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Advanced Mathematical Modeling in Engineering

Advanced Mathematical Modeling in Engineering is a research topic within Computational Theory and Mathematics. Science Explorer counts 56k research works in it since 1950. 15.0% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the development and application of multiscale methods for analyzing heterogeneous systems, particularly in the context of homogenization, finite element simulations, and porous media flow. The papers cover topics such as upscaling techniques, subsurface flow simulation, coarse-grained computation, and the use of microscopic simulators to perform system-level analysis.

  • Multiscale Methods
  • Heterogeneous
  • Homogenization
  • Finite Element
  • Porous Media
  • Elliptic Problems
  • Upscaling Techniques
  • Subsurface Flow
  • Coarse-Grained Computation
  • Microscopic Simulators
Research works
56k
fractional, since 1950
In the world top 10%
8.4k
per year above
Top-10% rate
15.0%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
+7%
the tick is no change

Which countries lead Advanced Mathematical Modeling in Engineering research?

By volume, China and the United States publish the most (1.9k and 751 works in 2022–2025).

By volume, 2022–2025

  1. 1 China 1.9k works
  2. 2 United States 751 works
  3. 3 Russia 603 works
  4. 4 France 519 works
  5. 5 Italy 479 works
  6. 6 Germany 443 works
  7. 7 India 280 works
  8. 8 Brazil 248 works
  9. 9 Japan 207 works
  10. 10 Morocco 190 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.

China: 34.3%United States: 13.3%Russia: 10.7%France: 9.2%6 others listed: 32.6%34%largest
China1,938 · 34.3%United States751 · 13.3%Russia603 · 10.7%France519 · 9.2%6 others listed1,847 · 32.6%

Shares of the rows listed above, not of the whole node.

Which institutions lead Advanced Mathematical Modeling in Engineering research?

By volume in 2022–2025, Lomonosov Moscow State University publishes the most Advanced Mathematical Modeling in Engineering research, followed by Centre National de la Recherche Scientifique and Southwest University.

Who are the leading researchers in Advanced Mathematical Modeling in Engineering?

The most-cited researchers publishing on Advanced Mathematical Modeling in Engineering include Stanley Osher, H. Eugene Stanley and Thomas J.R. Hughes.

  1. 1 Stanley Osher United States 8k citations
  2. 2 H. Eugene Stanley United States 5.5k citations
  3. 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 Mathematical Modeling in Engineering research done?

The largest centres of Advanced Mathematical Modeling in Engineering research in 2022–2025 are Beijing (China), Moscow (Russia), Paris (France) and Shanghai (China). Among places with at least 20 works in it, it is an unusually large share of all research in Beni Mellal.

Largest cities, 2022–2025

  1. 1 Beijing China 297 works
  2. 2 Moscow Russia 240 works
  3. 3 Paris France 160 works
  4. 4 Shanghai China 134 works
  5. 5 Nanjing China 101 works
  6. 6 Wuhan China 87 works
  7. 7 Chongqing China 77 works
  8. 8 Xi'an China 73 works
  9. 9 Tokyo Japan 70 works
  10. 10 Saint Petersburg Russia 69 works

Where it is the local speciality

  1. Beni MellalMA · 43.9 works40×
← less than its size predictsmore →

Location quotient: how much more of its research is in Advanced Mathematical Modeling in Engineering than the world average.

See Advanced Mathematical Modeling in Engineering on the map

Where is the best place to study Advanced Mathematical Modeling in Engineering?

Among universities, judged by research, Université Sultan Moulay Slimane, Imam Khomeini International University and Qassim 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.

0%20%40%mean 19.52%fractional works in this node (log) →share in the world top 10% →Université Sultan Moulay Slimane: 44, 32.6%Imam Khomeini International University: 14, 37.8%Qassim University: 20, 13.9%Lomonosov Moscow State University: 74, 7.8%Tunis El Manar University: 18, 13.1%Sidi Mohamed Ben Abdellah University: 26, 8.4%University of Palermo: 13, 34.1%Jimma University: 9, 32.3%Southwest University: 46, 7.9%Abdelmalek Essaâdi University: 14, 7.3%Imam Khomeini Intern…Université Sultan Mo…Qassim UniversityLomonosov Moscow Sta…
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1 Université Sultan Moulay SlimaneMorocco 68.132.6%40.2×44
2 Imam Khomeini International UniversityIran 61.137.8%30.2×14
3 Qassim UniversitySaudi Arabia 60.913.9%9.7×20 +293.3%
4 Lomonosov Moscow State UniversityRussia 58.97.8%10.9×74 +39.9%
5 Tunis El Manar UniversityTunisia 58.813.1%12.9×18 +205.6%
6 Sidi Mohamed Ben Abdellah UniversityMorocco 57.28.4%12.2×26 +612.9%
7 University of PalermoItaly 54.034.1%4.9×13 +521.4%
8 Jimma UniversityEthiopia 53.932.3%9.7×9
9 Southwest UniversityChina 52.27.9%10.6×46 +41.8%
10 Abdelmalek Essaâdi UniversityMorocco 51.37.3%10.6×14 +226.4%

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 Mathematical Modeling in Engineering research growing?

Output in 2018–2022 was 7% higher than in 2013–2017, peaking in 2024. The fastest-growing topics are Advanced Mathematical Modeling in Engineering.

19801990200020102020
grewheldshrank

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.