Yujia Chen

I am interested in the numerical solutions to partial differential equations (PDEs) on general smooth surfaces. Surface PDEs might arise from modelling the pattern formation on animal coat, describing surfactant diffusing along the interface of two immiscible fluids, image processing on curved surface, and so on. There are many ways to (numerically) solve surface PDEs, currently I am working with Colin Macdonald on the Closest Point Method.

I am focusing on elliptic PDEs on surfaces, including formulating the embedding PDE, constructing and analyzing difference schemes, and investigating efficient iterative solvers for the discretized sparse linear system. In particular, I am interested in the geometric multigrid method. For more details, see my research project page.

I am also interested in efficient implementation of the Closest Point Method, like parallel computing using petsc4py, which are python bindings for PETSc.