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Topic · Computational Mechanics

Advanced Numerical Analysis Techniques

Advanced Numerical Analysis Techniques is a research topic within Computational Mechanics. Science Explorer counts 42k 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 application of isogeometric analysis in computational engineering, particularly in the areas of structural analysis, fluid-structure interaction, shape optimization, and boundary element methods. The use of NURBS, finite elements, CAD, mesh refinement, T-splines, and their implementation in CNC machining are central to the research.

  • NURBS
  • Finite Elements
  • CAD
  • Mesh Refinement
  • T-splines
  • Structural Analysis
  • Fluid-structure Interaction
  • Shape Optimization
  • Boundary Element Method
  • CNC Machining
Research works
42k
fractional, since 1950
In the world top 10%
4.3k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+18%
the tick is no change
Largest producer
China
42% of the 10 largest, 2022-now
Advanced Numerical Analysis Techniques

Which countries lead Advanced Numerical Analysis Techniques research?

By volume, China and the United States publish the most (1.7k and 617 works in 2022-now).

By volume, 2022-now

  1. 1 China 1.7k works
  2. 2 United States 617 works
  3. 3 Germany 374 works
  4. 4 France 231 works
  5. 5 India 226 works
  6. 6 Italy 182 works
  7. 7 Japan 176 works
  8. 8 Türkiye 169 works
  9. 9 Russia 162 works
  10. 10 United Kingdom 121 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: 42.2%United States: 15.8%Germany: 9.6%France: 5.9%6 others listed: 26.5%42%largest
China1,652 · 42.2%United States617 · 15.8%Germany374 · 9.6%France231 · 5.9%6 others listed1,037 · 26.5%

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

Which institutions lead Advanced Numerical Analysis Techniques research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Advanced Numerical Analysis Techniques research, followed by Dalian University of Technology and Chinese Academy of Sciences.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 94 works
  2. 2 Dalian University of TechnologyChina 57 works
  3. 3 Chinese Academy of SciencesChina 49 works
  4. 4 Zhejiang UniversityChina 41 works
  5. 5 Shanghai Jiao Tong UniversityChina 40 works
  6. 6 Tsinghua UniversityChina 36 works
  7. 7 Huazhong University of Science and TechnologyChina 35 works
  8. 8 Russian Academy of SciencesRussia 34 works
  9. 9 University of Science and Technology of ChinaChina 32 works
  10. 10 Beihang UniversityChina 31 works

Who are the leading researchers in Advanced Numerical Analysis Techniques?

The most-cited researchers publishing on Advanced Numerical Analysis Techniques include Robert John Tibshirani, Trevor Hastie and Xiaogang Wang.

  1. 1 Robert John Tibshirani United States 396k citations
  2. 2 Trevor Hastie United States 301k citations
  3. 3 Xiaogang Wang China 260k citations
  4. 4 Andrew Zisserman United Kingdom 255k citations
  5. 5 Li Fei-Fei United States 225k citations
  6. 6 A. Meyer France 224k 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 Numerical Analysis Techniques?

The most cited paper in Advanced Numerical Analysis Techniques is "Active contours without edges" (Tony Fan-Cheong Chan, Luminita A. Vese, 2001), with 10,394 citations. Next come "UMAP: Uniform Manifold Approximation and Projection" (10,200) and "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement" (6,340).

Most cited papers
#PaperReleasedCitations
1 Active contours without edges Tony Fan-Cheong Chan, Luminita A. Vese · IEEE Transactions on Image Processing 2001 10,394
2 UMAP: Uniform Manifold Approximation and Projection Leland McInnes, John Healy, Nathaniel Saul et al. · The Journal of Open Source Software Open access 2 Sep 2018 10,200
3 Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement Thomas J.R. Hughes, J. Austin Cottrell, Yuri Bazilevs · Computer Methods in Applied Mechanics and Engineering Open access Feb 2005 6,340
4 Computational Geometry: Algorithms and Applications Mark de Berg, Otfried Cheong, Marc J. van Kreveld et al. · CERN Document Server (European Organization for Nuclear Research) 1997 4,503
5 ALGORITHMS FOR THE REDUCTION OF THE NUMBER OF POINTS REQUIRED TO REPRESENT A DIGITIZED LINE OR ITS CARICATURE David H. Douglas, Thomas K. Peucker · Cartographica The International Journal for Geographic Information and Geovisualization Dec 1973 4,256
All 99 most cited papers, with filters and sorting

Where is Advanced Numerical Analysis Techniques research done?

The largest centres of Advanced Numerical Analysis Techniques research in 2022-now are Beijing (China), Shanghai (China), Xi'an (China) and Wuhan (China).

Largest cities, 2022-now

  1. 1 BeijingChina 272 works
  2. 2 ShanghaiChina 114 works
  3. 3 Xi'anChina 95 works
  4. 4 WuhanChina 89 works
  5. 5 HangzhouChina 82 works
  6. 6 NanjingChina 77 works
  7. 7 DalianChina 76 works
  8. 8 MoscowRussia 71 works
  9. 9 TokyoJapan 67 works
  10. 10 ParisFrance 56 works
See Advanced Numerical Analysis Techniques on the map

Where is the best place to study Advanced Numerical Analysis Techniques?

Among universities, judged by research, Huazhong University of Science and Technology, Shanghai Jiao Tong University and Dalian University of Technology 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 20.85%fractional works in this field (log) →share of work in the world top 10% →Huazhong University …Shanghai Jiao Tong U…Dalian University of…École Polytechnique …
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
1Huazhong University of Science and TechnologyChina 77.536.1%4.1×35 +12.5%
2Shanghai Jiao Tong UniversityChina 74.825.2%3.0×40 +71.5%
3Dalian University of TechnologyChina 74.522.2%12.9×57 +1.4%
4École Polytechnique Fédérale de LausanneSwitzerland 69.421.9%8.0×15 +56.6%
5Tsinghua UniversityChina 69.223.6%3.4×36 +80.0%
6University of PaviaItaly 68.220.3%8.1×10 +27.0%
7Carnegie Mellon UniversityUnited States 63.522.9%6.7×13 +4.6%
8Zhejiang UniversityChina 62.615.0%3.2×41 +42.2%
9ETH ZurichSwitzerland 62.611.2%5.3×17 +54.2%
10Technical University of MunichGermany 62.510.1%6.8×28 +61.4%

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 Numerical Analysis Techniques, country by country

Is Advanced Numerical Analysis Techniques research growing?

Output in 2022-2025 was 18% higher than in 2018-2021, peaking in 2011. The fastest-growing topics are Advanced Numerical Analysis Techniques.

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 Numerical Analysis Techniques as a percentage of every work published that year, 0.028% in 2024.

still counting0.025%0.050%0.075%Advanced Numerical Analysis Techniques0.023% in 202519801990200020102020

Fractional works of Advanced Numerical Analysis Techniques 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 Numerical Analysis Techniques10.1% 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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