Numerical computation of interface problems

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 />

<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="{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>

<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 applying for <strong><em>PHD Computing FT</em></strong> and in the research information section that the research degree you wish to be considered for is <em><strong>Numerical computation of interface problems</strong></em> as well as <a href="https://eps.leeds.ac.uk/computing/staff/643/dr-thomas-ranner">Dr Thomas Ranner</a> as your proposed supervisor. Please state in the finance section that you are applying for the <em><strong>School of Computing Studentship 2025/26</strong></em>.</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> <p>Applications will be considered on an ongoing basis.  Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application.  We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</p> <p>Please note that you must provide the following documents in support of your application by the closing date of Thursday 31 July 2025:</p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date</li> <li>Research Proposal and Personal Statement outlining your interest in the project</li> <li>CV</li> </ul> <p><em>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p>

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.

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.

<p class="MsoNoSpacing" style="text-align:start; margin-bottom:12px">A highly competitive School of Computer Science Scholarship, providing full academic fees, together with a tax-free maintenance grant at the standard UKRI rate of £20,780 per year for 3.5 years.<br /> <br /> This opportunity is open to UK applicants only. There is 1 position available and if you are successful in securing an academic offer, this does not constitute an offer of funding. All candidates will be placed into the School of Computer Science Competition and selection is based on academic merit.</p> <p><strong>Important:</strong> Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p>

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