Research Interests
I am intereted in developing efficient, reliable and mathematically solid algorithms to accelerate scientific computation.
At PKU, I focused on the numerical analysis of the finite element methods. Particularly, I was fascinated by their deep connection with discrete geometry, homological algebra and exterior calculus. The discrete exact sequences of a Bernstein-Galfand-Galfand diagram are closely related to structure-preserving discretization of the corresponding PDE. I spent a summer working with Dr. Kaibo Hu on the finite elemet discretization of the conformal deformation complex. From a homological perspective, we revealed the intrinsic supersmoothness of symmetric and traceless finite elements, and showed the stability via explicit construction of the hierachical bubble complexes. Paper, A brief introduction in Chinese
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| The hierachical bubble conformal complexes on a single tetrahedron |