What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Partial differential equation
- Finite element method
The scientist’s investigation covers issues in Mathematical analysis, Numerical analysis, Finite element method, Navier–Stokes equations and Partial differential equation.
Olivier Pironneau has researched Mathematical analysis in several fields, including Stokes flow and Stokes' law.
His Numerical analysis study incorporates themes from Conjugate gradient method, Mixed finite element method, Biharmonic equation and Computational science.
His Finite element method research focuses on Euler equations and how it relates to Finite difference method, Discretization, Method of characteristics and Algorithm.
His Navier–Stokes equations research is multidisciplinary, incorporating elements of Turbulence and Incompressible flow.
His work on Finite volume method for one-dimensional steady state diffusion as part of general Partial differential equation research is often related to FTCS scheme and Shape design, thus linking different fields of science.
His most cited work include:
- Optimal Shape Design for Elliptic Systems (949 citations)
- On the transport-diffusion algorithm and its applications to the Navier-Stokes equations (556 citations)
- On optimum design in fluid mechanics (513 citations)
What are the main themes of his work throughout his whole career to date?
Olivier Pironneau spends much of his time researching Applied mathematics, Mathematical analysis, Finite element method, Mathematical optimization and Partial differential equation.
Olivier Pironneau combines subjects such as Lagrange multiplier, Numerical partial differential equations, Computational fluid dynamics, Grid and Calculus with his study of Applied mathematics.
His Computational fluid dynamics research is multidisciplinary, incorporating perspectives in Turbulence, Fluid mechanics and Inviscid flow.
His Mathematical analysis research focuses on Domain decomposition methods and how it connects with Algorithm.
His Finite element method research includes themes of Discretization, Incompressible flow and Numerical analysis.
His work deals with themes such as Valuation of options, Local volatility, Stochastic volatility, Shape optimization and Automatic differentiation, which intersect with Mathematical optimization.
He most often published in these fields:
- Applied mathematics (27.94%)
- Mathematical analysis (26.47%)
- Finite element method (26.47%)
What were the highlights of his more recent work (between 2012-2021)?
- Applied mathematics (27.94%)
- Mathematical optimization (21.57%)
- Finite element method (26.47%)
In recent papers he was focusing on the following fields of study:
Olivier Pironneau mostly deals with Applied mathematics, Mathematical optimization, Finite element method, Mechanics and Eulerian path.
His research integrates issues of Parareal algorithm, Parareal, Grid and Euler's formula in his study of Applied mathematics.
His Mathematical optimization research includes elements of Numerical differentiation, Differentiable function, Automatic differentiation and Malliavin calculus.
The Finite element method study combines topics in areas such as Numerical analysis and Mathematical analysis.
His biological study spans a wide range of topics, including Microchannel, Partial differential equation and Boundary, Free boundary problem.
His Mathematical analysis research incorporates elements of Shape optimization, Local property and Topology optimization.
Between 2012 and 2021, his most popular works were:
- Dynamic programming for mean-field type control (40 citations)
- Benchmark problems for numerical treatment of backflow at open boundaries (28 citations)
- An Energy Stable Monolithic Eulerian Fluid‐Structure Finite Element Method (16 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Partial differential equation
- Geometry
His primary scientific interests are in Finite element method, Fluid–structure interaction, Hyperelastic material, Eulerian path and Mechanics.
His Finite element method study frequently draws connections between related disciplines such as Numerical analysis.
His research in Fluid–structure interaction intersects with topics in Navier–Stokes equations, Displacement and Mathematical analysis.
His study looks at the relationship between Mathematical analysis and fields such as Topology optimization, as well as how they intersect with chemical problems.
Olivier Pironneau has included themes like Immersed boundary method, Conservation law and Continuum mechanics, Classical mechanics in his Hyperelastic material study.
His research in Conservation law focuses on subjects like Mixed finite element method, which are connected to Mathematical optimization.
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