McLachlan was born in Christchurch,New Zealand in 1964,[3] and studied mathematics at the University of Canterbury,graduating with a BSc (Hons) First Class in 1984.[4] One formative experience was in his last year of high school,where he had free rein to experiment with assembly language programming on the school PDP-11/10.[4]
McLachlan joined Massey University in Palmerston North in 1994,and began a collaboration with Reinout Quispel at La Trobe University that resulted in over 26 publications on geometric integration.[4] In 2002 he became Professor of Applied Mathematics at Massey,and spent a year's sabbatical at the University of Geneva,working with Gerhard Wanner and Ernst Hairer,and the Norwegian Academy of Sciences in Oslo.[5] In 2007 he won the prestigious Germund Dahlquist Prize,the first mathematician from the southern hemisphere to do so.[6] From 2008 to 2012,along with Stephen Marsland and Matt Perlmutter,he worked on a Marsden grant project "Geodesics in diffeomorphism groups:geometry and applications",designing efficient numerical integrators that preserved the geometric properties of systems.[7] In 2013,McLachlan was the LMS-NZMS Aitken Lecturer,delivering talks on geometric numerical integration to six UK universities.[8][9]
McLachlan is a Fellow of the New Zealand Mathematical Society (NZMS),and in 1998 organised the first of the annual Manawatu-Wellington Applied Mathematics Conferences. He was president of the NZMS in 2008–2009 and vice president in 2010,and edited the New Zealand Journal of Mathematics for six years.[4] Since 2016 he has been a Distinguished Professor in Massey's School of Fundamental Sciences.[10]
Research
McLachlan is a world leader in the field of geometric integration,a technique for the reliable simulation of large-scale complex systems,and in particular the use of symplectic techniques in the numerical analysis of differential equations.[4][11] This field,which McLachlan helped found in the 1990s,builds into its approach the underlying geometric structure of data sets.[10] Because it allows the simulation of large systems,it has the potential for solving practical problems in fields as disparate as the structure of liquids,climate cycles,the motion of the solar system,particles in circular accelerators,chaos in dynamical systems,and weather forecasting.[4][12][13] For example,during Hurricane Sandy in 2012,the European Centre for Medium-Range Weather Forecasts,using geometric integration models,correctly predicted the hurricane would suddenly turn 90 degrees towards New York six days in advance.[12] McLachlan's methods have been used in computational science to examine a possible celestial origin of the ice ages,biological models,and the dynamics of flexible structures.[12] His research contributed to a solar system simulation that revised the dates of geophysical epochs by millions of years.[10] Although his work in geometric numerical integration has a wide range of real-world applications,he considers himself a pure mathematician.[12]
McLachlan, Robert I. (1995). "On the Numerical Integration of Ordinary Differential Equations by Symmetric Composition Methods". SIAM Journal on Scientific Computing. 16 (1): 151–168. Bibcode:1995SJSC...16..151M. doi:10.1137/0916010.
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