What is he best known for?
The fields of study he is best known for:
- Quantum mechanics
- Mathematical analysis
- Geometry
His primary areas of investigation include Mathematical analysis, Discontinuous Galerkin method, Spectral method, Mathematical optimization and Boundary value problem.
Time domain is closely connected to Computational electromagnetics in his research, which is encompassed under the umbrella topic of Mathematical analysis.
His Discontinuous Galerkin method research incorporates elements of Time domain electromagnetics, Fractional calculus, Maxwell's equations, Rate of convergence and Solver.
In his work, Polar coordinate system, Stochastic optimization and Stochastic ordering is strongly intertwined with Collocation method, which is a subfield of Spectral method.
Jan S. Hesthaven interconnects Stability, Collocation and Applied mathematics in the investigation of issues within Mathematical optimization.
As a member of one scientific family, he mostly works in the field of Finite element method, focusing on Approximation theory and, on occasion, Partial differential equation.
His most cited work include:
- Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications (1449 citations)
- High-Order Collocation Methods for Differential Equations with Random Inputs (1213 citations)
- Nodal high-order methods on unstructured grids (624 citations)
What are the main themes of his work throughout his whole career to date?
His scientific interests lie mostly in Mathematical analysis, Discontinuous Galerkin method, Applied mathematics, Spectral method and Nonlinear system.
His Mathematical analysis study combines topics from a wide range of disciplines, such as Finite element method and Galerkin method.
His study in Discontinuous Galerkin method is interdisciplinary in nature, drawing from both Artificial neural network, Wave equation, Rate of convergence, Numerical analysis and Solver.
His research integrates issues of Basis, Stability, Conservation law and Mathematical optimization in his study of Applied mathematics.
His work deals with themes such as Algorithm, Greedy algorithm and Hamiltonian system, which intersect with Basis.
His research in Spectral method intersects with topics in Geometry and topology, Penalty method, Partial differential equation, Collocation method and Polynomial.
He most often published in these fields:
- Mathematical analysis (36.42%)
- Discontinuous Galerkin method (23.46%)
- Applied mathematics (22.53%)
What were the highlights of his more recent work (between 2018-2021)?
- Applied mathematics (22.53%)
- Artificial neural network (6.17%)
- Nonlinear system (11.73%)
In recent papers he was focusing on the following fields of study:
Jan S. Hesthaven focuses on Applied mathematics, Artificial neural network, Nonlinear system, Discontinuous Galerkin method and Conservation law.
His Applied mathematics study integrates concerns from other disciplines, such as Polygon mesh, Model order reduction, Stencil, Cartesian coordinate system and Finite volume method.
His studies examine the connections between Artificial neural network and genetics, as well as such issues in Algorithm, with regards to Basis, Type and Generalization.
His studies in Nonlinear system integrate themes in fields like Scheme, Order, Kriging and Euler equations.
His Discontinuous Galerkin method research is multidisciplinary, incorporating perspectives in Wave equation, Numerical analysis, Mathematical analysis, Classification of discontinuities and Hierarchical matrix.
His Discretization study in the realm of Mathematical analysis interacts with subjects such as Poromechanics.
Between 2018 and 2021, his most popular works were:
- Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem (82 citations)
- Data-driven reduced order modeling for time-dependent problems (56 citations)
- Flowfield Reconstruction Method Using Artificial Neural Network (38 citations)
In his most recent research, the most cited papers focused on:
- Quantum mechanics
- Mathematical analysis
- Geometry
Jan S. Hesthaven spends much of his time researching Artificial neural network, Algorithm, Applied mathematics, Conservation law and Model order reduction.
His Artificial neural network research integrates issues from Deep learning, Classification of discontinuities and Discontinuous Galerkin method.
His Discontinuous Galerkin method research is under the purview of Finite element method.
Jan S. Hesthaven has researched Algorithm in several fields, including Basis, Type, Leverage and Nonlinear system.
His work carried out in the field of Nonlinear system brings together such families of science as Uncertainty quantification, Partial differential equation and Kriging.
His research investigates the connection with Applied mathematics and areas like Dissipation which intersect with concerns in Hamiltonian system, Rate of convergence, Boundary, Curvilinear coordinates and Spectral element method.
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