D-Index & Metrics Best Publications
Anthony T. Patera

Anthony T. Patera

D-Index & Metrics

Discipline name D-index D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines. Citations Publications World Ranking National Ranking
Engineering and Technology D-index 58 Citations 15,106 137 World Ranking 748 National Ranking 328

Research.com Recognitions

Awards & Achievements

2013 - THE THOMAS J.R. HUGHES MEDAL For seminal contributions in spectral element methods, certified reduced-basis methods, a-posteriori error estimations and scale bridging methods applied to complex fluid flow problems

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Partial differential equation
  • Statistics

Anthony T. Patera spends much of his time researching Mathematical analysis, Partial differential equation, Applied mathematics, Basis and Numerical analysis. In his research on the topic of Mathematical analysis, Spectral method is strongly related with Finite element method. His work carried out in the field of Partial differential equation brings together such families of science as Projection, Nonlinear system, Pressure-correction method and Affine transformation.

His Applied mathematics study combines topics in areas such as Nearest-neighbor interpolation, Birkhoff interpolation, Spline interpolation, Interpolation and Mathematical optimization. His Basis research integrates issues from Estimator, Parametric statistics and Galerkin method. His study looks at the intersection of Numerical analysis and topics like Parameter space with Eigenvalues and eigenvectors.

His most cited work include:

  • A spectral element method for fluid dynamics: Laminar flow in a channel expansion (1628 citations)
  • An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations (926 citations)
  • Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations (816 citations)

What are the main themes of his work throughout his whole career to date?

Anthony T. Patera mostly deals with Mathematical analysis, Partial differential equation, Applied mathematics, Finite element method and Basis. His Mathematical analysis study incorporates themes from Navier–Stokes equations, Domain decomposition methods and Nonlinear system. He has included themes like Projection, Numerical analysis and Affine transformation in his Partial differential equation study.

His Applied mathematics study combines topics from a wide range of disciplines, such as Upper and lower bounds, Estimator, Mathematical optimization and Residual. His Finite element method research incorporates themes from Discretization, Helmholtz equation and Heat transfer. His study in Basis is interdisciplinary in nature, drawing from both Parametric statistics and Galerkin method.

He most often published in these fields:

  • Mathematical analysis (33.67%)
  • Partial differential equation (29.65%)
  • Applied mathematics (28.64%)

What were the highlights of his more recent work (between 2011-2020)?

  • Applied mathematics (28.64%)
  • A priori and a posteriori (16.08%)
  • Basis (22.11%)

In recent papers he was focusing on the following fields of study:

Applied mathematics, A priori and a posteriori, Basis, Partial differential equation and Mathematical analysis are his primary areas of study. His research in Applied mathematics intersects with topics in Reduction, Greedy algorithm, Residual, Space and Function. His Basis study integrates concerns from other disciplines, such as Element, Dimension and Reduction.

The study incorporates disciplines such as Algorithm, Helmholtz free energy, Finite element method and Model order reduction in addition to Partial differential equation. The concepts of his Finite element method study are interwoven with issues in Discretization and Elliptic partial differential equation, Nonlinear system. His work on Interpolation and Inverse Laplace transform as part of general Mathematical analysis study is frequently linked to Gauss–Jacobi quadrature, Gaussian quadrature and Gauss–Kronrod quadrature formula, therefore connecting diverse disciplines of science.

Between 2011 and 2020, his most popular works were:

  • A PRIORI CONVERGENCE OF THE GREEDY ALGORITHM FOR THE PARAMETRIZED REDUCED BASIS METHOD (199 citations)
  • An improved error bound for reduced basis approximation of linear parabolic problems (77 citations)
  • A Static condensation Reduced Basis Element method: approximation and a posteriori error estimation (77 citations)

In his most recent research, the most cited papers focused on:

  • Mathematical analysis
  • Statistics
  • Partial differential equation

Anthony T. Patera focuses on Applied mathematics, A priori and a posteriori, Mathematical analysis, Partial differential equation and Greedy algorithm. His Applied mathematics research includes elements of Reduction and Domain decomposition methods. His study of A priori and a posteriori brings together topics like Basis, Mathematical optimization, Discretization, Parametric statistics and Acoustics.

His studies in Mathematical optimization integrate themes in fields like Estimator and Bounded function. Anthony T. Patera has researched Mathematical analysis in several fields, including Bilinear interpolation and Constant. His work deals with themes such as Helmholtz free energy, Representation and Data mining, which intersect with Partial differential equation.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

A spectral element method for fluid dynamics: Laminar flow in a channel expansion

Anthony T Patera.
Journal of Computational Physics (1984)

2683 Citations

An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations

Maxime Barrault;Yvon Maday;Ngoc Cuong Nguyen;Anthony T. Patera.
Comptes Rendus Mathematique (2004)

1425 Citations

Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations

Gianluigi Rozza;D.B.P. Huynh;Anthony T. Patera.
Archives of Computational Methods in Engineering (2007)

1081 Citations

Spectral element methods for the incompressible Navier-Stokes equations

Yvon Maday;Anthony T. Patera.
IN: State-of-the-art surveys on computational mechanics (A90-47176 21-64). New York (1989)

820 Citations

Secondary instability of wall-bounded shear flows

Steven A. Orszag;Anthony T. Patera.
Journal of Fluid Mechanics (1983)

712 Citations

Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods

Christophe Prud'Homme;Dimitrios Rovas;Karen Veroy;Luc Machiels.
Journal of Fluids Engineering-transactions of The Asme (2002)

644 Citations

EFFICIENT REDUCED-BASIS TREATMENT OF NONAFFINE AND NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

Martin A. Grepl;Yvon Maday;Yvon Maday;Ngoc C. Nguyen;Anthony T. Patera.
Mathematical Modelling and Numerical Analysis (2007)

557 Citations

A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations

Martin Alexander Grepl;Anthony T. Patera.
Mathematical Modelling and Numerical Analysis (2005)

435 Citations

Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations

Jan S Hesthaven;Anthony T Patera.
(2010)

410 Citations

Domain Decomposition by the Mortar Element Method

C. Bernardi;Y. Maday;A. T. Patera.
(1993)

407 Citations

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