What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Finite element method
- Geometry
Thomas J. R. Hughes focuses on Finite element method, Mathematical analysis, Applied mathematics, Isogeometric analysis and Mixed finite element method.
He is interested in Galerkin method, which is a branch of Finite element method.
Thomas J. R. Hughes has included themes like Bending of plates, Incompressible flow and Boundary knot method in his Mathematical analysis study.
His Applied mathematics research integrates issues from Weighting, Geometry, Nonlinear system, Algorithm and Calculus.
Thomas J. R. Hughes has researched Isogeometric analysis in several fields, including Basis, Non-uniform rational B-spline, Basis function, Mathematical optimization and T-spline.
Thomas J. R. Hughes works mostly in the field of Mixed finite element method, limiting it down to topics relating to Extended finite element method and, in certain cases, Smoothed finite element method and Pressure-correction method.
His most cited work include:
- The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (4695 citations)
- Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations (4208 citations)
- Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement (3447 citations)
What are the main themes of his work throughout his whole career to date?
His main research concerns Finite element method, Mathematical analysis, Isogeometric analysis, Applied mathematics and Galerkin method.
His study focuses on the intersection of Finite element method and fields such as Computational fluid dynamics with connections in the field of Compressible flow.
His Mathematical analysis research is multidisciplinary, incorporating perspectives in Navier–Stokes equations, Nonlinear system, Boundary knot method and Discontinuous Galerkin method.
Thomas J. R. Hughes combines subjects such as Non-uniform rational B-spline, Basis function, T-spline, Discretization and Algorithm with his study of Isogeometric analysis.
As a part of the same scientific family, Thomas J. R. Hughes mostly works in the field of Applied mathematics, focusing on Classical mechanics and, on occasion, Mechanics.
His studies in Galerkin method integrate themes in fields like Convection–diffusion equation and Compressibility.
He most often published in these fields:
- Finite element method (44.79%)
- Mathematical analysis (28.22%)
- Isogeometric analysis (25.15%)
What were the highlights of his more recent work (between 2015-2021)?
- Isogeometric analysis (25.15%)
- Applied mathematics (24.95%)
- Finite element method (44.79%)
In recent papers he was focusing on the following fields of study:
His primary scientific interests are in Isogeometric analysis, Applied mathematics, Finite element method, Spline and Discretization.
His Isogeometric analysis research incorporates elements of Partition of unity, Partial differential equation, Basis function, Mathematical optimization and Trimming.
His research in Applied mathematics intersects with topics in Galerkin method, Numerical integration, Degree of a polynomial and Collocation.
Thomas J. R. Hughes is interested in Quadrilateral, which is a field of Finite element method.
His Discretization study is concerned with the larger field of Mathematical analysis.
His studies examine the connections between Mathematical analysis and genetics, as well as such issues in Nonlinear system, with regards to Curvilinear coordinates.
Between 2015 and 2021, his most popular works were:
- A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects (181 citations)
- A Review of Trimming in Isogeometric Analysis: Challenges, Data Exchange and Simulation Aspects (72 citations)
- Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: Geometric design and isogeometric analysis considerations (66 citations)
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