Mathematical theory of the attention mechanism and its applications in operator learning

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References

  1. Cao, S. (2021). Choose a Transformer: Fourier or Galerkin. In arXiv preprint arXiv:2105.14995.

   

Theory and applications of virtual element method for interface problems

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References

  1. Cao, S., Chen, L., Guo, R., & Lin, F. (2021). Immersed Virtual Element Methods for Elliptic Interface Problems.
  2. Cao, S., Chen, L., & Guo, R. (2021). A Virtual Finite Element Method for Two-Dimensional Maxwell Interface Problems with a Background Unfitted Mesh. Mathematical Models and Methods in Applied Sciences (M3AS), Accepted.
  3. Cao, S. (2021). A simple virtual element-based flux recovery on quadtree. In Electronic Research Archive: Special issue on recent advances in numerical analysis. https://doi.org/doi:10.3934/era.2021054
  4. Cao, S., & Chen, L. (2019). Anisotropic error estimates of the linear nonconforming virtual element methods. SIAM Journal on Numerical Analysis, 57(3), 1058–1081.
  5. Cao, S., & Chen, L. (2018). Anisotropic error estimates of the linear virtual element method on polygonal meshes. SIAM Journal on Numerical Analysis, 56(5), 2913–2939.

Acknowledgement

  • This research was supported in part by the National Science Foundation under grants DMS-1913080 and DMS-2136075.

   

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References

  1. Cao, S., Chen, L., & Huang, X. (2021). Error analysis of a decoupled finite element method for quad-curl problems. ArXiv Preprint ArXiv:2102.03396.
  2. Cao, S., Wang, C., & Wang, J. (2021). A New Numerical Method for Div-Curl Systems with Low Regularity Assumptions. In arXiv preprint arXiv:2101.03466.
  3. Cai, Z., Cao, S., & Falgout, R. (2016). Robust a posteriori error estimation for finite element approximation to H (curl) problem. Computer Methods in Applied Mechanics and Engineering, 309, 182–201.
  4. Cai, Z., & Cao, S. (2015). A recovery-based a posteriori error estimator for H(curl) interface problems. Computer Methods in Applied Mechanics and Engineering, 296, 169–195.

   

Finite element methods and other miscellaneous topics

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