Wave Research
This work is on short wave modelling using special finite elements at the School of Engineering, University of Durham. A brief resume of the work follows.
We consider progressive waves such that the time independent potential satisfies the Helmholtz equation, for example, the travelling wave diffracted from a body. In order to model the wave potential using finite elements it is usual to discretize the domain such that there are about ten nodal points per wavelength. However, such a procedure is computationally expensive and impractical if the waves are short. The goal is to be able to model accurately with few elements problems such as sonar and radar. Therefore we seek a new method in which the discretization of the domain is more economical. To do so, we express the complex potential in terms of the real wave envelope and the real phase, and expect that in most regions the functions vary much more gradually over the domain than does the oscillatory potential. Therefore instead of modelling the potential we model the wave envelope and the phase.
Papers related to the project are :
1 - P. Bettess and E.A. Chadwick, `Wave envelope examples for progressive waves', Int. Jour. Num. Meth. Eng., 38, pp.2487-2508 , 1995. (Postcript 350K)
2 - E.A. Chadwick and P. Bettess, `Modelling of progressive short waves using wave envelopes', Int. Jour. Num. Meth. Eng., 40, pp.3229-3245, 1997.(Postcript 500K)
3 - E.A. Chadwick, P. Bettess and O. Laghrouche, `Diffraction of short waves modelled using new mapped wave envelope finite and infinite elements', Int. Jour. Num. Meth. Eng., 1999 (submitted for publication). (Postcript 325K)