Leaderboards/Advanced Numerical Methods in Computational Mathematics

Advanced Numerical Methods in Computational Mathematics

Last updated July 7, 2026

Rising Stars

New and hot

Rising Stars Researchers

1
Qing Cheng
Tongji University
2
Pengzhan Jin
Beijing Institute of Big Data Research
3
Pasquale Claudio Africa
Scuola Internazionale Superiore di Studi Avanzati
4
Fukeng Huang
Bridge University
5
Lennart Linden
Technische Universität Dresden
6
Sumit Saini
Central University of Haryana
7
Théophile Chaumont-Frelet
Centre National de la Recherche Scientifique
8
Yulei Liao
National University of Singapore
9
Zheyuan Hu
National University of Singapore
10
Yizheng Wang
Bauhaus-Universität Weimar

Rising Stars Papers

1
Kolmogorov–Arnold-Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov–Arnold Networks
Computer Methods in Applied Mechanics and Engineering|2024
154 cit.
2
Tackling the curse of dimensionality with physics-informed neural networks
Neural Networks|2024
152 cit.
3
The deal.II library, Version 9.6
Journal of Numerical Mathematics|2024
97 cit.
4
Transfer Learning in Physics‐Informed Neurals Networks: Full Fine‐Tuning, Lightweight Fine‐Tuning, and Low‐Rank Adaptation
International journal of mechanical system dynamics|2025
39 cit.
5
DCEM: A deep complementary energy method for linear elasticity
International Journal for Numerical Methods in Engineering|2024
37 cit.
6
Hutchinson Trace Estimation for high-dimensional and high-order Physics-Informed Neural Networks
Computer Methods in Applied Mechanics and Engineering|2024
33 cit.
7
Two-stage attention network for fault diagnosis and retrieval of fault logs
Expert Systems with Applications|2024
17 cit.
8
On a New Class of BDF and IMEX Schemes for Parabolic Type Equations
SIAM Journal on Numerical Analysis|2024
14 cit.
9
Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker–Planck Equations
SIAM Journal on Scientific Computing|2025
11 cit.
10
Improved dendritic learning: Activation function analysis
Information Sciences|2024
10 cit.

Emerging Leaders

Gaining momentum

Emerging Leaders Researchers

1
Lorenzo Mascotto
University of Vienna
2
Blaž Hudobivnik
Leibniz University Hannover
3
James R. Maddison
Maxwell Institute for Mathematical Sciences
4
Jian-Ying Wu
South China University of Technology
5
Tiantang Yu
Hohai University
6
Franco Dassi
University of Milano-Bicocca
7
Yating Wang
Xi'an Jiaotong University
8
Théo Mary
Université Toulouse III - Paul Sabatier
9
Fei Wang
Xi'an Jiaotong University
10
Alban de Vaucorbeil
Deakin University

Emerging Leaders Papers

1
Mixed precision algorithms in numerical linear algebra
Acta Numerica|2022
123 cit.
2
Tunable selectivity on copper–bismuth bimetallic aerogels for electrochemical CO2 reduction
Applied Catalysis B: Environmental|2022
54 cit.
3
The role of stabilization in the virtual element method: A survey
Computers & Mathematics with Applications|2023
35 cit.
4
A new finite element method framework for axially functionally-graded nanobeam with stress-driven two-phase nonlocal integral model
Composite Structures|2022
33 cit.
5
Acute Sensitivity of Global Ocean Circulation and Heat Content to Eddy Energy Dissipation Timescale
Geophysical Research Letters|2022
31 cit.
6
Local randomized neural networks with discontinuous Galerkin methods for partial differential equations
Journal of Computational and Applied Mathematics|2024
31 cit.
7
The interior penalty virtual element method for the biharmonic problem
Mathematics of Computation|2023
23 cit.
8
Bend 3d mixed virtual element method for Darcy problems
Computers & Mathematics with Applications|2022
22 cit.
9
Stability and Interpolation Properties for Stokes-Like Virtual Element Spaces
Journal of Scientific Computing|2023
22 cit.
10
Local randomized neural networks with discontinuous Galerkin methods for diffusive-viscous wave equation
Computers & Mathematics with Applications|2023
22 cit.

Current Senior Leaders

Established & currently active

Current Senior Leaders Researchers

1
Kenneth V. Price
Universidade de Marília
2
Chi‐Wang Shu
Brown University
3
Thomas J.R. Hughes
The University of Texas at Austin
4
Yuri Bazilevs
Waseda University
5
Ivo Babuška
The University of Texas at Austin
6
Tayfun E. Tezduyar
Rice University
7
L. D. Marini
University of Minnesota
8
Anthony T. Patera
Massachusetts Institute of Technology
9
J.Z. Zhu
Xiamen University
10
A. Russo
University of Milano-Bicocca

Current Senior Leaders Papers

1
Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces
Journal of Global Optimization|1997
28.7k cit.
2
Efficient Implementation of Weighted ENO Schemes
Journal of Computational Physics|1996
6.5k cit.
3
Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
Computer Methods in Applied Mechanics and Engineering|2005
6.2k cit.
4
Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
Computer Methods in Applied Mechanics and Engineering|1982
5.3k cit.
5
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics|1989
4.9k cit.
6
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics|1988
4.7k cit.
7
The partition of unity finite element method: Basic theory and applications
Computer Methods in Applied Mechanics and Engineering|1996
3.4k cit.
8
Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces
Unknown Journal|2004
3.4k cit.
9
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis|2002
3.2k cit.
10
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation|1998
2.5k cit.

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