PhD

Introduction

I have recently (2005.02) commenced work on my PhD at the E&E department of The University of Stellenbosch under Prof. D.B. Davidson. Its topic is the application of FETD methods to humanitarian de-mining. In particular, the problem of obtaining the scattering from plastic landmines will be considered.

Scattering problems generally require an open, or infinite stratified region to be considered. Since FEM requires the whole computational domain to be meshed, infinite problems require schemes to terminate the mesh. In the FDTD community, the issue has been well addressed through the use of PMLs. While they may, and to some extent have been applied to FETD, their use is still quite immature, and some issues remain.

Focus Points

FETD Formulation

There are several possible choices here, including the use of the coupled first-order form of Maxwell's equations or the second order wave equations. The formulation chosen affects how, and under which circumstances explicit solutions may be obtained.

Mesh Termination

This will be a a very important topic. Accurate scattering calculations require very small reflections from the mesh boundaries. PMLs seem to be very promising, provided they can be made to work! Other approaches will certainly be considered.

High-order Elements

Scattering problems, where characteristics of a realistic earth needs to be taken into account will typically require the solution of electricaly fairly large problems. The use of higher order elements tend to improve computational efficiency on large problems, particularly with regards to numerical dispersion.

Curvilinear Elements

Standard triangular elements cannot conform exactly to curved geometries. When lower order elements are used, this is not a big problem, since the geometrical modelling error is commensurate with the field modelling error. With higher order elements, the geometrical error dominates the total error, resulting in them being no more efficient than lower order elements. Curvilinear elements can be formulated to use higer order geometrical approximation or other shape functions that allow them to conform exactly to certain geometries.