A fully funded three-year PhD studentship is available in the Department of Mathematics and Statistics at the University of Strathclyde, Glasgow, United Kingdom. The intra-disciplinary research will be supervised by Prof. Victorita Dolean and undertaken primarily within the Numerical Analysis and Scientific Computing group. Please see
https://www.strath.ac.uk/research/subjects/mathematicsstatistics/numericalanalysisscientificcomputing/ for details of the group’s research. The student will also have the opportunity to interact with the Applied Analysis group, facilitated by the second supervisor, Dr. Matthias Langer; see
https://www.strath.ac.uk/research/subjects/mathematicsstatistics/appliedanalysis/
Mathematical and numerical modelling is unavoidable nowadays when one tries to investigate and understand complex physical phenomena such as seismic or electromagnetic wave propagation problems. When developing realistic mathematical models for large-scale physical applications, one bottleneck in the procedure is often the efficient and effective solution of the resulting matrix equations. In addition to the inherent difficulties one can encounter in complex applications, we often experience extra difficulties when dealing with time-harmonic wave propagation problems. These difficulties stem from the indefinite or non-self-adjoint nature of the operators involved. This requires a paradigm shift in the design and analysis of solvers. The aim of this project is to build and analyse a new generation of spectral preconditioners based on generalised eigenvalue problems allowing a robust behaviour with respect to the physical properties of the medium. This requires a combination of numerical analysis and spectral analysis tools. The outcome will be both mathematical but also practical, as this will fundamentally change the state of the art of solvers and the results will be incorporated in open-source software.
Although the project will focus primarily on the time-harmonic Helmholtz equation, the techniques developed will be applicable to other equations of the same nature, arising in computational electromagnetism and seismology.
This is a very exciting project, which will allow the student to work at the interface between computational mathematics and analysis with a strong potential for application. The student will attend regular research seminars and events within the Mathematics and Statistics department, and so will have many opportunities to interact with a multi-disciplinary team and international collaborators and develop both technically and professionally.
Applicants should have, or be expecting to obtain in the near future, a first class or good 2.1 honours degree (or equivalent) in mathematics or a mathematical science.
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