World's Best Scientists 2026 revealed!

D-Index & Metrics

Mathematics

D-Index
39
Citations
6712
World Ranking
2190
National Ranking
923

Engineering and Technology

D-Index
49
Citations
11753
World Ranking
4233
National Ranking
1212

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.

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: 82 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 scientists 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientists 522–526 publications: 3 scientists 527–531 publications: 1 scientists 532–536 publications: 4 scientists 537+ publications: 100 scientists
42 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.

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.

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: 137 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.

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

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