D-Index & Metrics Best Publications

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
Mathematics D-index 52 Citations 29,452 115 World Ranking 474 National Ranking 242

Research.com Recognitions

Awards & Achievements

2013 - Fellow of the American Mathematical Society

2010 - SIAM Fellow For contribution to numerical analysis and scientific computing, particularly for conservation laws.

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Geometry
  • Partial differential equation

His main research concerns Mathematical analysis, Conservation law, Numerical analysis, Finite volume method and Partial differential equation. As part of his studies on Mathematical analysis, Randall J. LeVeque frequently links adjacent subjects like Incompressible flow. His Conservation law research incorporates themes from Riemann problem, Conservation form, Euler equations and Hyperbolic partial differential equation, Differential equation.

The various areas that he examines in his Hyperbolic partial differential equation study include Shock wave and Euler's formula. Randall J. LeVeque has included themes like Computation, Double-precision floating-point format, Classical mechanics and Round-off error in his Numerical analysis study. His Finite volume method research is multidisciplinary, incorporating elements of Adaptive mesh refinement, Software, Shallow water equations and Fortran.

His most cited work include:

  • Finite Volume Methods for Hyperbolic Problems (3920 citations)
  • Numerical methods for conservation laws (2916 citations)
  • the immersed interface method for elliptic equations with discontinuous coefficients and singular sources (1109 citations)

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

His primary scientific interests are in Mathematical analysis, Finite volume method, Conservation law, Numerical analysis and Partial differential equation. As a part of the same scientific study, Randall J. LeVeque usually deals with the Mathematical analysis, concentrating on Regular grid and frequently concerns with Cartesian coordinate system. His studies in Finite volume method integrate themes in fields like Shallow water equations, Software, Discontinuous Galerkin method and Adaptive mesh refinement.

His Software study combines topics from a wide range of disciplines, such as Python and Fortran. In Conservation law, he works on issues like Applied mathematics, which are connected to Linear equation and Iterative method. The Euler equations study combines topics in areas such as Shock wave, Mechanics, Blast wave, Shock tube and Boundary value problem.

He most often published in these fields:

  • Mathematical analysis (35.22%)
  • Finite volume method (24.35%)
  • Conservation law (17.83%)

What were the highlights of his more recent work (between 2016-2021)?

  • Seismology (10.43%)
  • Subduction (4.78%)
  • Mathematical analysis (35.22%)

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

His primary areas of investigation include Seismology, Subduction, Mathematical analysis, Partial differential equation and Adaptive mesh refinement. His research in the fields of Wave equation, Finite difference method and Truncation error overlaps with other disciplines such as Path integral formulation and Reflection. His work in Finite difference method addresses subjects such as Linear dispersion, which are connected to disciplines such as Finite volume method.

Randall J. LeVeque interconnects Singular value and Algorithm, Iterative method in the investigation of issues within Partial differential equation. His Iterative method study combines topics from a wide range of disciplines, such as Space, Conservation law, Scalar and Differential equation. In his study, Software is strongly linked to Domain, which falls under the umbrella field of Hyperbolic partial differential equation.

Between 2016 and 2021, his most popular works were:

  • On the Accuracy of Stable Schemes for 2d Scalar Conservation Laws (142 citations)
  • Probabilistic Tsunami Hazard Analysis: Multiple Sources and Global Applications (76 citations)
  • Transport Reversal for Model Reduction of Hyperbolic Partial Differential Equations (29 citations)

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

  • Mathematical analysis
  • Geometry
  • Algebra

His scientific interests lie mostly in Mathematical analysis, Shallow water equations, Partial differential equation, Breaking wave and Finite volume method. His Mathematical analysis research is multidisciplinary, incorporating perspectives in Iterative method and Scalar. His Shallow water equations research is multidisciplinary, incorporating elements of Depth averaged, CUDA and Computational science, Adaptive mesh refinement.

His Partial differential equation research incorporates themes from Singular value, Conservation law and Space. His work in Finite volume method covers topics such as Software which are related to areas like Numerical analysis. His Numerical analysis study combines topics in areas such as Riemann problem, Euler equations, Shock wave, Geometry and Compressibility.

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

Finite Volume Methods for Hyperbolic Problems

Randall J. LeVeque.
(2002)

7954 Citations

Numerical methods for conservation laws

Randall J. LeVeque.
(1990)

5726 Citations

Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-dependent Problems

Randall J. LeVeque.
(2007)

2301 Citations

the immersed interface method for elliptic equations with discontinuous coefficients and singular sources

Randall J. Leveque;Zhilin Li.
SIAM Journal on Numerical Analysis (1994)

1587 Citations

Balancing Source Terms and Flux Gradients in High-Resolution Godunov Methods

Randall J. LeVeque.
Journal of Computational Physics (1998)

1017 Citations

High-resolution conservative algorithms for advection in incompressible flow

Randall J. LeVeque.
SIAM Journal on Numerical Analysis (1996)

802 Citations

Wave Propagation Algorithms for Multidimensional Hyperbolic Systems

Randall J. LeVeque.
Journal of Computational Physics (1997)

748 Citations

A study of numerical methods for hyperbolic conservation laws with stiff source terms

R. J. LeVeque;H. C. Yee.
Journal of Computational Physics (1990)

571 Citations

Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension

Randall J. LeVeque;Zhilin Li.
SIAM Journal on Scientific Computing (1997)

567 Citations

Approximate Riemann Solvers

Randall J. LeVeque.
(1992)

543 Citations

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