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Collin Macdonald

Math wizard charts new algorithmic territory

May 28, 2009

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By Roberta Staley

Bunnies with stripes or spots, a dress that changes colour as you move or a near-perfect re-creation of the missing pieces of an ancient vase.

All these things are now possible—or at least the computations are—thanks to Colin Macdonald, who convocates June 3 with a PhD in mathematics from the Faculty of Science and the Governor General’s gold medal for scholastic excellence.

Macdonald’s PhD thesis provides a twist on partial differential equations (PDEs), which are used to model all kinds of natural processes. Computing numerical solutions to PDEs is a common tool for scientists making predictions and testing models. Until now, however, accurate computations for PDEs on curved surfaces—be it the plumpness of a rabbit, the drape of a dress or the topography of a continent’s coastline—have been difficult.

Macdonald helped develop a breakthrough: the "closest-point method," an algorithm that allows scientists to numerically solve PDE problems on curved surfaces. It has tremendous implications for applied science in fields ranging from biology to engineering and physics.

"What we’ve come up with," says Macdonald, "is a simple technique to study processes that interest a scientist on the actual object he or she is studying, be it the pattern formation on a zebra, weather patterns on Earth or de-icing on a curved airplane wing."

The young mathematician is now continuing his groundbreaking work, which is being published in the prestigious SIAM Journal on Scientific Computing and the Journal of Scientific Computing, on a postdoctoral fellowship from the Natural Science and Engineering Research Council at the University of California, Los Angeles.

And in addition to several major awards and speaking engagements, he has recently been offered a permanent lectureship at one of the most venerable universities in the U.K.

It’s heady stuff for the Wolfville, N.S. native who started his mathematics career at Acadia University. But despite all the accolades Macdonald remains humble and appreciative of his SFU support, particularly his advisor Steven Ruuth.

"I’ve been surrounded by great people the whole way through. It was the individual attention I got that convinced me that mathematics was something that I really wanted to do."

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