Applications of Solenoidal Elements in Computational Mechanics
by
Austin N.F. Mack
Faculty of Engineering, University of Technology, Sydney

A goal for researchers in computational mechanics for many years has been the development of a solenoidal (zero divergence) finite element.  The difficulty with this idea is the construction of an element in which the solution variables are constrained to be solenoidal by the nature of their interpolation functions.

The author has developed such an element for the solution of viscous incompressible flows.  Here, the solution variables are just the velocity components, since the pressure has been suppressed from the prime solution and can be retrieved when desired in the manner of an auxiliray variable.

Another application area where there are similar divergence constraints is the scattering of electromagnetic waves.  Here the solution variables are the field components (electric and magnetic).  The solution of such problems finds use across a broad spectrum, a particular one of which is the calculation of the radar return and the minimisation of this quantity.

Mathematical approaches and subsequent solutions for typical problems in both application areas will be presented.

Date received: August 8, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadr-08.