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

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

If you think any of the details on this page are incorrect, let us know.

Report an issue

We appreciate your kind effort to assist us to improve this page, it would be helpful providing us with as much detail as possible in the text box below:

Related Online Degrees & Career Pathways

Studying Mathematics in the USA opens numerous doors, especially when combined with complementary disciplines through online degrees. Many students explore related fields like finance, marketing, and business administration to enhance career prospects. For those interested in finance, pursuing an online masters in finance can be an affordable and practical choice to deepen quantitative skills and apply mathematical concepts to real-world financial problems.

Business-minded graduates often consider an MBA to climb the corporate ladder swiftly. Options such as the fastest mba online programs allow students to earn their degree efficiently without sacrificing quality. For those looking for an even quicker path, there are also 1 year mba options designed to accelerate career advancement in leadership roles.

Marketing is another popular field where mathematical and analytical skills are highly valued. Students can find some of the cheapest online marketing degree programs that combine affordability with strong earning potential, especially by leveraging data-driven marketing strategies.

Overall, integrating mathematics with these related online degrees enhances versatility and opens up diverse career pathways in finance, business, and marketing sectors.

Best Scientists Citing Zhiqiang Cai

Trending Scientists

Recently Published Articles