FYP

It has been a very long time since I write something on this blog. The main reason is that I have been occupied with my Final Year Project (FYP) for the whole semester. As the FYP is all over now, I shall share the fruit of my hard labor here.

My project is mainly a study of a relatively new numerical methods, the moving mesh methods, for solving time-dependent PDEs. I’ll share the abstract here and if the reader is interested, then the full report is available for download as well.

Abstract:

Moving mesh methods have gained substantial popularity over the past two decades as an adaptive strategy to solve time-dependent partial differential equations (PDEs). The main idea of moving mesh methods is to find an invertible mapping that maps localized structure in physical domain to a smooth one in computational domain. This can be done by introducing moving mesh PDEs (MMPDEs) that constitute the core of moving mesh methods. Two important characteristics of this method are the dynamic adaptation of mesh with the solution of physical PDEs and concentration of mesh points to region of large solution variations. Various numerical experiments are performed to illustrate the idea and highlight the advantages of moving mesh methods.

The full report is available here FYP Report. There are some numerical results that are converted into video clips but unfortunately, I haven’t figure out how to upload videos here.