World's Best Scientists 2026 revealed!
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Zhiqiang Cai

D-Index & Metrics

Discipline name D-Index World Ranking Current World Ranking National Ranking Current National Ranking Publications Citations
Mathematics 39 2191 1935 924 765 138 6712
Engineering and Technology 49 4235 4069 1213 1117 228 11753

Zhiqiang Cai publications per year

The chart shows the history of publications by Zhiqiang Cai between 1988 and 2025, highlighting the no. of papers published in each year and offering an overview of the publication velocity of this scholar. Zhiqiang Cai published across 38 years, from 1988 to 2025, averaging 7.1 papers a year. Output peaked at 24 publications in 2021. 16 of the 271 publications appeared in the last two years.

No. of publications
5 10 15 20
Bar chart. Horizontal axis: year, 1988 to 2025. Vertical axis: number of publications, 0 to 24. Peak 24 publications in 2021. 1988: 1 publication 1989: 1 publication 1990: 2 publications 1991: 1 publication 1992: 1 publication 1993: 2 publications 1994: 1 publication 1995: 1 publication 1996: 4 publications 1997: 2 publications 1998: 3 publications 1999: 5 publications 2000: 3 publications 2001: 3 publications 2002: 2 publications 2003: 4 publications 2004: 5 publications 2005: 10 publications 2006: 7 publications 2007: 8 publications 2008: 3 publications 2009: 12 publications 2010: 13 publications 2011: 5 publications 2012: 13 publications 2013: 7 publications 2014: 22 publications 2015: 11 publications 2016: 19 publications 2017: 12 publications 2018: 14 publications 2019: 15 publications 2020: 11 publications 2021: 24 publications 2022: 3 publications 2023: 5 publications 2024: 7 publications 2025: 9 publications
1988 2025

271 publications in total across all disciplines

View publications per year as a table
Zhiqiang Cai: publications per year, 1988 to 2025
Year Publications
1988 1
1989 1
1990 2
1991 1
1992 1
1993 2
1994 1
1995 1
1996 4
1997 2
1998 3
1999 5
2000 3
2001 3
2002 2
2003 4
2004 5
2005 10
2006 7
2007 8
2008 3
2009 12
2010 13
2011 5
2012 13
2013 7
2014 22
2015 11
2016 19
2017 12
2018 14
2019 15
2020 11
2021 24
2022 3
2023 5
2024 7
2025 9
Total 271
Download as CSV

Zhiqiang Cai publications per year - data summary

  • Zhiqiang Cai, a Mathematics scholar from Purdue University West Lafayette, has 271 publications recorded across 38 years, from 1988 to 2025.
  • The oldest publication on record dates to 1988 and the most recent to 2025.
  • The most productive year is 2021, with 24 publications.
  • The least productive years with any output are 1988, 1989, 1991, 1992 and others, with 1 publication each.
  • The rate of publication averages 7.1 papers per year over the whole span, or 7.1 per year counting only the 38 years with at least one publication.
  • The last 5 years on the chart (2021-2025) hold 48 publications, 18% of the career total.
  • Split into equal eras - 1988-2000: 27 publications (2.1 per year); 2001-2013: 92 publications (7.1 per year); 2014-2025: 152 publications (12.7 per year).
  • Comparing the opening and closing eras, the overall trend of publication is rising.

Zhiqiang Cai publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where Zhiqiang Cai sits on this spectrum.

No. of scientists
25 50 75 100
Bar chart with 100 bars. Horizontal axis: publications, 42–46 to 537+. Vertical axis: number of scientists, 0 to 112. Most scientists, 112, have 142–146 publications. The last bar groups every scientist with 537 publications or more. The highlighted bar, 137–141 publications, is where this scientist sits. 42–46 publications: 3 scientists 47–51 publications: 5 scientists 52–56 publications: 7 scientists 57–61 publications: 20 scientists 62–66 publications: 14 scientists 67–71 publications: 25 scientists 72–76 publications: 19 scientists 77–81 publications: 35 scientists 82–86 publications: 50 scientists 87–91 publications: 60 scientists 92–96 publications: 86 scientists 97–101 publications: 84 scientists 102–106 publications: 83 scientists 107–111 publications: 90 scientists 112–116 publications: 99 scientists 117–121 publications: 90 scientists 122–126 publications: 91 scientists 127–131 publications: 109 scientists 132–136 publications: 110 scientists 137–141 publications: 98 scientists 142–146 publications: 112 scientists 147–151 publications: 102 scientists 152–156 publications: 88 scientists 157–161 publications: 106 scientists 162–166 publications: 83 scientists 167–171 publications: 102 scientists 172–176 publications: 77 scientists 177–181 publications: 81 scientists 182–186 publications: 78 scientists 187–191 publications: 71 scientists 192–196 publications: 92 scientists 197–201 publications: 64 scientists 202–206 publications: 69 scientists 207–211 publications: 64 scientists 212–216 publications: 62 scientists 217–221 publications: 58 scientists 222–226 publications: 53 scientists 227–231 publications: 50 scientists 232–236 publications: 46 scientists 237–241 publications: 46 scientists 242–246 publications: 46 scientists 247–251 publications: 43 scientists 252–256 publications: 29 scientists 257–261 publications: 45 scientists 262–266 publications: 30 scientists 267–271 publications: 33 scientists 272–276 publications: 34 scientists 277–281 publications: 30 scientists 282–286 publications: 31 scientists 287–291 publications: 21 scientists 292–296 publications: 34 scientists 297–301 publications: 26 scientists 302–306 publications: 10 scientists 307–311 publications: 17 scientists 312–316 publications: 23 scientists 317–321 publications: 13 scientists 322–326 publications: 16 scientists 327–331 publications: 26 scientists 332–336 publications: 13 scientists 337–341 publications: 13 scientists 342–346 publications: 16 scientists 347–351 publications: 17 scientists 352–356 publications: 12 scientists 357–361 publications: 18 scientists 362–366 publications: 18 scientists 367–371 publications: 9 scientists 372–376 publications: 11 scientists 377–381 publications: 8 scientists 382–386 publications: 8 scientists 387–391 publications: 9 scientists 392–396 publications: 9 scientists 397–401 publications: 8 scientists 402–406 publications: 11 scientists 407–411 publications: 6 scientists 412–416 publications: 6 scientists 417–421 publications: 9 scientists 422–426 publications: 8 scientists 427–431 publications: 5 scientists 432–436 publications: 8 scientists 437–441 publications: 8 scientists 442–446 publications: 4 scientists 447–451 publications: 4 scientists 452–456 publications: 4 scientists 457–461 publications: 2 scientists 462–466 publications: 2 scientists 467–471 publications: 4 scientists 472–476 publications: 3 scientists 477–481 publications: 3 scientists 482–486 publications: 6 scientists 487–491 publications: 3 scientists 492–496 publications: 5 scientists 497–501 publications: 5 scientists 502–506 publications: 1 scientist 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientist 522–526 publications: 3 scientists 527–531 publications: 1 scientist 532–536 publications: 4 scientists 537+ publications: 100 scientists
42–46 publications 537+

This scientist: 138 publications — 31st percentile

31% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

View publications distribution as a table
Number of Mathematics scientists by publication count, Research.com 2026 ranking edition. Based on 3,584 ranked scientists.
Publications Scientists This scientist
42–46 3
47–51 5
52–56 7
57–61 20
62–66 14
67–71 25
72–76 19
77–81 35
82–86 50
87–91 60
92–96 86
97–101 84
102–106 83
107–111 90
112–116 99
117–121 90
122–126 91
127–131 109
132–136 110
137–141 98 138
142–146 112
147–151 102
152–156 88
157–161 106
162–166 83
167–171 102
172–176 77
177–181 81
182–186 78
187–191 71
192–196 92
197–201 64
202–206 69
207–211 64
212–216 62
217–221 58
222–226 53
227–231 50
232–236 46
237–241 46
242–246 46
247–251 43
252–256 29
257–261 45
262–266 30
267–271 33
272–276 34
277–281 30
282–286 31
287–291 21
292–296 34
297–301 26
302–306 10
307–311 17
312–316 23
317–321 13
322–326 16
327–331 26
332–336 13
337–341 13
342–346 16
347–351 17
352–356 12
357–361 18
362–366 18
367–371 9
372–376 11
377–381 8
382–386 8
387–391 9
392–396 9
397–401 8
402–406 11
407–411 6
412–416 6
417–421 9
422–426 8
427–431 5
432–436 8
437–441 8
442–446 4
447–451 4
452–456 4
457–461 2
462–466 2
467–471 4
472–476 3
477–481 3
482–486 6
487–491 3
492–496 5
497–501 5
502–506 1
507–511 6
512–516 4
517–521 1
522–526 3
527–531 1
532–536 4
537+ 100
Download as CSV

Zhiqiang Cai publication distribution in Mathematics in 2026 - data summary

  • The chart plots the publication count of all 3,584 Mathematics scientists ranked by Research.com in 2026, grouped into 100 ranges running from 42–46 to 537+ publications.
  • Zhiqiang Cai, a Mathematics scholar from Purdue University West Lafayette, records 138 publications - the 31st percentile of the discipline.
  • 31% of ranked Mathematics scientists score the same or lower than Zhiqiang Cai, and about 69% score higher.
  • The median of the discipline falls in the 172–176 publications range, and Zhiqiang Cai ranks below the median.
  • The most crowded range is 142–146 publications, holding 112 scientists (3% of the field).
  • 47% of the field sits in the lowest quarter of the value range (up to 162–166 publications), so the distribution leans towards the lower end of the scale.
  • The final bar has no upper bound: it groups every scientist with 537 publications or more, 100 scientists in all (3% of the field).

Zhiqiang Cai D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where Zhiqiang Cai sits on this spectrum.

No. of scientists
50 100 150
Bar chart with 57 bars. Horizontal axis: D-Index, 30 to 86+. Vertical axis: number of scientists, 0 to 174. Most scientists, 174, have 30 D-Index. The last bar groups every scientist with 86 D-Index or more. The highlighted bar, 39 D-Index, is where this scientist sits. 30 D-Index: 174 scientists 31 D-Index: 151 scientists 32 D-Index: 174 scientists 33 D-Index: 117 scientists 34 D-Index: 136 scientists 35 D-Index: 127 scientists 36 D-Index: 145 scientists 37 D-Index: 153 scientists 38 D-Index: 150 scientists 39 D-Index: 150 scientists 40 D-Index: 138 scientists 41 D-Index: 136 scientists 42 D-Index: 93 scientists 43 D-Index: 108 scientists 44 D-Index: 115 scientists 45 D-Index: 112 scientists 46 D-Index: 103 scientists 47 D-Index: 75 scientists 48 D-Index: 59 scientists 49 D-Index: 67 scientists 50 D-Index: 60 scientists 51 D-Index: 57 scientists 52 D-Index: 59 scientists 53 D-Index: 62 scientists 54 D-Index: 60 scientists 55 D-Index: 50 scientists 56 D-Index: 42 scientists 57 D-Index: 54 scientists 58 D-Index: 50 scientists 59 D-Index: 42 scientists 60 D-Index: 41 scientists 61 D-Index: 35 scientists 62 D-Index: 40 scientists 63 D-Index: 21 scientists 64 D-Index: 31 scientists 65 D-Index: 27 scientists 66 D-Index: 29 scientists 67 D-Index: 19 scientists 68 D-Index: 25 scientists 69 D-Index: 17 scientists 70 D-Index: 18 scientists 71 D-Index: 12 scientists 72 D-Index: 14 scientists 73 D-Index: 13 scientists 74 D-Index: 18 scientists 75 D-Index: 9 scientists 76 D-Index: 11 scientists 77 D-Index: 10 scientists 78 D-Index: 9 scientists 79 D-Index: 16 scientists 80 D-Index: 12 scientists 81 D-Index: 10 scientists 82 D-Index: 5 scientists 83 D-Index: 5 scientists 84 D-Index: 13 scientists 85 D-Index: 6 scientists 86+ D-Index: 99 scientists
30 D-Index 86+

This scientist: 39 D-Index — 41st percentile

41% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

View D-Index distribution as a table
Number of Mathematics scientists by D-index, Research.com 2026 ranking edition. Based on 3,584 ranked scientists.
D-Index Scientists This scientist
30 174
31 151
32 174
33 117
34 136
35 127
36 145
37 153
38 150
39 150 39
40 138
41 136
42 93
43 108
44 115
45 112
46 103
47 75
48 59
49 67
50 60
51 57
52 59
53 62
54 60
55 50
56 42
57 54
58 50
59 42
60 41
61 35
62 40
63 21
64 31
65 27
66 29
67 19
68 25
69 17
70 18
71 12
72 14
73 13
74 18
75 9
76 11
77 10
78 9
79 16
80 12
81 10
82 5
83 5
84 13
85 6
86+ 99
Download as CSV

Zhiqiang Cai D-index placement in Mathematics in 2026 - data summary

  • The chart plots the discipline H-index (D-index) of all 3,584 Mathematics scientists ranked by Research.com in 2026, grouped into 57 ranges running from 30 to 86+ D-Index.
  • Zhiqiang Cai, a Mathematics scholar from Purdue University West Lafayette, records 39 D-Index - the 41st percentile of the discipline.
  • 41% of ranked Mathematics scientists score the same or lower than Zhiqiang Cai, and about 59% score higher.
  • The median of the discipline falls in the 42 D-Index range, and Zhiqiang Cai ranks below the median.
  • The most crowded range is 30 D-Index, holding 174 scientists (5% of the field).
  • 58% of the field sits in the lowest quarter of the value range (up to 44 D-Index), so the distribution is heavily right-skewed and high scores are rare.
  • The final bar has no upper bound: it groups every scientist with 86 D-Index or more, 99 scientists in all (3% of the field).

Overview

Zhiqiang Cai is affiliated with Purdue University West Lafayette in the United States and specializes in engineering with a strong focus on computational methods. Their research spans several subfields including computational mechanics, statistical and nonlinear physics, mechanics of materials, computational theory and mathematics, and electrical and electronic engineering.

Their work prominently addresses advanced numerical methods in computational mathematics, with a particular emphasis on model reduction and neural networks. Key topics in their research include numerical methods in engineering, advanced mathematical modeling, electromagnetic simulation, and applications of neural networks.

Recent publications illustrate their focus on numerical techniques applied to partial differential equations and neural networks. Selected papers include:

  • Deep least-squares methods: An unsupervised learning-based numerical method for solving elliptic PDEs (2020, Journal of Computational Physics)
  • Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation (2021, Journal of Computational Physics)
  • Adaptive two-layer ReLU neural network: I. Best least-squares approximation (2022, Computers & Mathematics with Applications)
  • Least-squares ReLU neural network (LSNN) method for scalar nonlinear hyperbolic conservation law (2022, Applied Numerical Mathematics)
  • Adaptive two-layer ReLU neural network: II. Ritz approximation to elliptic PDEs (2022, Computers & Mathematics with Applications)

Frequent coauthors in their collaborative efforts include:

  • Min Liu
  • Jingshuang Chen
  • Cuiyu He
  • Difeng Cai
  • Shun Zhang

Their publications are often featured in venues such as arXiv (Cornell University), Computers & Mathematics with Applications, Journal of Computational Physics, Applied Numerical Mathematics, and Journal of Computational and Applied Mathematics.

Best Publications

  • Coh-Metrix: Analysis of text on cohesion and language

    Arthur C. Graesser;Danielle S. McNamara;Max M. Louwerse;Zhiqiang Cai

  • Automated Evaluation of Text and Discourse with Coh-Metrix

    Danielle S. McNamara;Arthur C. Graesser;Philip M. McCarthy;Zhiqiang Cai

  • Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients

    Thomas Y. Hou;Xiao-Hui Wu;Zhiqiang Cai

  • On the finite volume element method

    Zhiqiang Cai

  • First-order system least squares for second-order partial differential equations: part I

    Z. Cai;R. Lazarov;T. A. Manteuffel;S. F. McCormick

  • The finite volume element method for diffusion equations on general triangulations

    Zhiqiang Cai;Jan Mandel;Steve McCormick

  • First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

    Z. Cai;T. A. Manteuffel;S. F. McCormick

  • Question Understanding Aid (QUAID) A Web Facility that Tests Question Comprehensibility

    Arthur C. Graesser;Zhiqiang Cai;Max M. Louwerse;Frances Daniel

  • On the accuracy of the finite volume element method for diffusion equations on composite grids

    Zhiqiang Cai;Steve McCormick

  • Coh-Metrix Measures Text Characteristics at Multiple Levels of Language and Discourse.

    Arthur C. Graesser;Danielle S. McNamara;Zhiqang Cai;Mark Conley

  • Operation ARA: A computerized learning game that teaches critical thinking and scientific reasoning

    Diane F. Halpern;Keith Millis;Arthur C. Graesser;Heather Butler

  • Control-volume mixed finite element methods

    Z. Cai;J. E. Jones;S. F. McCormick;T. F. Russell

  • Least-Squares Methods for Linear Elasticity

    Zhiqiang Cai;Gerhard Starke

  • Discontinuous Galerkin Finite Element Methods for Interface Problems: A Priori and A Posteriori Error Estimations

    Zhiqiang Cai;Xiu Ye;Shun Zhang

  • Least-Squares Methods for Incompressible Newtonian Fluid Flow: Linear Stationary Problems

    Zhiqiang Cai;Barry Lee;Ping Wang

  • Analysis of Velocity-Flux First-Order System Least-Squares Principles for the Navier--Stokes Equations: Part I

    P. Bochev;Z. Cai;T. A. Manteuffel;S. F. McCormick

  • Magnetic Alginate/Chitosan Nanoparticles for Targeted Delivery of Curcumin into Human Breast Cancer Cells.

    Wenxing Song;Xing Su;David Alexander Gregory;Wei Li

  • A stable nonconforming quadrilateral finite element method for the stationary Stokes and Navier–Stokes equations

    Zhiqiang Cai;Jim Douglas;Xiu Ye

  • A Finite Element Method Using Singular Functions for the Poisson Equation: Corner Singularities

    Zhiqiang Cai;Seokchan Kim

  • Mixed finite element methods for incompressible flow: Stationary Stokes equations

    Zhiqiang Cai;Charles Tong;Panayot S. Vassilevski;Chunbo Wang

  • Recovery-Based Error Estimator for Interface Problems: Conforming Linear Elements

    Zhiqiang Cai;Shun Zhang

  • Automated Evaluation of Text and Discourse with Coh-Metrix: Introduction

    Danielle S. McNamara;Arthur C. Graesser;Philip M. McCarthy;Zhiqiang Cai

  • Automated Evaluation of Text and Discourse with Coh-Metrix: The Science and Technology That Led to Coh-Metrix

    Danielle S. McNamara;Arthur C. Graesser;Philip M. McCarthy;Zhiqiang Cai

Frequent Co-Authors

Arthur C. Graesser
Arthur C. Graesser University of Memphis
Danielle S. McNamara
Danielle S. McNamara Arizona State University
Diane F. Halpern
Diane F. Halpern Claremont McKenna College
James W. Pennebaker
James W. Pennebaker The University of Texas at Austin
David Williamson Shaffer
David Williamson Shaffer University of Wisconsin–Madison
Scott A. Crossley
Scott A. Crossley Vanderbilt University
Xiu Ye
Xiu Ye University of Arkansas at Little Rock
Thomas A. Manteuffel
Thomas A. Manteuffel University of Colorado Boulder
Stephen F. McCormick
Stephen F. McCormick University of Colorado Boulder
Roger Azevedo
Roger Azevedo University of Central Florida

External Links

Personal website of Zhiqiang Cai Google Scholar page

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Best Scientists Citing Zhiqiang Cai

Danielle S. McNamara

Danielle S. McNamara

Arizona State University

Publications: 163

Arthur C. Graesser

Arthur C. Graesser

University of Memphis

Publications: 94

Scott A. Crossley

Scott A. Crossley

Vanderbilt University

Publications: 89

Thomas A. Manteuffel

Thomas A. Manteuffel

University of Colorado Boulder

Publications: 45

Sidney K. D'Mello

Sidney K. D'Mello

University of Colorado Boulder

Publications: 42

Zhangxin Chen

Zhangxin Chen

University of Calgary

Publications: 26

Dragan Gasevic

Dragan Gasevic

Monash University

Publications: 24

Zhimin Zhang

Zhimin Zhang

Wayne State University

Publications: 23

Xiu Ye

Xiu Ye

University of Arkansas at Little Rock

Publications: 22

Raytcho Lazarov

Raytcho Lazarov

Texas A&M University

Publications: 19

Panayot S. Vassilevski

Panayot S. Vassilevski

Lawrence Livermore National Laboratory

Publications: 19

Stephen F. McCormick

Stephen F. McCormick

University of Colorado Boulder

Publications: 19

Thomas Y. Hou

Thomas Y. Hou

California Institute of Technology

Publications: 18

Assyr Abdulle

Assyr Abdulle

École Polytechnique Fédérale de Lausanne

Publications: 17

Carsten Carstensen

Carsten Carstensen

Humboldt-Universität zu Berlin

Publications: 16

Jinchao Xu

Jinchao Xu

Pennsylvania State University

Publications: 16

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