Prof C S Chen, of the University of Nevada in Las Vegas, visited the Lodge recently to carry out collaborative research with Dr Youssef Rashed, Head of the Damage Mechanics Division of WIT. C S Chen was a Research Fellow at WIT for the Academic Year 1996/97 and since then has continued to interact with researchers at the Institute.
Prof Chen's lecture was on "Meshless Methods for Scientific Computation". The major theme of the meshless technology is to solve the science and engineering problems without tedious meshing of the physical domain or boundary. As a result, significant saving in computer modelling has been achieved. These novel techniques are still at an early stage of development and intensive research is still ongoing at a rapid pace.
In his talk, Prof Chen described two types of meshless methods using the state-of-the-art radial basis functions. The first meshless method was a boundary type method, which evolved from the boundary element method. In this approach, the given partial differential equation is split into two parts representing the particular and homogeneous solution. The dual reciprocity method, which uses radial basis functions, has been employed to evaluate the particular solution, while the method of fundamental solutions has been used to obtain the homogeneous solution. The second method is a domain-type method, which is related to the finite element method. This is called Kansa's method and was originally introduced in 1990. An introduction of the basic establishment was also given. To demonstrate the effectiveness of these two methods, numerical results of elliptic and parabolic problems were also given. The meshless method is particularly attractive for problems of high dimension and irregular domain.
Wessex Institute