My research encompasses (1) the development of efficient algorithms that address fundamental computational issues in applications like molecular dynamics, quantum chemistry, inverse problems, machine learning and deep learning, etc. (2) the mathematical analysis that reveals the "lubricant" and caveats when dealing with computationally challenging problems ranging from low to high dimensions.

Research Interests


  • [ link ][ view ] D. Cai, E. Chow, L. Erlandson, Y. Saad, and Y. Xi,

    SMASH: Structured Matrix Approximation by Separation and Hierarchy

    Numerical Linear Algebra with Applications (2018)
  • [ link ][ view ] D. Cai, Z. Cai,

    A Hybrid A Posteriori Error Estimator for Conforming Finite Element Approximations

    Comput. Methods Appl. Mech. Eng., 339 (2018), 320-340
  • [ link ][ view ] D. Cai and P. S. Vassilevski,

    Eigenvalue Problems for Exponential Type Kernels

    Computational Methods in Applied Mathematics, 20(1), pp. 61-78. (2019)
  • [ link ][ view ] D. Cai, Z. Cai, and S. Zhang,

    Robust Equilibrated A Posteriori Error Estimator for Higher Order Finite Element Approximations to Diffusion Problems

    Numerische Mathematik, 144, pp. 1-21(2020)
  • [ link ][ view ] L. Erlandson, D. Cai, Y. Xi, and E. Chow,

    Accelerating Parallel Hierarchical Matrix-Vector Products via Data-Driven Sampling

    34th IEEE International Parallel and Distributed Processing Symposium (IPDPS), pp. 749-758 (2020)
  • [ link ][ view ] D. Cai, J. Xia,

    A Stable Matrix Version of The Fast Multipole Method: Stabilization Strategies and Examples

    Electronic Transactions on Numerical Analysis, accepted
  • [ link ][ view ] D. Cai, Z. Cai

    Hybrid A Posteriori Error Estimators for Conforming Finite Element Approximations to Stationary Convection-Diffusion-Reaction equations

  • [ link ][ view ] D. Cai, J. Nagy, and Y. Xi

    Fast and Stable Deterministic Approximation of General Symmetric Kernel Matrices in High Dimensions

  • [][] A paper (to be submitted)
  • [][] Another paper (to be submitted)
  • [][] Reserve your spot (in preparation)
  • [][] My research interests are spontaneous (to be rejected)

Copyright © 2021 Difeng Cai