions Multiscale Modeling and Simulation; Vol. 19; No. 2;

Chen, Jiajie; Hou, Thomas Y. et al. (2021) On the Finite Time Blowup of the De Gregorio Model for the 3D Euler Equations Communications on Pure and Applied Mathematics; Vol. 74; No. 6;

Chen, Jiajie; Hou, Thomas Y. (2021) Finite Time Blowup of 2D Boussinesq and 3D Euler Equations with C^(1,α) Velocity and Boundary Communications in Mathematical Physics; Vol. 383; No. 3;

Chen, Yifan; Hou, Thomas Y. (2021) Function approximation via the subsampled Poincaré inequality Discrete and Continuous Dynamical Systems - Series A; Vol. 41; No. 1;

Chen, Jiajie; Hou, Anthony et al. (2020) A prototype knockoff filter for group selection with FDR control Information and Inference; Vol. 9; No. 2;

Zhang, Zhiwen; Rosakis, Phoebus et al. (2020) A Minimal Mechanosensing Model Predicts Keratocyte Evolution on Flexible Substrates Journal of the Royal Society Interface; Vol. 17; No. 166;

Luo, Guo; Hou, Thomas Y. (2019) Formation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: A Numerics Guided Study SIAM Review; Vol. 61; No. 4;

Hou, Thomas Y.; Lam, Ka Chun et al. (2019) Solving Bayesian inverse problems from the perspective of deep generative networks Computational Mechanics; Vol. 64; No. 2;

Hou, Thomas Y.; Ma, Dingjiong et al. (2019) A Model Reduction Method for Multiscale Elliptic Pdes with Random Coefficients Using an Optimization Approach Multiscale Modeling and Simulation; Vol. 17; No. 2;

Chen, Jiajie; Hou, Anthony et al. (2019) A pseudo knockoff filter for correlated features Information and Inference; Vol. 8; No. 2;

Hou, Thomas Y.; Huang, De et al. (2019) A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition Multiscale Modeling and Simulation; Vol. 17; No. 1;

Hou, Thomas Y.; Jin, Tianling et al. (2018) Potential Singularity for a Family of Models of the Axisymmetric Incompressible Flow Journal of Nonlinear Science; Vol. 28; No. 6;

Hou, Thomas Y.; Liu, Pengfei et al. (2018) Global regularity for a family of 3D models of the axi-symmetric Navier–Stokes equations Nonlinearity; Vol. 31; No. 5;

Hou, Thomas Y.; Huang, De et al. (2018) An Adaptive Fast Solver for a General Class of Positive Definite Matrices Via Energy Decomposition Multiscale Modeling and Simulation; Vol. 16; No. 2;

Hou, Thomas Y.; Zhang, Pengchuan (2017) Sparse operator compression of higher-order elliptic operators with rough coefficients Research in the Mathematical Sciences; Vol. 4; No. 1;

Choi, Kyudong; Hou, Thomas Y. et al. (2017) On the Finite-Time Blowup of a One-Dimensional Model for the Three-Dimensional Axisymmetric Euler Equations Communications on Pure and Applied Mathematics; Vol. 70; No. 11;

Liu, ChunGuang; Shi, ZuoQiang et al. (2017) A two-level method for sparse time-frequency representation of multiscale data Science China Mathematics; Vol. 60; No. 10;

Hou, Thomas Y.; Hwang, Feng-Nan et al. (2017) An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients Journal of Computational Physics; Vol. 336;

Hou, Thomas Y.; Li, Qin et al. (2017) Exploring the locally low dimensional structure in solving random elliptic PDEs Multiscale Modeling & Simulation; Vol. 15; No. 2;

Hou, Thomas Y.; Li, Qin et al. (2017) A sparse decomposition of low rank symmetric positive semi-definite matrices Multiscale Modeling and Simulation; Vol. 15; No. 1;

Bao, Yuequan; Shi, Zuoqiang et al. (2017) Identification of time-varying cable tension forces based on adaptive sparse time-frequency analysis of cable vibrations Structural Control and Health Monitoring; Vol. 24; No. 3;

Schaeffer, Hayden; Hou, Thomas Y. (2016) An Accelerated Method for Nonlinear Elliptic PDE Journal of Scientific Computing; Vol. 69; No. 2;

Chung, Eric; Efendiev, Yalchin et al. (2016) Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods Journal of Computational Physics; Vol. 320;

Hou, Thomas Y.; Liu, Pengfei (2016) Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficient Discrete and Continuous Dynamical Systems; Vol. 36; No. 8;

Huang, Norden E.; Daubechies, Ingrid et al. (2016) Adaptive data analysis: theory and applications Philosophical Transactions A: Mathematical, Physical and Engineering Sciences; Vol. 374; No. 2065;

Hou, Thomas Y.; Shi, Zuoqiang (2016) Extracting a shape function for a signal with intra-wave frequency modulation Philosophical Transactions A: Mathematical, Physical and Engineering Sciences; Vol. 374; No. 2065;

Hou, Thomas Y.; Shi, Zuoqiang (2016) Sparse time-frequency decomposition based on dictionary adaptation Philosophical Transactions A: Mathematical, Physical and Engineering Sciences; Vol. 374; No. 2065;

Hou, Thomas Y.; Liu, Pengfei et al. (2016) A Model Reduction Method for Elliptic PDEs with Random Input Using the Heterogeneous Stochastic FEM Framework Bulletin of the Intitute of Mathematics Academia Sinica; Vol. 11; No. 1;

Tavallali, Peyman; Hou, Thomas Y. et al. (2015) On the convergence and accuracy of the cardiovascular intrinsic frequency method Royal Society Open Science; Vol. 2; No. 12;

Liu, Chunguang; Shi, Zuoqiang et al. (2015) On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data Multiscale Modeling and Simulation; Vol. 13; No. 3;

Zhang, Zhiwen; Ci, Maolin et al. (2015) A Multiscale Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients Multiscale Modeling and Simulation; Vol. 13; No. 1;

Hou, Thomas Y.; Liu, Pengfei (2015) A heterogeneous stochastic FEM framework for elliptic PDEs Journal of Computational Physics; Vol. 281;

Hou, Thomas Y.; Shi, Zuoqiang et al. (2015) Sparse Time Frequency Representations and Dynamical Systems Communications in Mathematical Sciences; Vol. 13; No. 3;

Tavallali, Peyman; Hou, Thomas Y. et al. (2014) Extraction of Intrawave Signals Using the Sparse Time-Frequency Representation Method Multiscale Modeling and Simulation; Vol. 12; No. 4;

Luo, Guo; Hou, Thomas Y. (2014) Potentially singular solutions of the 3D axisymmetric Euler equations Proceedings of the National Academy of Sciences of the United States of America; Vol. 111; No. 36;

Zhang, Zhiwen; Hu, Xin et al. (2014) Adaptive ANOVA-Based Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficient Communications in Computational Physics; Vol. 16; No. 3;

Hou, Thomas Y.; Shi, Zuoqiang et al. (2014) Convergence of a data-driven time–frequency analysis method Applied and Computational Harmonic Analysis; Vol. 37; No. 2;

Pahlevan, Niema M.; Tavallali, Peyman et al. (2014) Intrinsic frequency for a systems approach to haemodynamic waveform analysis with clinical applications Journal of the Royal Society Interface; Vol. 11; No. 98;

Hou, Thomas Y.; Lei, Zhen et al. (2014) On Finite Time Singularity and Global Regularity of an Axisymmetric Model for the 3D Euler Equations Archive for Rational Mechanics and Analysis; Vol. 212; No. 2;

Luo, Guo; Hou, Thomas Y. (2014) Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation Multiscale Modeling & Simulation; Vol. 12; No. 4;

Ci, Maolin; Hou, Thomas Y. et al. (2014) A Multiscale Model Reduction Method for Partial Differential Equations ESAIM-Mathematical Modelling and Numerical Analysis; Vol. 48; No. 2;

Hou, Thomas Yizhao; Shi, Zuoqiang (2013) Sparse time-frequency representation of nonlinear and nonstationary data Science China Mathematics; Vol. 56; No. 12;

Efendiev, Yalchin; Galvis, Juan et al. (2013) Generalized multiscale finite element methods (GMsFEM) Journal of Computational Physics; Vol. 251;

Shi, Yuan; Li, King-Fai et al. (2013) A decadal microwave record of tropical air temperature from AMSU-A/aqua observations Climate Dynamics; Vol. 41; No. 5-6;

Hou, Thomas Y.; Shi, Zuoqiang (2013) Data-driven time–frequency analysis Applied and Computational Harmonic Analysis; Vol. 35; No. 2;

Cheng, Mulin; Hou, Thomas Y. et al. (2013) A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations I: Derivation and algorithms Journal of Computational Physics; Vol. 242;

Cheng, Mulin; Hou, Thomas Y. et al. (2013) A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations II: Adaptivity and generalizations Journal of Computational Physics; Vol. 242;

Hou, T. Y.; Hu, X. et al. (2013) Multiscale modeling of incompressible turbulent flows Journal of Computational Physics; Vol. 232; No. 1;

Miller, Cass T.; Dawson, Clint N. et al. (2013) Numerical simulation of water resources problems: Models, methods, and trends Advances in Water Resources; Vol. 51;

Hou, Thomas Y.; Shi, Zuoqiang et al. (2012) On singularity formation of a 3D model for incompressible Navier–Stokes equations Advances in Mathematics; Vol. 230; No. 2;

Hou, Thomas Y.; Shi, Zuoqiang (2012) Dynamic growth estimates of maximum vorticity for 3D incompressible Euler equations and the SQG model Discrete and Continuous Dynamical Systems; Vol. 32; No. 5;

Hou, Thomas Y.; Shi, Zuoqiang (2011) Adaptive data analysis via sparse time-frequency representation Advances in Adaptive Data Analysis; Vol. 3; No. 1-2;

Hou, Thomas Y.; Tai, Xue-Cheng (2011) Introduction Advances in Adaptive Data Analysis; Vol. 3; No. 1-2; Sparse Representation of Multiscale Data and Images: Theory and Applications, 14-17 December 2009 , Singapore

Hou, Thomas Y.; Li, Congming et al. (2011) On Singularity Formation of a Nonlinear Nonlocal System Archive for Rational Mechanics and Analysis; Vol. 199; No. 1;

Hou, Thomas Y.; Tai, Xue-Cheng (2011) Introduction Advances in Adaptive Data Analysis; Vol. 3; No. 1-2;

Chu, C.-C.; Graham, I. G. et al. (2010) A new multiscale finite element method for high-contrast elliptic interface problems Mathematics of Computation; Vol. 79; No. 272;

Hou, Thomas Y.; Lei, Zhen (2009) On the Partial Regularity of a 3D Model of the Navier-Stokes Equations Communications in Mathematical Physics; Vol. 287; No. 2;

Hou, Thomas Y.; Lei, Zhen (2009) On the stabilizing effect of convection in three-dimensional incompressible flows Communications on Pure and Applied Mathematics; Vol. 62; No. 4;

Hou, Thomas Y.; Liang, Dong (2009) Multiscale analysis for convection dominated transport equations Discrete and Continuous Dynamical Systems; Vol. 23; No. 1-2;

Hou, Thomas Y. (2009) Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier–Stokes equations Acta Numerica; Vol. 18;

Hou, Thomas Y.; Wetton, Brian R. (2009) Stable Fourth Order Stream-Function Methods for Incompressible Flows with Boundaries Journal of Computational Mathematics; Vol. 27; No. 4;

Hou, Thomas Y.; Shi, Zuoqiang (2008) Removing the Stiffness of Elastic Force from the Immersed Boundary Method for the 2D Stokes Equations Journal of Computational Physics; Vol. 227; No. 21;

Hou, T. Y.; Shi, Z. (2008) An efficient semi-implicit immersed boundary method for the Navier–Stokes equations Journal of Computational Physics; Vol. 227; No. 20;

Hou, Thomas Y.; Lei, Zhen et al. (2008) Global Regularity of the 3D Axi-symmetric Navier-Stokes Equations with Anisotropic Data Communications in Partial Differential Equation; Vol. 33; No. 9;

Efendiev, Y.; Hou, T. et al. (2008) Multiscale simulations of porous media flows in flow-based coordinate system Computational Geosciences; Vol. 12; No. 3;

Dostert, P.; Efendiev, Y. et al. (2008) Multiscale finite element methods for stochastic porous media flow equations and application to uncertainty quantification Computer Methods in Applied Mechanics and Engineering; Vol. 197; No. 43-44;

Hou, Thomas Y.; Li, Congming (2008) Dynamic stability of the three-dimensional axisymmetric Navier-Stokes equations with swirl Communications on Pure and Applied Mathematics; Vol. 61; No. 5;

Hou, Thomas Y.; Yang, Danping et al. (2008) Multiscale Analysis and Computation for the Three-Dimensional Incompressible Navier–Stokes Equations Multiscale Modeling and Simulation; Vol. 6; No. 4;

Hou, Thomas Y.; Li, Ruo (2007) Computing nearly singular solutions using pseudo-spectral methods Journal of Computational Physics; Vol. 226; No. 1;

Hou, T. Y.; Stredie, V. G. et al. (2007) Mathematical modeling and simulation of aquatic and aerial animal locomotion Journal of Computational Physics; Vol. 225; No. 2;

Hou, Thomas Y.; Li, Ruo (2007) Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations Discrete and Continuous Dynamical Systems; Vol. 18; No. 4;

Efendiev, Y.; Hou, T. Y. (2007) Multiscale finite element methods for porous media flows and their applications Applied Numerical Mathematics; Applied Numerical Mathematics; Vol. 57; No. 5-7; International Conference on Scientific Computing, Jun. 04-08, 2005 , Nanjing Univ, Nanjing, China

Hou, Thomas Y. (2007) Organized structures, memory, and the decay of turbulence Proceedings of the National Academy of Sciences of the United States of America; Vol. 104; No. 16;

Tang, Shao-Qiang; Liu, Wing K. et al. (2007) Bridging Atomistic/Continuum Scales in Solids with Moving Dislocations Chinese Physics Letters; Vol. 24; No. 1;

Hou, Thomas Y.; Westhead, Andrew et al. (2006) A Framework for Modeling Subgrid Effects for Two-Phase Flows in Porous Media Multiscale Modeling & Simulation; Vol. 5; No. 4;

Hou, Thomas Y.; Li, Ruo (2006) Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations Journal of Nonlinear Science; Vol. 16; No. 6;

Hou, Thomas Y.; Li, Congming (2006) On Global Well-Posedness of the Lagrangian Averaged Euler Equations SIAM Journal on Mathematical Analysis; Vol. 38; No. 3;

Hou, T. Y.; Stredie, V. G. et al. (2006) A 3D Numerical Method for Studying Vortex Formation Behind a Moving Plate Communications in Computational Physics; Vol. 1; No. 2;

Deng, Jian; Hou, Thomas Y. et al. (2006) Improved Geometric Conditions for Non-Blowup of the 3D Incompressible Euler Equation Communications in Partial Differential Equations; Vol. 31; No. 2;

Efendiev, Y.; Hou, T. et al. (2006) Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models SIAM Journal on Scientific Computing; Vol. 28; No. 2;

Hou, Thomas Y.; Yang, Danping et al. (2005) Multiscale analysis in Lagrangian formulation for the 2-D incompressible Euler equation Discrete and Continuous Dynamical Systems; Vol. 13; No. 5;

Hou, Thomas Y. (2005) Multiscale modelling and computation of fluid flow International Journal for Numerical Methods in Fluids; Vol. 47; No. 8-9; 8th ICFD Conference on Numerical Methods for Fluid Dynamics, 20-30 March 2005 , Oxford, England

Deng, Jian; Hou, Thomas Y. et al. (2005) Geometric Properties and Nonblowup of 3D Incompressible Euler Flow Communications in Partial Differential Equations; Vol. 30; No. 1-2;

Fetecau, R. C.; Hou, T. Y. (2004) A modified particle method for semilinear hyperbolic systems with oscillatory solutions Methods and Applications of Analysis; Vol. 11; No. 4;

Efendiev, Y.; Hou, T. Y. et al. (2004) Multiscale Finite Element Methods for Nonlinear Problems and their Applications Communications in Mathematical Sciences; Vol. 2; No. 4;

Hou, Thomas Y.; Wu, Xiao-Hui et al. (2004) Removing the cell resonance error in the multiscale finite element method via a Petrov-Galerkin formulation Communications in Mathematical Sciences; Vol. 2; No. 2;

Hou, Thomas Y.; Yang, Dan-ping et al. (2004) Homogenization of incompressible Euler equations Journal of Computational Mathematics; Vol. 22; No. 2;

Hou, Thomas Y.; Hu, Gang et al. (2003) Singularity formation in three-dimensional vortex sheets Physics of Fluids; Vol. 15; No. 1;

Chen, Zhiming; Hou, Thomas Y. (2002) A mixed multiscale finite element method for elliptic problems with oscillating coefficients Mathematics of Computation; Vol. 72; No. 242;

Aarnes, Jørg; Hou, Thomas Y. (2002) Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios Acta Mathematicae Applicatae Sinica, English Series; Vol. 18; No. 1;

Ceniceros, Hector D.; Hou, Thomas Y. (2000) The singular perturbation of surface tension in Hele-Shaw flows Journal of Fluid Mechanics; Vol. 409;

Efendiev, Yalchin R.; Hou, Thomas Y. et al. (2000) Convergence of a nonconforming multiscale finite element method SIAM Journal on Numerical Analysis; Vol. 37; No. 3;

Ceniceros, Hector D.; Hou, Thomas Y. et al. (1999) Numerical study of Hele-Shaw flow with suction Physics of Fluids; Vol. 11; No. 9;

Ceniceros, Hector D.; Hou, Thomas Y. (1999) Dynamic generation of capillary waves Physics of Fluids; Vol. 11; No. 5;

Hou, Thomas Y.; Wu, Xiao-Hui et al. (1998) Effect of finite computational domain on turbulence scaling law in both physical and spectral spaces Physical Review E; Vol. 58; No. 5;

Hou, Thomas Yizhao (1998) Numerical Study of Free Interface Problems Using Boundary Integral Methods Documenta Mathematica; Vol. Extra ; No. Volume;

Hou, Thomas Y.; Wu, Xiao-Hui (1997) A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media Journal of Computational Physics; Vol. 134; No. 1;

Beale, J. Thomas; Hou, Thomas Y. et al. (1996) Convergence of a Boundary Integral Method for Water Waves SIAM Journal on Numerical Analysis; Vol. 33; No. 5;

Hou, Thomas Y.; Wetton, Brian T. R. (1993) Second-Order Convergence of a Projection Scheme for the Incompressible Navier–Stokes Equations with Boundaries SIAM Journal on Numerical Analysis; Vol. 30; No. 3;