Thomas Hou

Q: What Schools Are Affiliated With Thomas Hou

Thomas Hou is affiliated with the following schools: California Institute of Technology, University of California, Los Angeles, South China University of Technology, New York University

Thomas Hou's AcademicInfluence.com Rankings

Thomas Hou

Mathematics

#3411

World Rank

#5037

Historical Rank

#1272

USA Rank

Applied Mathematics

#87

World Rank

#100

Historical Rank

#44

USA Rank

Measure Theory

#1536

World Rank

#1909

Historical Rank

#513

USA Rank

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Mathematics

Why Is Thomas Hou Influential?

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According to Wikipedia, Thomas Yizhao Hou is the Charles Lee Powell Professor of Applied and Computational Mathematics in the Department of Computing and Mathematical Sciences at the California Institute of Technology. He is known for his work in numerical analysis and mathematical analysis.

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Thomas Hou's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media (1997) (1759)
A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows (1996) (893)
Multiscale Finite Element Methods: Theory and Applications (2009) (588)
Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients (1999) (575)
Removing the stiffness from interfacial flows with surface tension (1994) (510)
Generalized multiscale finite element methods (GMsFEM) (2013) (507)
A mixed multiscale finite element method for elliptic problems with oscillating coefficients (2003) (461)
GLOBAL WELL-POSEDNESS OF THE VISCOUS BOUSSINESQ EQUATIONS (2004) (412)
Convergence of a Nonconforming Multiscale Finite Element Method (2000) (311)
Why nonconservative schemes converge to wrong solutions: error analysis (1994) (295)
A Hybrid Method for Moving Interface Problems with Application to the Hele-Shaw Flow (1997) (274)
Accurate multiscale finite element methods for two-phase flow simulations (2006) (268)
Analysis of upscaling absolute permeability (2002) (264)
Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics (2006) (225)
Boundary integral methods for multicomponent fluids and multiphase materials (2001) (212)
Multiscale Finite Element Methods for Nonlinear Problems and Their Applications (2004) (209)
Computing nearly singular solutions using pseudo-spectral methods (2007) (201)
Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models (2006) (185)
A new multiscale finite element method for high-contrast elliptic interface problems (2010) (181)
An efficient dynamically adaptive mesh for potentially singular solutions (2001) (179)
Growth rates for the linearized motion of fluid interfaces away from equilibrium (1993) (159)
The long-time motion of vortex sheets with surface tension (1997) (158)
Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods (2016) (154)
Adaptive Data Analysis via Sparse Time-Frequency Representation (2011) (153)
Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations (2006) (153)
Multiscale finite element methods for porous media flows and their applications (2007) (145)
Convergence of the point vortex method for the 2-D euler equations (1990) (143)
Data-driven time-frequency analysis (2012) (139)
Potentially singular solutions of the 3D axisymmetric Euler equations (2013) (134)
Geometric Properties and Nonblowup of 3D Incompressible Euler Flow (2004) (131)
Hyperbolic Problems: Theory, Numerics, Applications (2003) (123)
Removing the Cell Resonance Error in the Multiscale Finite Element Method via a Petrov-Galerkin Formulation (2004) (112)
Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation (2014) (106)
Improved Geometric Conditions for Non-Blowup of the 3D Incompressible Euler Equation (2006) (101)
Dynamic stability of the three‐dimensional axisymmetric Navier‐Stokes equations with swirl (2008) (94)
Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios (2002) (87)
On the stabilizing effect of convection in three‐dimensional incompressible flows (2009) (82)
Blowup or no blowup? The interplay between theory and numerics (2008) (79)
Convergence of a Boundary Integral Method for Water Waves (1996) (79)
Identification of time‐varying cable tension forces based on adaptive sparse time‐frequency analysis of cable vibrations (2017) (78)
Numerical simulation of water resources problems: Models, methods, and trends (2013) (78)
A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations I: Derivation and algorithms (2013) (78)
Dispersive approximations in fluid dynamics (1991) (75)
Coarse-gradient Langevin algorithms for dynamic data integration and uncertainty quantification (2006) (62)
Convergence of a finite difference scheme for the Navier-Stokes equations using vorticity boundary conditions (1992) (61)
Homogenization of linear transport equations with oscillatory vector fields (1992) (60)
A Level-Set Approach to the Computation of Twinning and Phase-Transition Dynamics (1999) (60)
Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier–Stokes equations (2009) (60)
Global Regularity of the 3D Axi-Symmetric Navier–Stokes Equations with Anisotropic Data (2008) (55)
ON THE FINITE-TIME BLOWUP OF A 1D MODEL FOR THE 3D AXISYMMETRIC EULER EQUATIONS (2014) (55)
Sparse operator compression of higher-order elliptic operators with rough coefficients (2017) (54)
A pseudo-spectral multiscale method: Interfacial conditions and coarse grid equations (2006) (54)
An efficient semi-implicit immersed boundary method for the Navier-Stokes equations (2008) (53)
Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficient (2015) (52)
Parametric vertical coordinate formulation for multiscale, Boussinesq, and non-Boussinesq ocean modeling (2006) (52)
Multiscale finite element methods for stochastic porous media flow equations and application to uncertainty quantification (2008) (52)
A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations II: Adaptivity and generalizations (2013) (52)
Dynamic Stability of the 3D Axi-symmetric Navier-Stokes Equations with Swirl (2006) (51)
A CURVILINEAR LEVEL SET FORMULATION FOR HIGHLY DEFORMABLE FREE SURFACE PROBLEMS WITH APPLICATION TO SOLIDIFICATION (1998) (49)
Numerical Solutions to Free Boundary Problems (1995) (49)
Multi-valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems (1993) (49)
A Variant of the EMD Method for Multi-Scale Data (2009) (48)
Numerical study of Hele-Shaw flow with suction (1999) (47)
Convergence of a data-driven time-frequency analysis method (2013) (44)
Multiscale Modeling and Computation of Incompressible Flow (2002) (43)
Multiscale modelling and computation of fluid flow (2005) (42)
Flow based oversampling technique for multiscale finite element methods (2008) (42)
Second-order convergence of a projection scheme for the incompressible Navier-Stokes equations with boundaries (1993) (39)
Removing the stiffness of elastic force from the immersed boundary method for the 2D Stokes equations (2008) (39)
Level set dynamics and the non-blowup of the 2D quasi-geostrophic equation (2006) (38)
On the Finite Time Blowup of the De Gregorio Model for the 3D Euler Equations (2019) (37)
Removing the Stiffness of Curvature in Computing 3-D Filaments (1998) (37)
A Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients (2013) (37)
Convergence of the point vortex method for the 3‐D euler equations (1990) (36)
Geometry related convergence results for domain decomposition algorithms (1991) (35)
On the stability of the unsmoothed Fourier method for hyperbolic equations (1994) (33)
Convergence of a non-stiff boundary integral method for interfacial flows with surface tension (1998) (33)
Dynamic generation of capillary waves (1999) (32)
Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations (2007) (32)
On the Partial Regularity of a 3D Model of the Navier-Stokes Equations (2009) (32)
Extracting a shape function for a signal with intra-wave frequency modulation (2015) (31)
Finite Time Blowup of 2D Boussinesq and 3D Euler Equations with $$C^{1,\alpha }$$ Velocity and Boundary (2019) (31)
Particle method approximation of oscillatory solutions to hyperbolic differential equations (1989) (30)
Convergence of a variable blob vortex method for the Euler and Navier-Stokes equations (1990) (30)
On singularity formation of a 3D model for incompressible Navier–Stokes equations (2009) (30)
Multi-scale phenomena in complex fluids : modeling, analysis and numerical simulation (2009) (30)
An Efficient Boundary Integral Method for the Mullins-Sekerka Problem (1996) (28)
Numerical Approximations to Multiscale Solutions in Partial Differential Equations (2003) (28)
Intrinsic frequency for a systems approach to haemodynamic waveform analysis with clinical applications (2014) (28)
Convergence of a boundary integral method for 3-D water waves (2001) (28)
Numerical Analysis of Multiscale Problems (2012) (28)
Self-similar singularity of a 1D model for the 3D axisymmetric Euler equations (2014) (28)
Convergence of a point vortex method for vortex sheets (1991) (26)
Convergence of the Grid-free point Vortex method for the three-dimensional Euler equations (1991) (25)
Well-posedness of linearized motion for 3-D water waves far from equilibrium (1996) (24)
A MULTISCALE FINITE ELEMENT METHOD FOR PDES WITH OSCILLATORY COEFFICIENTS (1997) (23)
Exploring the Locally Low Dimensional Structure in Solving Random Elliptic PDEs (2016) (23)
On the Finite-Time Blowup of a 1D Model for the 3D Incompressible Euler Equations (2013) (22)
On Global Well-Posedness of the Lagrangian Averaged Euler Equations (2006) (22)
A Multiscale Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients (2015) (22)
New stability estimates for the 2‐D vortex method (1991) (22)
Sparse Time Frequency Representations and Dynamical Systems (2013) (21)
On Finite Time Singularity and Global Regularity of an Axisymmetric Model for the 3D Euler Equations (2012) (21)
An adaptive ANOVA-based data-driven stochastic method for elliptic PDEs with random coefficient (2014) (20)
Mathematical modeling and simulation of aquatic and aerial animal locomotion (2007) (20)
Multiscale Analysis and Computation for the Three-Dimensional Incompressible Navier-Stokes Equations (2008) (19)
Sparse time-frequency decomposition based on dictionary adaptation (2016) (19)
Sparse time-frequency representation of nonlinear and nonstationary data (2013) (18)
Bridging atomistic/continuum scales in solids with moving dislocations (2007) (18)
On Singularity Formation of a Nonlinear Nonlocal System (2009) (18)
Extraction of Intrawave Signals Using the Sparse Time-Frequency Representation Method (2014) (18)
Effect of finite computational domain on turbulence scaling law in both physical and spectral spaces (1998) (16)
On the Well-Posedness of Two Fluid Interfacial Flows with Surface Tension (1993) (15)
Nonexistence of Local Self-Similar Blow-up for the 3D Incompressible Navier-Stokes Equations (2006) (15)
POTENTIALLY SINGULAR SOLUTIONS OF THE 3D INCOMPRESSIBLE (2013) (15)
A Model Reduction Method for Multiscale Elliptic Pdes with Random Coefficients Using an Optimization Approach (2018) (15)
Homogenization for semilinear hyperbolic systems with oscillatory data (1988) (15)
STABLE FOURTH-ORDER STREAM-FUNCTION METHODS FOR INCOMPRESSIBLE FLOWS WITH BOUNDARIES * (2009) (15)
A lagrangian finite element method for the 2‐D euler equations (1990) (15)
The Convergence of an Exact Desingularization for Vortex Methods (1993) (15)
Multiscale analysis in Lagrangian formulation for the 2-D incompressible Euler equation (2005) (14)
Computation of oscillatory solutions to hyperbolic differential equations using particle methods (1988) (14)
Singularity formation in three-dimensional vortex sheets (2001) (14)
Fast Global Convergence for Low-rank Matrix Recovery via Riemannian Gradient Descent with Random Initialization (2020) (13)
Homogenization of incompressible Euler equations (2004) (13)
On the convergence and accuracy of the cardiovascular intrinsic frequency method (2015) (13)
Multiscale modeling of incompressible turbulent flows (2013) (13)
Spatial and temporal stability issues for interfacial flows with surface tension (1994) (13)
A heterogeneous stochastic FEM framework for elliptic PDEs (2014) (13)
A Framework for Modeling Subgrid Effects for Two-Phase Flows in Porous Media (2006) (13)
Potential Singularity for a Family of Models of the Axisymmetric Incompressible Flow (2018) (12)
An Accelerated Method for Nonlinear Elliptic PDE (2016) (11)
Homogenization and convergence of the vortex method for 2 - d euler equations with oscillatory vorti (1990) (11)
A Sparse Decomposition of Low Rank Symmetric Positive Semidefinite Matrices (2016) (11)
Numerical Study of Nearly Singular Solutions of the 3-D Incompressible Euler Equations (2006) (10)
Almost optimal convergence of the point vortex method for vortex sheets using numerical filtering (1999) (10)
The singular perturbation of surface tension in Hele-Shaw flows (2000) (10)
Asymptotically self-similar blowup of the Hou-Luo model for the 3D Euler equations (2021) (10)
Potential singularity of the 3D Euler equations in the interior domain (2021) (10)
On the Stabilizing Effect of Convection in 3 D Incompressible Flows (2008) (9)
Eigendecomposition of Domain Decomposition Interface Operators for Constant Coefficient Elliptic Problems (1991) (9)
Sparse + low-energy decomposition for viscous conservation laws (2015) (9)
Coastal hydrodynamics of ocean waves on beach (2001) (9)
A 3D Numerical Method for Studying Vortex Formation Behind a Moving Plate (2006) (9)
An Adaptive Fast Solver for a General Class of Positive Definite Matrices Via Energy Decomposition (2017) (9)
Multiscale analysis for convection dominated transport equations (2008) (9)
Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions (2020) (8)
A prototype knockoff filter for group selection with FDR control (2017) (8)
A decadal microwave record of tropical air temperature from AMSU-A/aqua observations (2013) (8)
Potentially Singular Behavior of the 3D Navier–Stokes Equations (2021) (7)
Numerical Analysis of Multiscale Problems - Volume 83 (2014) (7)
Formation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: A Numerics Guided Study (2019) (7)
A Level Set Formulation for the 3D Incompressible Euler Equations (2005) (7)
Solving Bayesian inverse problems from the perspective of deep generative networks (2019) (7)
Exponentially convergent multiscale methods for high frequency heterogeneous Helmholtz equations (2021) (7)
A Nearly Optimal Existence Result for Slightly Perturbed 3-D Vortex Sheets (2003) (6)
Sparse Time-Frequency decomposition by adaptive basis pursuit (2013) (6)
A potential two-scale traveling wave singularity for 3D incompressible Euler equations (2022) (5)
A Fast Hierarchically Preconditioned Eigensolver Based On Multiresolution Matrix Decomposition (2018) (5)
MULTISCALE ANALYSIS AND COMPUTATION FOR THE 3D INCOMPRESSIBLE NAVIER-STOKES EQUATIONS (5)
A Multiscale Model Reduction Method for Partial Differential Equations (2014) (5)
A minimal mechanosensing model predicts keratocyte evolution on flexible substrates (2018) (5)
On singularity formation of a 3 D model for incompressible Navier – Stokes equations (2010) (5)
Multiscale Elliptic PDEs Upscaling and Function Approximation via Subsampled Data (2020) (5)
Quantum Transport: Modelling, Analysis and Asymptotics - Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 11 - 16, 2006 (2008) (5)
Growth rates for the linearized motion of 3-D fluid interfaces with surface tension far from equilibrium (1998) (5)
Hyperbolic problems : theory, numerics, applications : proceedings of the ninth International Conference on Hyperbolic Problems held in CalTech, Pasadena, March 25-29, 2002 (2003) (5)
Dynamic Growth Estimates of Maximum Vorticity for 3D Incompressible Euler Equations and the SQG Model (2010) (5)
On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data (2015) (5)
A new stabilizing technique for boundary integral methods for water waves (2001) (5)
Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization (2019) (4)
Organized structures, memory, and the decay of turbulence (2007) (4)
A new desingularization for vortex methods (1992) (4)
Mixed Multiscale Finite Element Methods on Adaptive Unstructured Grids Using Limited Global Information (2009) (4)
Global regularity for a family of 3D models of the axi-symmetric Navier–Stokes equations (2017) (4)
An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients (2017) (4)
Function approximation via the subsampled Poincaré inequality (2019) (4)
Multiscale Computations for Flow and Transport in Heterogeneous Media (2008) (4)
Potential Singularity Formation of 3D Axisymmetric Navier-Stokes Equations with Degenerate Variable Diffusion Coefficients (2021) (4)
Some Analysis of the Knockoff Filter and its Variants (2017) (4)
Special Issue on Multiscale Modeling in Biology (2005) (4)
Multiscale analysis and computation for flows in heterogeneous media (2016) (3)
Multiscale Computation of Fluid Flow in Heterogeneous Media (2005) (3)
Sparse Time-Frequency decomposition by dictionary learning (2013) (3)
Multiscale computations for flow and transport in porous media (2009) (3)
Sparse Time-Frequency Decomposition for Multiple Signals with Same Frequencies (2015) (3)
Adaptive data analysis: theory and applications (2016) (3)
Numerical Study of Free Interface Problems Using Boundary Integral Methods (1998) (3)
On the Partial Regularity of a 3 D Model of the Navier-Stokes Equations (2008) (3)
The nearly singular behavior of the 3D Navier-Stokes equations (2021) (2)
A pseudo knockoff filter for correlated features (2017) (2)
A Model Reduction Method for Elliptic Pdes with Random Input Using the Heterogeneous Stochastic Fem Framework (2016) (2)
Seafloor Characterization from Spatial Variation of Multibeam Backscatter vs. (2001) (2)
Data-Driven Stochastic Multiscale Method (2010) (1)
On the stability of the unsmoothed Fourier method forhyperbolic (1996) (1)
Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference (2021) (1)
A two-level method for sparse time-frequency representation of multiscale data (2017) (1)
RESONANCE ERROR IN MULTISCALE FINITE ELEMENT METHODS (1997) (1)
A modified particle method for semilinear hyperbolic systems with oscillatory solutions (2004) (1)
Finite Time Blow-up of a 3D Model for Incompressible Euler Equations (2012) (1)
On the Local Well-posedness of a 3D Model for Incompressible Navier-Stokes Equations with Partial Viscosity (2011) (1)
A Data-Driven Stochastic Method (2012) (1)
An Ecien t Semi-Implicit Immersed Boundary Method for the Navier-Stokes Equations (2008) (1)
Multiscale computation of isotropic homogeneous turbulentflow (2006) (1)
Asymptotic Escape of Spurious Critical Points on the Low-rank Matrix Manifold (2021) (1)
Multiscale Simulation Framework for Coupled Fluid Flow and Mechanical Deformation (2016) (1)
Potential Singularity for a Family of Models of the Axisymmetric Incompressible Flow (2017) (0)
Special Section on Multiscale Modeling in Materials and Life Sciences (2005) (0)
A P ] 1 1 A pr 2 00 6 Level Set Dynamics and the Non-blowup of the 2 D Quasi-geostrophic Equation (2006) (0)
Fast Solver for Graph Laplacian via Operator Compression and Multiresolution Matrix Decomposition (2017) (0)
An Accelerated Method for Nonlinear Elliptic PDE (2016) (0)
A pr 2 01 3 Generalized Multiscale Finite Element Methods ( GMsFEM ) (2018) (0)
N A ] 2 5 Fe b 20 12 Data-Driven Time-Frequency Analysis (2016) (0)
Potential Singularity Formation of Incompressible Axisymmetric Euler Equations with Degenerate Viscosity Coefficients (2021) (0)
On the non-uniqueness of the instantaneous frequency (2016) (0)
Introduction (2011) (0)
Introduction to the Theory of Incompressible Inviscid Flows (2009) (0)
2 Flow based oversampling for multiscale finite element methods (2007) (0)
The subsampled Poincar\' e inequality for functional recovery (2019) (0)
A brief introduction to Theodore Yao-Tsu Wu (2016) (0)
Recent Progress on the Search of 3D Euler Singularities (2013) (0)
Multi-Scale Finite Element Approximation for Transport in Heterogeneous Porous Media (2002) (0)
HOMOGENIZATION OF INCOMPRESSIBLE EULER EQUATIONS ∗1) (2006) (0)
POTENTIAL SINGULARITY FORMATION OF 3D INCOMPRESSIBLE AXISYMMETRIC NAVIER–STOKES EQUATIONS WITH DEGENERATE DIFFUSION COEFFICIENTS (2021) (0)
International Conference on Multiscale Methods and Partial Differential Equations. (2006) (0)
Noctilucent Cloud Detection with the Rayleigh Lidar at Poker Flat Research Range (2002) (0)
Stable and Efficient Numerical Approximations for Fluid Free Surfaces. (1996) (0)
A Multiscale Finite Element Method for Computing Wave Propagation and Scattering in Heterogeneous Media. (1999) (0)
Stable Self-Similar Profiles for Two 1D Models of the 3D Axisymmetric Euler Equations (2016) (0)
A model reduction method for multiscale elliptic PDEs with locally degenerate coefficients (2013) (0)
Semi-Lagrangian Reconstruction Techniques for Transient Multiscale Problems (2019) (0)
M E ] 3 1 A ug 2 01 7 A Pseudo Knockoff Filter for Correlated Features (2017) (0)
FOR CONVECTION DOMINATED TRANSPORT EQUATIONS (2008) (0)
A class of robust numerical methods for solving dynamical systems with multiple time scales (2019) (0)
Exponentially Convergent Multiscale Finite Element Method (2022) (0)
Nonexisten e of Lo al Self-Similar Blow-up for the 3D In ompressible Navier-Stokes Equations (2016) (0)
M E ] 2 2 Ju l 2 01 9 A Pseudo Knockoff Filter for Correlated Features (2019) (0)
A Relay-Zone Technique for Computing Dynamic Dislocations (2007) (0)
The Dual Role of Convection in 3D Navier-Stokes Equations (2011) (0)
Sparse time-frequency representation of nonlinear and nonstationary data (2013) (0)
Numerical Methods for the Computation of Propagating Phase Boundaries. (1997) (0)
Fourier Continuation for Exact Derivative Computation in Physics-Informed Neural Operators (2022) (0)
Multiscale Modeling and Simulation: The Interplay Beween Mathematics and Engineering Applications (2009) (0)
Author ' s personal copy Flow based oversampling technique for multiscale finite element methods (2007) (0)
Modified sparse time – frequency representation for heart – aorta system : intrinsic frequency algorithm (2014) (0)
Global Regularity of the 3 D AxiSymmetric Navier – Stokes Equations 1623 angular velocity and vorticity components of the 3 D axisymmetric Navier – Stokes equations (2008) (0)
2 3 M ar 2 01 2 Finite Time Blow-up of a 3 D Model for Incompressible Euler Equations (2012) (0)

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Published Works

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What Schools Are Affiliated With Thomas Hou?

Thomas Hou's AcademicInfluence.com Rankings