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Topic · Computational Theory and Mathematics

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. 10.0% 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%
5.6k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+13%
the tick is no change
Largest producer
China
35% of the 10 largest, 2022-now
Advanced Mathematical Modeling in Engineering

Which countries lead Advanced Mathematical Modeling in Engineering research?

By volume, China and the United States publish the most (2.2k and 812 works in 2022-now).

By volume, 2022-now

  1. 1 China 2.2k works
  2. 2 United States 812 works
  3. 3 Russia 629 works
  4. 4 France 546 works
  5. 5 Italy 506 works
  6. 6 Germany 478 works
  7. 7 India 306 works
  8. 8 Brazil 263 works
  9. 9 Japan 221 works
  10. 10 Morocco 195 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: 35.3%United States: 13.3%Russia: 10.3%France: 8.9%6 others listed: 32.2%35%largest
China2,156 · 35.3%United States812 · 13.3%Russia629 · 10.3%France546 · 8.9%6 others listed1,969 · 32.2%

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

Which institutions lead Advanced Mathematical Modeling in Engineering research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Advanced Mathematical Modeling in Engineering research, followed by Russian Academy of Sciences and Lomonosov Moscow State University.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 247 works
  2. 2 Russian Academy of SciencesRussia 197 works
  3. 3 Lomonosov Moscow State UniversityRussia 76 works
  4. 4 Chinese Academy of SciencesChina 58 works
  5. 5 Southwest UniversityChina 46 works
  6. 6 Université Sultan Moulay SlimaneMorocco 44 works
  7. 7 Sapienza University of RomeItaly 42 works
  8. 8 Politecnico di MilanoItaly 40 works
  9. 9 Central South UniversityChina 39 works
  10. 10 St Petersburg UniversityRussia 36 works

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

The most-cited researchers publishing on Advanced Mathematical Modeling in Engineering include A. Meyer, Albert-Ĺaszló Barabási and Harry Eugene Stanley.

  1. 1 A. Meyer France 224k citations
  2. 2 Albert-Ĺaszló Barabási United States 223k citations
  3. 3 Harry Eugene Stanley United States 198k citations
  4. 4 R. W. L. Jones United Kingdom 189k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Advanced Mathematical Modeling in Engineering?

The most cited paper in Advanced Mathematical Modeling in Engineering is "Generating optimal topologies in structural design using a homogenization method" (Martin Philip Bendsøe, Noboru Kikuchi, 1988), with 7,508 citations. Next come "Elastic properties of reinforced solids: Some theoretical principles" (4,905) and "Perturbation Methods" (4,699).

Most cited papers
#PaperReleasedCitations
1 Generating optimal topologies in structural design using a homogenization method Martin Philip Bendsøe, Noboru Kikuchi · Computer Methods in Applied Mechanics and Engineering Nov 1988 7,508
2 Elastic properties of reinforced solids: Some theoretical principles R. Hill · Journal of the Mechanics and Physics of Solids Sep 1963 4,905
3 Perturbation Methods A. H. Nayfeh, Vimal Singh · IEEE Transactions on Systems Man and Cybernetics May 1978 4,699
4 Optimal shape design as a material distribution problem Martin Philip Bendsøe · Structural and Multidisciplinary Optimization Dec 1989 4,565
5 Compact sets in the spaceL p (O,T; B) Jacques Simon · Annali di Matematica Pura ed Applicata (1923 -) Open access Dec 1986 4,138
All 100 most cited papers, with filters and sorting

Where is Advanced Mathematical Modeling in Engineering research done?

The largest centres of Advanced Mathematical Modeling in Engineering research in 2022-now 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-now

  1. 1 BeijingChina 324 works
  2. 2 MoscowRussia 249 works
  3. 3 ParisFrance 168 works
  4. 4 ShanghaiChina 144 works
  5. 5 NanjingChina 107 works
  6. 6 WuhanChina 96 works
  7. 7 Xi'anChina 82 works
  8. 8 ChongqingChina 79 works
  9. 9 TokyoJapan 74 works
  10. 10 GuangzhouChina 72 works

Where it is the local speciality

  1. Beni MellalMA · 43.9 works37×
← less than its size predicts1×more →

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, Politecnico di Milano and Korea 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%60%mean 22.16%fractional works in this field (log) →share of work in the world top 10% →Korea UniversityUniversité Sultan Mo…Politecnico di MilanoImam Khomeini Intern…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Université Sultan Moulay SlimaneMorocco 69.425.9%42.8×44 +680.7%
2Politecnico di MilanoItaly 63.222.7%7.5×40 +34.6%
3Korea UniversitySouth Korea 62.247.7%2.4×11 +59.1%
4Imam Khomeini International UniversityIran 54.722.4%32.5×14 +99.0%
5Southwest UniversityChina 53.76.8%11.3×46 +28.8%
6Paderborn UniversityGermany 52.533.0%10.1×10 +90.9%
7Lomonosov Moscow State UniversityRussia 52.24.8%11.9×76 -0.9%
8Beijing Normal UniversityChina 51.514.1%4.9×29 +50.2%
9City University of Hong KongChina 51.219.0%4.1×18 +108.0%
10Bielefeld UniversityGermany 50.925.2%9.0×16 +154.8%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Advanced Mathematical Modeling in Engineering, country by country

Is Advanced Mathematical Modeling in Engineering research growing?

Output in 2022-2025 was 13% higher than in 2018-2021, peaking in 2024. The fastest-growing topics are Advanced Mathematical Modeling in Engineering.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Advanced Mathematical Modeling in Engineering as a percentage of every work published that year, 0.041% in 2024.

still counting0.050%0.10%Advanced Mathematical Modeling in Engineering0.033% in 202519801990200020102020

Fractional works of Advanced Mathematical Modeling in Engineering over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Advanced Mathematical Modeling in Engineering9.8% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

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.

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