What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Geometry
- Partial differential equation
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.
His most cited work include:
- A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media (1393 citations)
- A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows (672 citations)
- Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients (434 citations)
What are the main themes of his work throughout his whole career to date?
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.
He most often published in these fields:
- Mathematical analysis (53.42%)
- Euler equations (22.37%)
- Singularity (17.35%)
What were the highlights of his more recent work (between 2013-2021)?
- Mathematical analysis (53.42%)
- Applied mathematics (15.98%)
- Algorithm (14.61%)
In recent papers he was focusing on the following fields of study:
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.
Between 2013 and 2021, his most popular works were:
- Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods (125 citations)
- Potentially singular solutions of the 3D axisymmetric Euler equations (118 citations)
- Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation (58 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Geometry
- Partial differential equation
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
- Basis function which is related to area like Finite element method, Interpolation, Boundary value problem, Rank and Basis,
- Nonlinear system and related Dynamical systems theory.
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