Thomas Y. Hou

Publication Activity (10 Years)

Years Active: 1991-2023
Publications (10 Years): 40

Top Topics

Finite Element Methods

Top Venues

Multiscale Model. Simul.

J. Comput. Phys.

SIAM/ASA J. Uncertain. Quantification

Publications

Jiajie Chen, Thomas Y. Hou
Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data II: Rigorous Numerics. CoRR (2023)
Thomas Y. Hou, Shumao Zhang
Initial Vorticity for A Large Range of α. Part II: the N-Dimensional Case. CoRR (2022)
Thomas Y. Hou, Shumao Zhang
Initial Vorticity for A Large Range of α. Part I: the 3-Dimensional Case. CoRR (2022)
Haydn Maust, Zongyi Li, Yixuan Wang, Daniel V. Leibovici, Oscar P. Bruno, Thomas Y. Hou, Anima Anandkumar
Fourier Continuation for Exact Derivative Computation in Physics-Informed Neural Operators. CoRR (2022)
Yifan Chen, Thomas Y. Hou
Multiscale Elliptic PDE Upscaling and Function Approximation via Subsampled Data. Multiscale Model. Simul. 20 (1) (2022)
Yifan Chen, Thomas Y. Hou, Yixuan Wang
Exponentially Convergent Multiscale Finite Element Method. CoRR (2022)
Shumao Zhang, Pengchuan Zhang, Thomas Y. Hou
Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference. ICML (2021)
Thomas Y. Hou
The nearly singular behavior of the 3D Navier-Stokes equations. CoRR (2021)
Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang
Asymptotic Escape of Spurious Critical Points on the Low-rank Matrix Manifold. CoRR (2021)
Yifan Chen, Thomas Y. Hou, Yixuan Wang
Exponentially convergent multiscale methods for high frequency heterogeneous Helmholtz equations. CoRR (2021)
Shumao Zhang, Pengchuan Zhang, Thomas Y. Hou
Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference. CoRR (2021)
Yifan Chen, Thomas Y. Hou, Yixuan Wang
Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions. Multiscale Model. Simul. 19 (2) (2021)
Thomas Y. Hou
Potential singularity of the 3D Euler equations in the interior domain. CoRR (2021)
Thomas Y. Hou, De Huang
Potential Singularity Formation of 3D Axisymmetric Navier-Stokes Equations with Degenerate Variable Diffusion Coefficients. CoRR (2021)
Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang
Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization. SIAM J. Math. Data Sci. 2 (3) (2020)
Yifan Chen, Thomas Y. Hou, Yixuan Wang
Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions. CoRR (2020)
Yifan Chen, Thomas Y. Hou
Multiscale Elliptic PDEs Upscaling and Function Approximation via Subsampled Data. CoRR (2020)
Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang
Fast Global Convergence for Low-rank Matrix Recovery via Riemannian Gradient Descent with Random Initialization. CoRR (2020)
Thomas Y. Hou, Dingjiong Ma, Zhiwen Zhang
A Model Reduction Method for Multiscale Elliptic Pdes with Random Coefficients Using an Optimization Approach. Multiscale Model. Simul. 17 (2) (2019)
Thomas Y. Hou, Zhongjian Wang, Zhiwen Zhang
A class of robust numerical methods for solving dynamical systems with multiple time scales. CoRR (2019)
Guo Luo, Thomas Y. Hou
Formation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: A Numerics Guided Study. SIAM Rev. 61 (4) (2019)
Thomas Y. Hou, De Huang, Ka Chun Lam, Ziyun Zhang
A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition. Multiscale Model. Simul. 17 (1) (2019)
Yifan Chen, Thomas Y. Hou
The subsampled Poincar\' e inequality for functional recovery. CoRR (2019)
Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang
Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization. CoRR (2019)
Thomas Y. Hou, De Huang, Ka Chun Lam, Ziyun Zhang
A Fast Hierarchically Preconditioned Eigensolver Based On Multiresolution Matrix Decomposition. CoRR (2018)
Thomas Y. Hou, Tianling Jin, Pengfei Liu
Potential Singularity for a Family of Models of the Axisymmetric Incompressible Flow. J. Nonlinear Sci. 28 (6) (2018)
Thomas Y. Hou, De Huang, Ka Chun Lam, Pengchuan Zhang
An Adaptive Fast Solver for a General Class of Positive Definite Matrices Via Energy Decomposition. Multiscale Model. Simul. 16 (2) (2018)
Thomas Y. Hou, Qin Li, Pengchuan Zhang
Exploring the Locally Low Dimensional Structure in Solving Random Elliptic PDEs. Multiscale Model. Simul. 15 (2) (2017)
Thomas Y. Hou, Zuoqiang Shi
Sparse Time-Frequency Decomposition for Multiple Signals with Same Frequencies. Adv. Data Sci. Adapt. Anal. 9 (4) (2017)
Thomas Y. Hou, Feng-Nan Hwang, Pengfei Liu, Chien-Chou Yao
An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients. J. Comput. Phys. 336 (2017)
Thomas Y. Hou, Qin Li, Pengchuan Zhang
A Sparse Decomposition of Low Rank Symmetric Positive Semidefinite Matrices. Multiscale Model. Simul. 15 (1) (2017)
Eric T. Chung, Yalchin Efendiev, Thomas Y. Hou
Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods. J. Comput. Phys. 320 (2016)
Hayden Schaeffer, Thomas Y. Hou
An Accelerated Method for Nonlinear Elliptic PDE. J. Sci. Comput. 69 (2) (2016)
Thomas Y. Hou, Zuoqiang Shi
Sparse Time-Frequency decomposition for multiple signals with same frequencies. CoRR (2015)
Thomas Y. Hou, Pengfei Liu
A heterogeneous stochastic FEM framework for elliptic PDEs. J. Comput. Phys. 281 (2015)
Thomas Y. Hou, Zuoqiang Shi
Extracting a shape function for a signal with intra-wave frequency modulation. CoRR (2015)
Chunguang Liu, Zuoqiang Shi, Thomas Y. Hou
On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data. Multiscale Model. Simul. 13 (3) (2015)
Zhiwen Zhang, Maolin Ci, Thomas Y. Hou
A Multiscale Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients. Multiscale Model. Simul. 13 (1) (2015)
Chunguang Liu, Thomas Y. Hou, Zuoqiang Shi
On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data. CoRR (2015)
Thomas Y. Hou, Qin Li, Hayden Schaeffer
Sparse + low-energy decomposition for viscous conservation laws. J. Comput. Phys. 288 (2015)
Guo Luo, Thomas Y. Hou
Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation. Multiscale Model. Simul. 12 (4) (2014)
Peyman Tavallali, Thomas Y. Hou, Zuoqiang Shi
Extraction of Intrawave Signals Using the Sparse Time-Frequency Representation Method. Multiscale Model. Simul. 12 (4) (2014)
Mulin Cheng, Thomas Y. Hou, Zhiwen Zhang
A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations II: Adaptivity and generalizations. J. Comput. Phys. 242 (2013)
Thomas Y. Hou, Zuoqiang Shi
Sparse Time-Frequency decomposition by adaptive basis pursuit. CoRR (2013)
Yalchin Efendiev, Juan Galvis, Thomas Y. Hou
Generalized multiscale finite element methods (GMsFEM). J. Comput. Phys. 251 (2013)
Thomas Y. Hou, Zuoqiang Shi, Peyman Tavallali
Convergence of a data-driven time-frequency analysis method CoRR (2013)
Thomas Y. Hou, Zuoqiang Shi, Peyman Tavallali
Sparse Time Frequency Representations and Dynamical Systems. CoRR (2013)
Mulin Cheng, Thomas Y. Hou, Zhiwen Zhang
A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations I: Derivation and algorithms. J. Comput. Phys. 242 (2013)
Yalchin Efendiev, Juan Galvis, Thomas Y. Hou
Generalized Multiscale Finite Element Methods (GMsFEM) CoRR (2013)
Mulin Cheng, Thomas Y. Hou, Mike P. Yan, Zhiwen Zhang
A Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients. SIAM/ASA J. Uncertain. Quantification 1 (1) (2013)
Thomas Y. Hou, Zuoqiang Shi
Adaptive Data Analysis via Sparse Time-Frequency Representation. Adv. Data Sci. Adapt. Anal. 3 (1-2) (2011)
Thomas Y. Hou, Xue-Cheng Tai
Introduction. Adv. Data Sci. Adapt. Anal. 3 (1-2) (2011)
Thomas Y. Hou, Mike P. Yan, Zhaohua Wu
A Variant of the EMD Method for Multi-Scale Data. Adv. Data Sci. Adapt. Anal. 1 (4) (2009)
Thomas Y. Hou, Danping Yang, Hongyu Ran
Multiscale Analysis and Computation for the Three-Dimensional Incompressible Navier-Stokes Equations. Multiscale Model. Simul. 6 (4) (2008)
Thomas Y. Hou, Zuoqiang Shi
An efficient semi-implicit immersed boundary method for the Navier-Stokes equations. J. Comput. Phys. 227 (20) (2008)
Thomas Y. Hou, Zuoqiang Shi
Removing the Stiffness of Elastic Force from the Immersed Boundary Method for the 2D Stokes Equations CoRR (2008)
Thomas Y. Hou, Zuoqiang Shi
Removing the stiffness of elastic force from the immersed boundary method for the 2D Stokes equations. J. Comput. Phys. 227 (21) (2008)
Thomas Y. Hou, Valentin G. Stredie, Theodore Yao-Tsu Wu
Mathematical modeling and simulation of aquatic and aerial animal locomotion. J. Comput. Phys. 225 (2) (2007)
Thomas Y. Hou, Ruo Li
Computing nearly singular solutions using pseudo-spectral methods. J. Comput. Phys. 226 (1) (2007)
Thomas Y. Hou, Wuan Luo, Boris Rozovskii, Hao-Min Zhou
Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics. J. Comput. Phys. 216 (2) (2006)
Paul Dostert, Yalchin Efendiev, Thomas Y. Hou, Wuan Luo
Coarse-gradient Langevin algorithms for dynamic data integration and uncertainty quantification. J. Comput. Phys. 217 (1) (2006)
Thomas Y. Hou, Ruo Li
Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations. J. Nonlinear Sci. 16 (6) (2006)
Shaoqiang Tang, Thomas Y. Hou, Wing Kam Liu
A pseudo-spectral multiscale method: Interfacial conditions and coarse grid equations. J. Comput. Phys. 213 (1) (2006)
Thomas Y. Hou, Andrew Westhead, Danping Yang
A Framework for Modeling Subgrid Effects for Two-Phase Flows in Porous Media. Multiscale Model. Simul. 5 (4) (2006)
Thomas Y. Hou, Congming Li
On Global Well-Posedness of the Lagrangian Averaged Euler Equations. SIAM J. Math. Anal. 38 (3) (2006)
Yalchin Efendiev, Thomas Y. Hou, Wuan Luo
Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models. SIAM J. Sci. Comput. 28 (2) (2006)
Yalchin Efendiev, Victor Ginting, Thomas Y. Hou, Richard E. Ewing
Accurate multiscale finite element methods for two-phase flow simulations. J. Comput. Phys. 220 (1) (2006)
Zhiming Chen, Thomas Y. Hou
A mixed multiscale finite element method for elliptic problems with oscillating coefficients. Math. Comput. 72 (242) (2003)
Thomas Y. Hou, Pingwen Zhang
A new stabilizing technique for boundary integral methods for water waves. Math. Comput. 70 (235) (2001)
Yalchin R. Efendiev, Thomas Y. Hou, Xiao-hui Wu
Convergence of a Nonconforming Multiscale Finite Element Method. SIAM J. Numer. Anal. 37 (3) (2000)
Russel E. Caflisch, Thomas Y. Hou, John S. Lowengrub
Almost optimal convergence of the point vortex method for vortex sheets using numerical filtering. Math. Comput. 68 (228) (1999)
Thomas Y. Hou, Xiao-hui Wu, Zhiqiang Cai
Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Math. Comput. 68 (227) (1999)
Héctor D. Ceniceros, Thomas Y. Hou
Convergence of a non-stiff boundary integral method for interfacial flows with surface tension. Math. Comput. 67 (221) (1998)
Thomas Y. Hou, John S. Lowengrub, Michael J. Shelley
The Convergence of an Exact Desingularization for Vortex Methods. SIAM J. Sci. Comput. 14 (1) (1993)
Tony F. Chan, Thomas Y. Hou
Eigendecomposition of Domain Decomposition Interface Operators for Constant Coefficient Elliptic Problems. SIAM J. Sci. Comput. 12 (6) (1991)