Homepage : http://personal.strath.ac.uk/a.ramage/
My main expertise lies in numerical linear algebra, which is a vital component of scientific computation that impacts strongly on a wide range of disciplines in academia and in technology-based industries. Specifically, it involves the design and analysis of algorithms and software for the basic matrix operations which underpin most technical computing applications. My particular focus is on developing efficient solution methods for numerical models of partial differential equations, wth a primary interest in preconditioning linear solvers.
Having graduated from the University of St Andrews, I completed a PhD at the University of Bristol (under the supervision of Dr A. Wathen) on preconditioning for Galerkin finite element equations, and I have worked on preconditioners and fast solvers for a large part of my career. My early work, beginning with postdoctoral research funded by EPSRC and Nuclear Electric plc, was primarily in the area of computational fluid dynamics, working on solving Navier-Stokes and convection-diffusion equations. My work has always been highly motivated by practical applications and since arriving at the University of Strathclyde I have continued that theme, with projects in, for example, modelling soil-structure interaction and tunnelling in geotechnical engineering, option pricing in financial mathematics and liquid crystal displays. This research has frequently involved working with industrial partners such as Oasys Ltd (the software house of Arup) and Hewlett-Packard. I have long-standing collaborations with researchers in the United States and Sweden, as well as ongoing projects with colleagues in academia and industry in the UK. This has been enabled in part by the award of Research Fellowships from the Leverhulme Trust (in 1999, to enable a sabbatical year spent working with Professor Howard Elman at the University of Maryland) and EPSRC (in 2005, a Springboard Fellowship with Hewlett-Packard for liquid crystal device modelling). I have also obtained several research grants to support PhD students and postdoctoral researchers.
More recently, I have also become interested in the application of linear algebra to modern challenges in data analysis. This led to the award of a second Leverhulme Research Fellowship in 2017/18 to support a project to develop multilevel preconditioning for data assimilation problems in numerical weather forecasting. I plan to extend this research to other modern sensor networks in applications such as Future Cities.