Applied Mathematics

This is a general topic which covers but not limited to the mathematical tools I use.

Singular integrals

Vortex dynamic models usually require evaluations for integrals with a singular or weakly singular kernel, or solving an integral equation of the following type:

Fourier–Floquet–Hill method

A spectral method solves eigenvalue problems for linear differential equations with periodic operator.

Center manifold theory

A thin fluid film with slow-varying dynamic such as coating over a substrate can be modeled by the concept of center manifolds.