Applied and Computational Mathematics Research Group
Our research in applied and computational mathematics includes: theoretical and applied fluid mechanics, mathematics and mechanics of solids, mathematical biology, applied analysis, and numerical analysis and scientific computing.
Our research in the area of applied and computational mathematics is informed by problems at the interface with physical sciences, biological sciences and engineering and there are many productive interdisciplinary collaborations within Cardiff University and further afield.
Our national and international collaborators include research groups at Imperial, Oxford, Cambridge, Warwick, Swansea, Canberra, Curtin (Perth), Perth, Delft, Northwestern, Ljubljana and Montréal.
The group hosts the Cardiff University Student Chapter of the Society for Industrial and Applied Mathematics and the Institute of Mathematics and its Applications (SIAM-IMA Student Chapter) which encompasses postgraduate students and faculty members from across the University who are interested in mathematics or scientific computing and their real-world applications.
The main areas of research within the current group are:
Theoretical and applied fluid mechanics
Free-surface flows, dynamics of liquid films and jets, hydrodynamic stability theory, laminar-turbulent transition mechanisms, boundary-layer and wake flow instabilities, boundary layer flow control, viscoelastic flows, bubble dynamics, constitutive modelling of polymeric liquids.
Mathematics and mechanics of solids
Nonlinear elasticity, contact problems, limit states analysis, constitutive modelling in materials science.
The development of mathematical, computational and statistical methods to address biological and medical problems.
Inverse problems in materials modelling, homogenisation and the mechanics of composites.
Numerical analysis and scientific computing
The development of algorithms for the numerical solution of partial differential applications.
Head of Group
All seminars are held on Tuesday 14:10-15:00 in Room M/0.34, Mathematics Institute, Senghennydd Road, Cardiff, unless stated otherwise.
Programme organiser and contact: Dr Angela Mihai
|3 March 2020||Dr Zahir Hussain,|
Manchester Metropolitan University
To be confirmed
|11 February 2020||Dr Paul Ledger,|
To be confirmed
|4 February 2020||Dr Hermes Gadelha,|
University of Bristol
To be confirmed
28 January 2020
Dr Pierre Ricco, University of Sheffield
To be confirmed
26 November 2019
Dr Eugeny Buldakov, UCL
Numerical Lagrangian modelling of extreme ocean waves
The presentation discusses the development of a numerical solver where a simple finite-difference technique applied directly to Lagrangian equations of motion of inviscid fluid. Stability of the numerical scheme and numerical dispersion relation are analysed and method of improving numerical dispersion is suggested and implemented. Problem of wave breaking is discussed and a dissipative breaking model is developed. A 2D version of the solver is then applied to extreme ocean waves. An extreme event in random sea is described as a deterministic focussed wave group with an amplitude spectrum related to the spectrum of the underlying random process. Evolution of such a wave group is modelled in a Lagrangian numerical wave tank and results are compared with experiments.
19 November 2019
Professor Alison Raby, University of Plymouth
Extreme waves and the structures that dare to stand
Historic lighthouses, seawalls and breakwaters are still standing after many years, having endured an incredible battering. In the past, methods of designing structures in the coastal zone were empirical, with much of the understanding acquired by considering previous failures. More recently, our understanding of the nature of waves has encouraged a statistical approach, using long random wave realisations to identify worst responses. This presentation will describe the novel use of a design wave in the coastal zone, using a series of experimental campaigns on physical models exposed to extreme wave loading, particularly focusing on rock lighthouses.
12 November 2019
Professor Peter Schmid, Imperial College
Koopman analysis and dynamic modes
Koopman analysis is a mathematical technique that embeds nonlinear dynamical systems into a linear framework based on a sequence of observables of the state vector. Computing the proper embeddings that result in a closed linear system requires the extraction of the eigenfunctions of the Koopman operator from data. Dynamic modes approximate these eigenfunctions via a tailored data-matrix decomposition. The associated spectrum of this decomposition is given by a convex optimization problem that balances data-conformity with sparsity of the spectrum. The Koopman-dynamic mode process will be discussed and illustrated on physical examples.
5 November 2019
Professor Derek Moulton, University of Oxford
Morphorods: the mechanics of growing elastic rods
Filamentary structures display a wide range of patterns and behaviours, such as in polymers, vines, axons, trachea, and elephant trunks, to name a few. Mechanically, a key feature prevalent in biological filaments is growth. Growth is the critical element underlying biological pattern formation and may also be utilised in other ways, for instance to generate movement or provide mechanical support against external loads. Due to their inherent slenderness, the mechanical behaviour of growing filaments is well-characterised by a one-dimensional continuum representation. We have in recent years developed a framework for modelling such structures by including growth in classical elastic rod equations; we term these morphoelastic rods or simply morphorods.
In this talk I will first briefly outline our framework and demonstrate the variety of applications and patterns that can be generated. I will then turn to our current efforts to confront the significant challenge of incorporating tissue level properties in the morphorod setting. A motivating example is in gravitropic growth, in which a branch or stem develops curvature in response to an external field (gravity). To model such a multiscale process we have developed a robust system of mapping from growth in a 3D finite elasticity setting to a 1D morphorod.
22 October 2019
Professor Catherine Powell, University of Manchester
Adaptive stochastic Galerkin approximation for parameter-dependent linear elasticity problems
In this talk, we give an overview of some recent work on the use of stochastic Galerkin mixed finite element methods (SG-MFEMs) for performing forward uncertainty quantification in parameter-dependent linear elasticity equations. Starting from a three-field PDE model in which the Young's modulus is represented as an affine function of a set of parameters, we discuss how to implement SG-MFEM approximation and introduce a novel a posteriori error estimation scheme. We examine the error in the natural weighted norm with respect to which the weak formulation is stable. Exploiting the connection between this norm and the underlying PDE operator also leads to an efficient preconditioning strategy.
Unlike standard residual-based error estimation schemes, the proposed strategy requires the solution of auxiliary problems on carefully constructed detail spaces on both the spatial and parameter domains. We establish upper and lower bounds for the SG-MFEM approximation error in terms of the proposed estimator. The constants in the bounds are independent of the Poisson ratio as well as the SG-MFEM discretisation parameters, meaning that the estimator is robust in the incompressible limit.
Finally, we briefly discuss proxies for the error reduction associated with potential enrichments of the SG-MFEM spaces and use these to develop an adaptive algorithm that terminates when the estimated error falls below a user-prescribed tolerance.
15 October 2019
Dr Ian Griffiths, University of Oxford
iPhones, Dysons and Cheerios: using fluid dynamics to aid technology
As technology continues to advance, new strategies involving a range of scientific disciplines are required. Mathematicians can provide frameworks to predict operating regimes and manufacture techniques. In this talk we show how mathematics can be used to help in the fabrication of precision glass, for smartphones and new flexible devices; the development of superior filters for vacuum cleaners; and the manufacture of unusual cereal shapes (like Nestlé Alphabet cereals).
8 October 2019
Professor Jonathan Healey, Keel University
Fractal neutral curves in the linear stability of shear flows
Rayleigh showed that the linear stability properties of inviscid shear
2019/20 events will be advertised here when the schedule is confirmed.