Dr. Colin Macdonald, gave a lecture titled ”Numerical Computation on Curved Surfaces” at AMSS on 17, April 2019.
In the talk, despite the appearance sometimes given in textbooks, not all differential equations were posed on straight lines and rectangles. This talk introduced some techniques based on simple finite differences and interpolation for computing numerical solutions to partial differential equations posed on curved surfaces and other general domains.
One application was modelling animal coat pattern formation using reaction-diffusion equations. They also looked at some other examples such as curve evolution, bulk-surface coupling, point clouds, visual effects, image processing, and mesh generation.
Dr. Colin Macdonald is from University of British Columbia. He works on numerical analysis and scientific computing. He completed his PhD in 2008 with Steve Ruuth (SFU), then started a postdoc with Stan Osher (UCLA), before becoming an Instructor at Oxford in 2009. He returned to Canada in 2015, and is currently an associate professor at the University of British Columbia. Colin has a second-place Leslie Fox prize in numerical analysis from 2009 and was the 2010 recipient of the SIAM Richard C.~DiPrima prize in applied mathematics.