Bath Numerical Analysis Seminar
Fridays at 12.15 at Wolfson 4W 1.7. All talks will be broadcast on Zoom.
Everyone is welcome at these talks.
| Date | Speaker | Title |
| 7 Feb 2025 | Andreas Kyprianou (University of Warwick) |
Proton beam de-energisation and the Bragg peak for cancer therapy via jump diffusion stochastic differential equations
Proton beam therapy is a relatively modern way of treating cancer. In short, protons are accelerated to around 2/3 the speed of light and projected into the body in the direction of cancerous tissues. Subatomic interactions slow the protons down causing energy deposition into tissue. The less energy protons have, the greater the number of subatomic interactions and the greater the rate at which energy is deposed. This results in the proton beam having an approximate “end point” where the majority of the initial energy in the beam is deposited. Rather obviously, this needs to be positioned into cancerous tissues and accuracy is essential. In this talk we discuss a mathematical model of the proton beam, grounded in the subatomic physics, taking the form of a (7+1)-dimensional SDE which has both diffusive and jump components. A fundamental modelling question of this class of SDEs pertains to constructing a well-defined meaning of “rate of energy deposition” in the three dimensions of space and how relates to Monte Carlo simulation. Ultimately this boils down to the existence of an occupation density for the SDE, which, in turn requires us to work with fundamental ideas from Malliavin calculus. This work is part of a larger body of research that is currently being undertaken in collaboration with colleagues in the MaThRad programme grant. |
| 14 Feb 2025 | Colin Cotter (Imperial College London) |
Parallel-in-time methods for atmosphere simulation using time diagonalisation
The goal of parallel-in-time methods is to employ parallelism in the time direction in addition to the space direction, in the hope of obtaining further parallel speedups at the limits of what is possible due to spatial parallelism with domain decomposition alone. Recently diagonalisation techniques have emerged as a way of solving the coupled system for the solution of a differential equation at several timesteps simultaneously. One approach, sometimes referred to as “ParaDiag II” involves preconditioning this “all-at-once” system obtained from time discretisation of a linear constant coefficient ODE (perhaps obtained as the space discretisation of a time dependent PDE) with a nearby system that can be diagonalised in time, allowing the solution of independent blocks in parallel. For nonlinear PDEs this approach can form the basis of a preconditioner within a Newton-Krylov method for the all-at-once system after time averaging the (now generally time dependent) Jacobian system. After some preliminary description of the ParaDiag II approach, I will present results from our investigation of ParaDiag II applied to some testcases from the hierarchy of models used in the development of dry dynamical cores for atmosphere models, including performance benchmarks. Using these results I will identify the key challenges in obtaining further speedups and identify some directions to address these. |
| 21 Feb 2025 | Eike Mueller (University of Bath) |
High-order IMEX-HDG timestepping methods for the incompressible Euler equations
Discretisation methods that are of high order in space and time are highly desirable when solving the equations of fluid dynamics since they show superlinear convergence and make efficient use of modern computer hardware. We develop an efficient timestepping method for the incompressible Euler equations based on combining implicit-explicit (IMEX) time-integrators, high-order Hybridised Discontinuous Galerkin (HDG) discretisations and splitting methods. The two computational bottlenecks are the calculation of a tentative velocity and the solution of a velocity-pressure system to enforce incompressibility. The second solve is preconditioned with a non-nested hybridised multigrid preconditioner as proposed by Cockburn, Dubois, Gopalakrishnan and Tan for the Schur-complement system that arises from static condensation to eliminate the pressure/velocity unknowns in favour of variables on the mesh-facets. The tentative velocity solve is preconditioned with ILU0. With this choice of preconditioners, the number of solver iterations depends only weakly on the polynomial degree and the grid-spacing; in other words, empirically the method is approximately h- and p-robust. As a consequence, the cost of a single timestep is roughly proportional to the total number of unknowns. At high order this allows the computation of highly accurate solutions at a low computational cost. The code has been implemented in Firedrake, using static condensation technology and PETSc to construct a fairly complex solver/preconditioner. Numerical results are presented for the simulation of a two-dimensional Taylor-Green vertex. |
| 21 Feb 2025 | Sam McCallum (University of Bath) |
Efficient gradients for Neural ODEs
Training Neural ODEs requires backpropagating through an ODE solve. The state-of-the-art backpropagation algorithm is recursive checkpointing that balances recomputation with memory cost. In this talk, I will introduce a class of algebraically reversible ODE solvers that significantly improve upon both the time and memory cost of recursive checkpointing. |
| 28 Feb 2025 | Henry Lockyer (University of Bath) |
TBC
TBC |
| 28 Feb 2025 | Sergey Dolgov (University of Bath) |
TBC
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| 7 Mar 2025 | Eric Hester (University of Bath) |
TBC
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| 7 Mar 2025 | Michael Murray (University of Bath) |
TBC
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| 14 Mar 2025 | Sam Flynn (National Physical Laboratory) |
TBC
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| 21 Mar 2025 | Jemma Shipton (University of Exeter) |
TBC
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| 28 Mar 2025 | Poppy Nikou (UCL Hospitals NHS Foundation Trust) |
TBC
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| 28 Mar 2025 | Mathew Southerby (UCL Hospitals NHS Foundation Trust) |
TBC
TBC |
| 4 Apr 2025 | Cristopher Salvi (Imperial College London) |
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| 4 Apr 2025 | Maud Lemercier (University of Oxford) |
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| 25 Apr 2025 | Ben Tapley (SINTEF, AI and Analytics group) |
TBC
TBC |
| 2 May 2025 | Patrick Fahy (University of Bath) |
TBC
TBC |
| 2 May 2025 | Max Scott (University of Bath) |
TBC
TBC |
Subscribe to seminar calendar
You can subscribe to the NA calendar directly from your calendar client, including Outlook, Apple’s iCalendar or Google calendar. The web address of the calendar is this ICS link which you will need to copy.
To subscribe to a calendar in Outlook:
- In Calendar view, select “Add Calendar” (large green +)
- Select “From Internet”
- Copy paste the ICS link, click OK, and click Yes to subscribe.
To subscribe to a calendar in iCalendar, please follow these instructions. Copy paste the ICS link in “web address”.
To subscribe to a calendar in Google Calendar:
- Go to link.
- On the left side go to "Other Calendars" and click on the dropdown.
- Choose "Add by URL".
- Copy paste the ICS link in the URL of the calendar.
- Click on "Add Calendar" and wait for Google to import your events. This creates a calendar with a somewhat unreadable name.
- To give a readable name to the calendar, click on the three vertical dots sign next to the newly created calendar and select Settings.
- Choose a name for the calendar, eg. Numerical Analysis @ Bath, and click back button on top left.
How to get to Bath
See here for instructions how to get to Bath. Please email James Foster (jmf68@bath.ac.uk) and Aaron Pim (arp46@bath.ac.uk) if you intend to come by car and require a parking permit for Bath University Campus for the day.Tips for giving talks
Tips for new students on giving talks
Since the audience of the NA seminar contains both PhD students and staff with quite wide interests and backgrounds, the following are some guidelines/hints to make sure people don't give you evil looks at lunch afterwards.
Before too much time passes in your talk, ideally the audience should know the answers to the following 4 questions:
- What is the problem you're considering?
- Why do you find this interesting?
- What has been done before on this problem/what's the background?
- What is your approach/what are you going to talk about?
There are lots of different ways to communicate this information. One way, if you're doing a slide show, could be for the first 4 slides to cover these 4 questions; although in this case you may want to revisit these points later on in the talk (e.g. to give more detail).
Remember:
- "vertebrate style" (structure hidden inside - like the skeleton of a vertebrate) = good for detective stories, bad for maths talks.
- "crustacean style" (structure visible from outside - like the skeleton of a crustacean) = bad for detective stories, good for maths talks.