Numerical computation of interface problems

PGR-P-1156

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Key facts

Type of research degree: PhD
Application deadline: Ongoing deadline
Project start date: Monday 3 October 2022
Country eligibility: International (open to all nationalities, including the UK)
Funding: Competition funded
Source of funding: Doctoral training partnership
Supervisors: Dr Thomas Ranner
Schools: School of Computing
Research groups/institutes: Applied Computing in Biology, Medicine and Health, Computational Science and Engineering

<h2 class="heading hide-accessible">Summary</h2>

Interface problems arise in many different areas of engineering, physical and life sciences. A typical example is the interface between two immiscible fluids separated by an interface governed by surface tension. A more complicated example would involve an active swimming (micro-) organism moving through different fluids. In this project, we are interested in developing moving mesh finite element methods for their dynamical simulation. We aim to produce efficient, accurate and robust computational tools. <br /> <br /> The specific aspect of the project to be worked on will depend on the strengths of the candidate. Good projects in this area could include: <br /> <br /> Mathematical or numerical analysis of the underlying partial differential equation system and our finite element approach. This could be based on our abstract framework [1], <br /> <br /> Developing and/or analysing novel approaches for transporting the computational mesh. This could be based on the discrete DeTurck trick [2], <br /> <br /> Developing and implementing methods and models for a specific application area such as active swimmers (in a variety of environments), tumour growth, surfactants, or any other relevant problem. <br /> <br /> Informal enquires are welcome from all potential candidates. For more details, please contact Dr Thomas Ranner (T.Ranner@leeds.ac.uk). <br /> <br />

<h2 class="heading hide-accessible">Full description</h2>

<p lang="EN-US" paraeid="{3a7344c4-423f-4a0a-ada4-1e67c8ec1862}{38}" paraid="1585495973" xml:lang="EN-US"><em>References </em></p> <p lang="EN-US" paraeid="{e66e2e58-d29c-4403-81a2-b06bb054ba89}{60}" paraid="1560897064" xml:lang="EN-US">[1] C M Elliott, T Ranner, A unified theory for continuous-in-time evolving finite element space approximations to partial differential equations in evolving domains, IMA Journal of Numerical Analysis, Volume 41, Issue 3, July 2021, Pages 1696–1845, <a href="https://doi.org/10.1093/imanum/draa062" rel="noreferrer noopener" target="_blank">https://doi.org/10.1093/imanum/draa062</a> </p> <p lang="EN-US" paraeid="{e66e2e58-d29c-4403-81a2-b06bb054ba89}{247}" paraid="1344043597" xml:lang="EN-US">[2] C M Elliott, H Fritz, On algorithms with good mesh properties for problems with moving boundaries based on the Harmonic Map Heat Flow and the DeTurck trick, SMAI journal of computational mathematics, Volume 2, 2016, Pages 141-176, <a href="https://doi.org/10.5802/smai-jcm.12" rel="noreferrer noopener" target="_blank">https://doi.org/10.5802/smai-jcm.12</a> </p> <p lang="EN-US" paraeid="{9cc91930-07b7-4441-a911-c403318f0543}{199}" paraid="1148328789" xml:lang="EN-US"><strong>Background </strong></p> <p lang="EN-US" paraeid="{c2c3e3b3-7a28-43fc-9109-f499c8555bc6}{91}" paraid="908000757" xml:lang="EN-US">PhD students are sought in the School of Computing at the University of Leeds, UK. These studentships form part of a larger collaborative and interdisciplinary project led by Prof. Netta Cohen and Dr. Thomas Ranner. </p> <p lang="EN-US" paraeid="{5d86dc08-9c0f-4133-ac74-63d8683dc1b4}{179}" paraid="390037780" xml:lang="EN-US">We study the neuromechanical basis of behaviour in the nematode worm C. elegans. Research combines biological experiments, mathematical and computational modelling of the neural control as well as investigations of the physics of the worm and its interaction with the environment. Projects may be envisioned within this multidisciplinary setting. You will join a multi-disciplinary, dynamic, and creative group within the School of Computing at the University of Leeds, with close ties to the Fluid Dynamics Centre for Doctoral Training and to the Faculty of Biological Sciences. </p> <p lang="EN-US" paraeid="{030e33e0-f34d-4a75-ae9b-3ed0374b972f}{115}" paraid="148529965" xml:lang="EN-US"><strong>Entry requirements </strong></p> <p lang="EN-US" paraeid="{030e33e0-f34d-4a75-ae9b-3ed0374b972f}{140}" paraid="488880397" xml:lang="EN-US">Candidates should have a strong undergraduate degree in a relevant area (including but not restricted to mathematics, physics or computer science). A suitable candidate for this project should have some knowledge of aspects of the design, analysis and/or implementation of finite element methods for partial differential equations. Prior experience in research (e.g. a Masters degree or work in industry) is a plus. </p>

<h2 class="heading">How to apply</h2>

<p>Formal applications for research degree study should be made online through the <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University's website</a>. Please state clearly in the Planned Course of Study section that you are applyig for <em><strong>PHD Computing FT</strong></em> and in the research information section that the research degree you wish to be considered for is <em><strong>Numerical computations of interface problems</strong></em> as well as <a href="https://eps.leeds.ac.uk/staff/643/Dr_Thomas_Ranner">Dr Thomas Ranner</a> as your proposed supervisor.</p> <p>If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below).</p>

<h2 class="heading heading--sm">Entry requirements</h2>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

<h2 class="heading heading--sm">English language requirements</h2>

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.5 overall with at least 6.5 in writing and at least 6.0 in reading, listening and speaking or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.

<h2 class="heading">Funding on offer</h2>

<p><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p><strong>UK</strong> – The <a href="https://phd.leeds.ac.uk/funding/209-leeds-doctoral-scholarships-2022">Leeds Doctoral Scholarships</a>, <a href="https://phd.leeds.ac.uk/funding/53-school-of-computing-scholarship">School of Computing Scholarship </a>, <a href="https://phd.leeds.ac.uk/funding/198-akroyd-and-brown-scholarship-2022">Akroyd & Brown</a>, <a href="https://phd.leeds.ac.uk/funding/199-frank-parkinson-scholarship-2022">Frank Parkinson</a> and <a href="https://phd.leeds.ac.uk/funding/204-boothman-reynolds-and-smithells-scholarship-2022">Boothman, Reynolds & Smithells</a> Scholarships are available to UK applicants.  <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds. </p> <p><strong>Non-UK</strong> – The <a href="https://phd.leeds.ac.uk/funding/53-school-of-computing-scholarship">School of Computing Scholarship </a> is available to support the additional academic fees of Non-UK applicants. The <a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a> is available to nationals of China. The <a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a> is available to support US citizens. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals starting from September/October 2021.</p>

<h2 class="heading">Contact details</h2>

<p>For further information about this project, please contact Dr Thomas Ranner<br /> e: <a href="mailto:T.Ranner@leeds.ac.uk">T.Ranner@leeds.ac.uk</a></p> <p>For further information regarding your application, please contact Doctoral College Admissions<br /> e: <a href="mailto:phd@engineering.leeds.ac.uk">phd@engineering.leeds.ac.uk</a></p>

<h3 class="heading heading--sm">Linked funding opportunities</h3>