Postgraduate studentship: Solvers for optimal control of time-dependent PDEs
Applications are invited for a postgraduate studentship to work on Solvers for optimal control of time-dependent PDEs under the supervision of Dr Andy Wathen. This DPhil studentship will start on 1 October 2012, and will be based at the Oxford Centre for Collaborative Applied Mathematics (OCCAM).
OCCAM, established with substantial funding from KAUST GRP, is part of the Mathematical Institute at the University of Oxford. OCCAM is engaged in a wide range of applied and computational mathematics projects in collaboration with scientists from other disciplines. The portfolio is organised under the broad headings of Methodologies (M), Resources, Energy and Environment (REE), Biosciences and Bioengineering (BB), and Materials Science and Engineering (MSE). For more information about OCCAM, see http://www.maths.ox.ac.uk/occam.
It is often the case that engineers use numerical methods for optimization and the numerical solution of partial differential equations (NPDE) to aid with design or feasibility studies: for many problems the overarching desire is to optimize some quantity or quantities whilst remaining faithful to the physics. Most aerodynamic computations, for example, are to discover better (or best) wing or blade shapes or to determine for a given body what are the least extreme conditions under which failure might occur. Such problems naturally combine optimization and NPDE: they lead to problems of PDE-constrained optimization. For such problems the computation of gradients required for the optimization leads necessarily to the need to solve the adjoint PDE as well as the original PDE. For steady state PDEs much has been achieved in recent years and now there is a relatively well-understood theory and several capable methods. It is not surprising that the success of these methods depends largely on whether the underlying linear algebraic equations are of small enough dimension that they can be solved. This may be a significant problem for steady PDEs, but it has been regarded as an overwhelming one for time-dependent PDEs. In very recent work, we have been able to identify a radical and apparently feasible way to solve such time-dependent PDE-constrained optimization problems and this project is aimed at developing and understanding these ideas.
This studentship is attached to New College.
This project is one of three on offer from OCCAM. The funding situation is complex because the studentships come from two sources. One studentship is funded by the University of Oxford, is open to students of all nationalities, and covers full stipend (currently £13,590) and College and University fees at the international rate. The remaining two studentships are fully funded by the EPSRC and are restricted to UK/EU students only (eligible non UK students will receive a fees-only award). We will allocate the studentships to the projects after the interviews, with the aim of providing full funding for all three of the students, if this is possible.
These studentships fall outside the University’s Gathered Field process. Applications should be made online at www.ox.ac.uk/admissions/postgraduate_courses and should include a CV, covering letter, three references and a transcript of your undergraduate degree. If you are unable to apply online, you can request a paper form from https://uni-of-oxford.custhelp.com/app/ask/.
Applications must arrive by the end of the day on Thursday 9 February 2012. Please quote the correct reference BK/11/21 in your covering letter. References can also be sent directly to Margaret Sloper (email graduate [dot] studies [-at-] maths [dot] ox [dot] ac [dot] uk) by the closing date. For further details of the projects, including the application process, please see:
www.maths.ox.ac.uk/notices/vacancies
Email: graduate [dot] studies [-at-] maths [dot] ox [dot] ac [dot] uk
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