CIAM & SigmaOpt seminar, UNiSA
Speaker: Professor Robert M. Corless (The University of Western Ontario, Canada)
Title: High-order, High-accuracy Solution of a Nonlinear PDE Arising in a Two-dimensional Heat Transfer Model
Time: 2:30 pm (ACDT – Adelaide time), 3:00pm (AEDT), Monday 9 December 2013
Venue: Room Q1-01, Mawson Lakes Campus
Also available on the Access Grid network (venue: UniSA).
Abstract:
A classical nonlinear PDE used for modelling heat transfer between concentric cylinders by fluid convection and also for modelling porous flow can be solved by hand using a low-order perturbation method.
Extending this solution to higher order using computer algebra is surprisingly hard owing to exponential growth in the size of the series terms, naively computed.
In the mid-1990s, so-called Large Expression Management tools were invented to allow construction and use of so-called computation sequences or straight-line programs to extend the solution to 11th order.
The cost of the method was O(N8) in memory, high but not exponential.
Twenty years of doubling of computer power allows this method to get 15 terms.
A new method, which reduces the memory cost to O(N4), allows us to compute to N=30.
At this order, singularities can reliably be detected using the quotient–difference algorithm.
This allows confident investigation of the solutions, for different values of the Prandtl number.
This work is joint with Yiming Zhang (PhD Oct 2013).
Seminar Convenor: Dr C. Yalcin Kaya (Yalcin.Kaya@unisa.edu.au)
Technical contact: Richard Rawinski (Richard.Rawinski@unisa.edu.au)
This talk will be broadcast using Access Grid Technology from The University of South Australia.
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It is an event organized by AMSI, SigmaOpt (ANZIAM Special Interest Group in Mathematical Optimization) and the Centre for Industrial and Applied Mathematics (CIAM) at University of South Australia.
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