2013 - Fellow of the American Mathematical Society
2011 - Fellow of the American Academy of Arts and Sciences
2009 - SIAM Fellow For contributions to fluid mechanics and multiscale analysis.
2005 - THE J. TINSLEY ODEN MEDAL For his outstanding contributions in developing innovative multiscale analysis and computational methods, and their applications to flows in porous media and turbulence.
1990 - Fellow of Alfred P. Sloan Foundation
His primary scientific interests are in Mathematical analysis, Finite element method, Euler equations, Boundary value problem and Singularity. His Mathematical analysis research is multidisciplinary, incorporating perspectives in Compressibility and Nonlinear system. Thomas Y. Hou has researched Finite element method in several fields, including Oversampling and Homogenization.
His biological study deals with issues like Incompressible flow, which deal with fields such as Euler's formula and Vortex sheet. His study in Boundary value problem is interdisciplinary in nature, drawing from both Grid, Geometry, Extended finite element method and Finite volume method. The various areas that he examines in his Singularity study include Instability, Inviscid flow, Classical mechanics and Vortex, Vorticity.
Thomas Y. Hou focuses on Mathematical analysis, Euler equations, Singularity, Applied mathematics and Algorithm. His Mathematical analysis research integrates issues from Rotational symmetry, Navier–Stokes equations, Compressibility, Vortex and Nonlinear system. His work deals with themes such as Singular solution, Vortex stretching, Vorticity and Euler's formula, which intersect with Euler equations.
His Singularity study deals with Inviscid flow intersecting with Conservative vector field. His Applied mathematics study combines topics from a wide range of disciplines, such as Basis function and Finite element method. His studies examine the connections between Finite element method and genetics, as well as such issues in Flow, with regards to Computation.
His main research concerns Mathematical analysis, Applied mathematics, Algorithm, Basis function and Euler equations. His research in Mathematical analysis intersects with topics in Grid and Rotational symmetry. His work carried out in the field of Applied mathematics brings together such families of science as Elliptic pdes and Reduction.
His research integrates issues of Time–frequency representation, Instantaneous phase, Lasso and Feature selection in his study of Algorithm. His studies in Basis function integrate themes in fields like Function, Rate of convergence, Boundary value problem and Finite element method. The concepts of his Euler equations study are interwoven with issues in Finite time, Vorticity, Singularity, Boundary and Euler's formula.
Thomas Y. Hou spends much of his time researching Mathematical analysis, Euler equations, Singularity, Instantaneous phase and Applied mathematics. His research in Mathematical analysis intersects with topics in Reduction and Invertible matrix. His Euler equations research includes elements of Rotational symmetry, Boundary, Euler's formula, Discretization and Domain.
His Instantaneous phase research incorporates themes from Algorithm, Waveform, Noise and Hilbert–Huang transform. Thomas Y. Hou has researched Algorithm in several fields, including Time–frequency representation and Mathematical optimization. His Applied mathematics study also includes
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A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media
Thomas Y. Hou;Xiao-Hui Wu.
Journal of Computational Physics (1997)
A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows
Y.C. Chang;T.Y. Hou;B. Merriman;S. Osher.
Journal of Computational Physics (1996)
Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
Thomas Y. Hou;Xiao-Hui Wu;Zhiqiang Cai.
Mathematics of Computation (1999)
Removing the stiffness from interfacial flows with surface tension
Thomas Y. Hou;John S. Lowengrub;Michael J. Shelley.
Journal of Computational Physics (1994)
A mixed multiscale finite element method for elliptic problems with oscillating coefficients
Zhiming Chen;Thomas Y. Hou.
Mathematics of Computation (2003)
Generalized multiscale finite element methods (GMsFEM)
Yalchin Efendiev;Yalchin Efendiev;Juan Galvis;Juan Galvis;Thomas Y. Hou.
Journal of Computational Physics (2013)
GLOBAL WELL-POSEDNESS OF THE VISCOUS BOUSSINESQ EQUATIONS
Thomas Y. Hou;Congming Li.
Discrete and Continuous Dynamical Systems (2004)
Why nonconservative schemes converge to wrong solutions: error analysis
Thomas Y. Hou;Philippe G. Le Floch.
Mathematics of Computation (1994)
Convergence of a Nonconforming Multiscale Finite Element Method
Yalchin R. Efendiev;Thomas Y. Hou;Xiao-Hui Wu.
SIAM Journal on Numerical Analysis (2000)
A Hybrid Method for Moving Interface Problems with Application to the Hele-Shaw Flow
Thomas Y. Hou;Zhilin Li;Stanley Osher;Hongkai Zhao.
Journal of Computational Physics (1997)
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