Advanced Numerical Methods in Computational Mathematics
Advanced Numerical Methods in Computational Mathematics is a research topic within Computational Mechanics. Science Explorer counts 38k research works in it since 1950. 19.0% of them reached the world's top 10% most cited for their field and year.
This cluster of papers represents advancements in finite element methods, particularly focusing on their application to fluid-structure interaction problems. The papers cover topics such as discontinuous Galerkin methods, high-order schemes, adaptive mesh refinement, stabilized methods, multiscale modeling, preconditioners, variational methods, and PDE-constrained optimization.
- Finite Element Methods
- Fluid-Structure Interaction
- Discontinuous Galerkin Methods
- High-Order Schemes
- Adaptive Mesh Refinement
- Stabilized Methods
- Multiscale Modeling
- Preconditioners
- Variational Methods
- PDE-Constrained Optimization
- Research works
- 38k fractional, since 1950
- In the world top 10%
- 7.2k per year above
- Top-10% rate
- 19.0% share of its works in the world top 10%
- Growth, 2013–17 → 2018–22
- -3% the tick is no change
Which countries lead Advanced Numerical Methods in Computational Mathematics research?
By volume, China and the United States publish the most (1.4k and 687 works in 2022–2025).
By volume, 2022–2025
- 1 China 1.4k works
- 2 United States 687 works
- 3 Germany 378 works
- 4 France 303 works
- 5 India 209 works
- 6 Italy 206 works
- 7 Russia 183 works
- 8 United Kingdom 134 works
- 9 Spain 116 works
- 10 Japan 86 works
How concentrated that is
The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.
Shares of the rows listed above, not of the whole node.
Which institutions lead Advanced Numerical Methods in Computational Mathematics research?
By volume in 2022–2025, Centre National de la Recherche Scientifique publishes the most Advanced Numerical Methods in Computational Mathematics research, followed by Xinjiang University and Xi'an Jiaotong University.
By volume, 2022–2025
- 1 Centre National de la Recherche ScientifiqueFrance 43 works
- 2 Xinjiang UniversityChina 38 works
- 3 Xi'an Jiaotong UniversityChina 35 works
- 4 Shandong UniversityChina 32 works
- 5 Politecnico di MilanoItaly 28 works
- 6 Xiangtan UniversityChina 26 works
- 7 Leibniz University HannoverGermany 24 works
- 8 Shandong Normal UniversityChina 22 works
- 9 Zhengzhou UniversityChina 22 works
- 10 Shanghai Jiao Tong UniversityChina 21 works
Who are the leading researchers in Advanced Numerical Methods in Computational Mathematics?
The most-cited researchers publishing on Advanced Numerical Methods in Computational Mathematics include Stanley Osher, Ted Belytschko and Thomas J.R. Hughes.
- 1 Stanley Osher United States 8k citations
- 2 Ted Belytschko United States 4.1k citations
- 3 Thomas J.R. Hughes United States 3.7k citations
Ranked by citations received across their whole record, among researchers with at least three works on this topic.
Where is Advanced Numerical Methods in Computational Mathematics research done?
The largest centres of Advanced Numerical Methods in Computational Mathematics research in 2022–2025 are Beijing (China), Paris (France), Moscow (Russia) and Shanghai (China). Among places with at least 20 works in it, it is an unusually large share of all research in Xiangtan.
Largest cities, 2022–2025
Where it is the local speciality
- XiangtanCN · 30.4 works14×
Location quotient: how much more of its research is in Advanced Numerical Methods in Computational Mathematics than the world average.
Where is the best place to study Advanced Numerical Methods in Computational Mathematics?
Among universities, judged by research, Politecnico di Milano, Leibniz University Hannover and Rice University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.
One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.
| # | University | Score | Top 10% | Specialisation | Works | Growth |
|---|---|---|---|---|---|---|
| 1 | Politecnico di MilanoItaly | 61.6 | 24.0% | 8.4× | 28 | +10.2% |
| 2 | Leibniz University HannoverGermany | 57.5 | 16.8% | 17.8× | 24 | +0.1% |
| 3 | Rice UniversityUnited States | 57.0 | 23.5% | 11.8× | 12 | +36.6% |
| 4 | Indian Institute of Technology RoorkeeIndia | 54.7 | 37.8% | 4.3× | 9 | +164.9% |
| 5 | Indian Institute of Technology GuwahatiIndia | 54.1 | 4.7% | 12.5× | 20 | +175.3% |
| 6 | Istituto di Matematica Applicata e Tecnologie InformaticheItaly | 53.7 | 24.8% | 203.3× | 8 | -6.6% |
| 7 | Hong Kong Polytechnic UniversityHong Kong | 51.9 | 28.4% | 3.5× | 14 | +54.3% |
| 8 | Politecnico di TorinoItaly | 50.8 | 17.7% | 8.2× | 18 | +11.8% |
| 9 | Xinjiang UniversityChina | 49.6 | 3.6% | 18.4× | 38 | -0.8% |
| 10 | University of StuttgartGermany | 49.0 | 12.8% | 10.9× | 18 | -18.7% |
Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.
Is Advanced Numerical Methods in Computational Mathematics research growing?
Output in 2018–2022 was 3% lower than in 2013–2017, peaking in 2014. The fastest-growing topics are Advanced Numerical Methods in Computational Mathematics.
The same series as a ribbon — one cell per year, darker for more. The line above answers how much; this answers when.
Which topics inside it are moving
Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.