| Title | Computational Methods for Signorini Problems |
|---|---|
| Speaker | Joyce Aitchison, Cranfield University, RMCS Shrivenham, UK |
| Date | Thursday, 22nd August 2002 |
| Time | 11:10 -- 12:00 |
| Venue | Computer Science - Room 152 |
| Abstract | A Signorini problem is an elliptic partial
differential equation where some of the boundary conditions are in the
form of inequalities involving the unknown function and its derivative
together with a complementarity relation. Such problems arise in the modelling
of a variety of physical phenomena which involve the determination of
an unknown free boundary. Signorini problems are often recast as variational inequalities and hence solved directly by the finite element method. This is computationally expensive and necessitates the calculation of variables throughout the region, whereas, in these problems, the primary interest is usually in the boundary. This makes the boundary element method an attractive alternative, but the disadvantage is that the inequality boundary conditions cannot be solved directly. In this talk we will outline the use of the boundary element method for the solution of free boundary problems. We then describe an iterative algorithm for handling the inequality boundary conditions which could be used with any method for solving the differential equation, and provide an outline proof that the algorithm converges when used with analytic methods. The formulation of a typical free boundary problem as a Signorini problem will be described and results presented using the iterative method in conjunction with the boundary element method. |
| About the speaker | Joyce Aitchison is Head of the Applied Mathematics &
Operational Research Group at RMCS Shrivenham (Cranfield University) in
the UK. She is currently a visiting fellow in the School of Mathematics
& Statistics at ADFA. Her research interests are in the mathematical modelling and numerical solution of practical problems arising from scientific and industrial applications, with a particular interest in mathematical models of manufacturing processes and free surface flows. She has a wide interest in applied numerical analysis, particularly in the numerical solution of partial differential equations. |
For more information on this seminar, please email: Joyce Aitchison
For information on our seminar program, suggestions for seminars, or mailing list updates, please email: seminars@cs.adfa.edu.au or see: http://www.cs.adfa.edu.au/seminars/2003/
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