Hi! I'm a senior undergraduate student at Davidson College, majoring in Mathematics (honors) and Computer Science. I'm currently working with Dr. Tim Chartier on my honors thesis in applied math track about dominance graph and ranking. I'm also continuing to work with my Summer Geometry Institute (SGI) research group at MIT led by Paul Zhang on hex mesh decomposition.
I'm broadly interested in geometry processing, computer graphics, graph theory as well as data analytics.
Find my CV here
Email: cyfan [at] davidson [dot] edu

Publication

• Paul Zhang, Judy Chiang, Xinyi Fan, and Klara Mundilova. Hexahedral Singularity Decomposition. International Meshing Roundtable 2022 (Accepted with revisions)

Research Experiences

Hexahedral Singular Decomposition

The hexahedral(hex) mesh has a set of vertices that is not adjacent to any singular edges(with and without singularities), where singular edges are edges that adjacent to anything other than 4 hexes. In this research, we show that all eight of the most common singular nodes are decomposable into just singular curves. Further, we show that all singular nodes, regardless of edge valence, are locally decomposable. We are currently implementing the generalized code in MATLAB for the decomposition. We also submitted a paper for review. SGI site

Elastic Shell Simplification

We notice that most of the computations utilize the linear operator such as the Laplacian, which simplify the mesh while preserving part of the mesh’s spectrum. Meanwhile, in elastic problems, inverting the Hessian of shell energies is still a computational expensive problem. Using MATLAB, we adapted the spectrum-based simplification to the shell Hessian and produce the coarsening of the shell to speed up the computation for any follow-up problems. SGI site

Optimal Addressing Schemes for Different Families of Graphs

We identified several families of eigensharp graphs including various subfamilies of block graphs, prism graphs, and torus graphs. Using mathematical software packages such as Mathematica, Java, and SageMath, we performed computational proofs and identify patterns for different types of graphs. We also showed the optimal addressing scheme for additional graph families such as flower graphs, spider graphs, wheel graphs, and stacked prism graphs. We prepared a paper for submission on this topic. REU site

Host-Parasitoid Population Dynamic Modeling

In this research fellowship, we utilized the discrete-time Nicholson-Bailey model to implement dynamic modeling on parasitoid population. Using MATLAB and Java, we created two models: synchronous and asynchronous attack by parasitoids and hyper-parasitoids. We also performed numerical and qualitative analysis of ODE systems as well as the stability analysis of a discrete dynamical system. REU site