Research

My research interests lie primarily in the application of mathematics to scientific problems in physics and engineering. I have developed expertise in numerical partial differential equations (PDEs), stability analysis, domain decomposition methods, compact algorithm methods, multiscale methods, operator splitting methods, and mathematical modeling. I am particularly interested in studying PDEs that model highly oscillatory problems, such as Helmholtz equations.

Below are some of the topics explored in my research.

If you'd like to know more, please see my List of Publications and Research Statement.

Stability Analysis

Stability is a crucial property required for the study of numerical PDEs. I explore two main types of stability. In conventional stability analysis we focus on the step size of the algorithm. In cases where the algorithm is unstable in a conventional sense, it can be interesting to consider non-conventional stability analysis which emphasises the influence of certain physical parameters.