《再别南大》 May 5, 2010
Posted by choonyee in University.1 comment so far
大学毕业在即，写了一首《再别南大》与同学们共勉之。
骊歌冉冉晕开时，岁月悠悠四夏驰。
大学之道未闻知，茫然背考为何值？
花香鸟语树成荫，夜宵琴声众成群。
若干年后喜相聚，当歌对酒叹光阴。
注释：
- 骊歌：离别之歌， 毕业之歌。
- 冉冉：慢慢地。
- 晕开：散开。取自方文山作品《青花瓷》，“月色被打捞起，晕开了结局。”
- 四夏：新加坡常年如夏，故一夏一年，四夏四年。
- 大学之道：取自四书之一《大学》开篇第一句，“大学之道，在明明德，在亲民，在止于至善。
- 闻知：见闻，知道。
- 背考：背书考试。
- 众成群：众学生三五成群。含贬义，指学生按照国籍而分群。
- 若干年后：几年之后。
- 当歌对酒：取自曹操《短歌行》开篇第一句，“对酒当歌，人生几何？”
FYP May 5, 2010
Posted by choonyee in Mathematics.add a comment
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.
