Matthias Heil

Maths & Cycling


I am a Professor of Applied Mathematics in the Department of Mathematics at the University of Manchester.

  • Research
  • My research is focused on the mathematical modelling and computational solution of problems in fluid and solid mechanics, as well as other interesting problems, incl. those arising through consultancy work for industry.
  • Things I have worked on include:
    • Fluid-structure interaction (FSI):
      • Flow in collapsible tubes
      • Pulmonary airway closure and reopening (free-surface flows in elastic vessels)
      • The suppression of viscous fingering in elastic-walled Hele-Shaw cells
      • Poroelastic FSI modelling of syringomyelia
      • Development of efficient preconditioners / solvers for such problems
    • Newtonian and non-Newtonian free-surface flows
    • Topological fluid mechanics and vortex dynamics
    • Wrinkling and buckling of thin elastic sheets/shells
    • Various other projects from Glaciology to biomedical problems
    • Scientific computing -- oomph-lib
  • Most of my papers are on google scholar. Have a look -- they are all lovely!
  • Here are some recent collaborators:
  • I am always interested in supervising keen PhD students. Here are some who are currently taking (or have recently taken) the ride:
  • I am happy to supervise MSc projects or summer internships. Send me an email if you want to find out more and/or want to get involved.
  • oomph-lib
  • oomph-lib
  • oomph-lib is the open-source object-oriented multi-physics finite-element library, hosted on GitHub at
    It is the main workhorse of our group, and is currently maintained jointly with Andrew Hazel (the co-founder/co-architect of the project all those years ago) and Puneet Matharu. Regular contributions and bug fixes are provided by many local and external collaborators.
  • The code is extremely well documented. Have a look at
    to get a feeling for the capabilities and the many detailed tutorials.
    Flow in a collapsible tube, simulated with oomph-lib
    Flow in a collapsible tube, simulated with oomph-lib
  • We are always looking for people to get involved, so if you like maths, physics, C++ (and chocolate biscuits!) get in touch and feel free to join our weekly oomph-lunch.
  • Teaching etc
  • Giving a lecture
  • I currently teach the following courses:
    • MATH20401: Vector Calculus and PDEs
    • MATH35002: Viscous Fluids
    Sadly, course materials are only available via Blackboard.
  • In the past I have taught:
    • MATH10222: ODEs and applications
    • MATH30201: Elasticity
  • I am also spending a fair amount of time in my role as the Department's PGR Director, meaning (in acroynym free form!) that I look after our lovely PhD students from an administrative point of view.


When I don't do hard sums, I tend to sit on my bike... Needless to say that I'm on .


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