Distinguished Professor Robert McLachlan staff profile picture

Contact details +64 (06) 356 9099  ext. 84652

Distinguished Professor Robert McLachlan PhD, BSc(H)

Distinguished Professor

School of Fundamental Sciences

Robert McLachlan studied at Canterbury and Caltech and has worked at the University of Colorado at Boulder and ETH Zurich. He has been a research fellow at the Isaac Newton Institute, Cambridge, the Mathematical Sciences Research Institute, Berkeley, and the Center for Advanced Study, Oslo. Since its founding in the early 1990s he has been a leader in the new field of geometric numerical integration, a technique for the reliable simulation of large-scale complex systems, especially those arising in computational physics and chemistry.

Professional

Contact details

  • Ph: 06 951 7652
    Location: ScB3.22, Science Tower B
    Campus: Turitea

Qualifications

  • Doctor of Philosophy - California Institute of Technology (1990)
  • Bachelor of Science (Hons) - University of Canterbury (1984)

Research Expertise

Research Interests

Numerical solution of differential equations, especially geometric numerical integration.

Numerical analysis including optimization and image processing.

Thematics

Resource Development and Management

Area of Expertise

Field of research codes
Algebraic Structures in Mathematical Physics (010501): Applied Mathematics (010200): Applied Mathematics not elsewhere classified (010299): Calculus of Variations, Systems Theory and Control Theory (010203): Dynamical Systems in Applications (010204): Integrable Systems (Classical and Quantum) (010502): Mathematical Aspects of Classical Mechanics, Quantum Mechanics and Quantum Information Theory (010503): Mathematical Physics (010500): Mathematical Sciences (010000): Numerical and Computational Mathematics (010300): Numerical Solution of Differential and Integral Equations (010302): Optimisation (010303): Theoretical and Applied Mechanics (010207)

Keywords

Numerical analysis, scientific computation, simulation, symplectic integrators, image processing.

Research Projects

Summary of Research Projects

Position Current Completed
Project Leader 1 3

Current Projects

Project Title: Geometric numerical integration: new structures and applications

Date Range: 2015 - 2019

Funding Body: Royal Society of New Zealand

Project Team:

Completed Projects

Project Title: Geometric Integration

Geometric integration is a novel approach to simulating the motion of large systems. The new methods, inspired by chaos theory but driven by the demands of modern applications are faster, more reliable, and often simpler than traditional approaches. They are being used in areas as diverse as the celestial origin of the ice ages, the structure of liquids, polymers, and biomolecules, quantum mechanics and nanodevices, biological models, chemical reactiondiffusion systems, the dynamics of flexible structures, and weather forecasting. Although diverse, these systems have certain things in common that makes them amenable to the new approach. They all preserve some underlying geometric structure which influences the qualitative nature of the phenomena they produce. In geometric integration these properties are built into the numerical method, which gives the method markedly superior performance, especially during long simulations. In our research we are exploring the geometric or structural features that systems can have, the implications for their long-time dynamics, and how to design efficient numerical integrators that preserve these geometric properties.
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Date Range: 2008 - 2012

Funding Body: Marsden Fund - Full

Project Team:

Research Outputs

Teaching and Supervision

Summary of Doctoral Supervision

Position Current Completed
Supervisor 1 6
Co-supervisor 1 7

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