LabCompass

Zhiqiang Cai

Engineering · Purdue University West Lafayette

OpenAlex ORCID
Established · publishing since 1988
Advanced Numerical Methods in Computational MathematicsNumerical methods in engineeringAdvanced Mathematical Modeling in EngineeringElectromagnetic Simulation and Numerical MethodsComputational Fluid Dynamics and Aerodynamics

Publications

127

Citations

4,617

Est. group size

~2

Recurring co-author estimate

Active years

38

Publishing since 1988

Research summary
AI-generated

Zhiqiang Cai works on numerical methods for solving partial differential equations (PDEs), which are mathematical equations describing physical processes like fluid flow, heat transfer, and electromagnetics. Recent work focuses on combining traditional finite element techniques with neural-network-based methods (such as least-squares and Deep Ritz approaches) to approximate solutions to PDEs, including problems with discontinuities, fractional derivatives, and elliptic or hyperbolic equations. This research is aimed at developing more accurate and adaptive computational tools for engineering and scientific simulation.

Finite element and numerical PDE methodsNeural-network-based PDE solvers (least-squares, Deep Ritz)Error estimation and adaptive methodsFractional Laplacian and meshless methodsConvection-diffusion-reaction and hyperbolic conservation laws

Publication output has grown from about 3 papers per year a decade ago to a steady average of roughly 5 per year over the last five years, with a peak of 8 in 2022.

Generated by claude-sonnet-5 from public bibliographic data · Jul 20, 2026

Publication cadence
Publications per year over the last 10 years — averaging 5.0/year recently
2017: 3 publications172018: 3 publications182019: 3 publications192020: 5 publications202021: 6 publications212022: 8 publications8222023: 5 publications232024: 7 publications242025: 5 publications2526
Recent publications
Publishes in
  • Computers & Mathematics with Applications×7
  • arXiv (Cornell University)×7
  • Computer Methods in Applied Mechanics and Engineering×4
  • Journal of Computational Physics×3
  • Applied Numerical Mathematics×3
Similar researchers
By research-topic overlap
  • Chen Liu

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  • Yulong Xing

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  • Yu Leng

    Engineering · Purdue University West Lafayette

  • Jie Shen

    Engineering · Purdue University West Lafayette

This profile was generated automatically from public scholarly data (OpenAlex). Group size and activity levels are estimates derived from co-authorship patterns.

Last updated Jul 20, 2026.

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