## SIAM UKIE Annual Meeting 2017

## Time Table

09:15–10:00 | Registration in Collins Building, Richmond Street, Glasgow G1 1XQ |

10:00–10:10 | Welcome |

10:10–10:55 | Nick Higham: The Rise of Multiprecision Computations |

11:00–11:30 | Lyuba Chumakova: Cytoskeleton self-organization in epithelial cells: the role of mathematics in resolving a biological causality question |

11:35–12:20 | Sarah Waters: Mathematical Models for Tissue Engineering: Problems in Deformable and Reactive Porous Media (IMA Sponsored Talk) |

12:30–13:30 | Lunch and Poster Session |

13:30–14:00 | Business Session, open to all |

14:00–14:30 | Angela Mihai: Microstructure-Based Hyperelastic Models for Cellular Solids |

14:35–15:05 | Marta Betcke: Accelerated Photoacoustic Imaging |

15:10–15:40 | Tea/Coffee |

15:40–16:25 | Jeremy Morley: The Challenges of Geospatial Research |

16:25–16:30 | Poster Prize announcement and end of meeting |

## Posters

**Fatemah Al Mukahal (University of Strathclyde)**

Non-Newtonian Rivulet Flow

Non-Newtonian Rivulet Flow

*Gravity-driven flow of a thin uniform rivulet of a generalised Newtonian fluid down a vertical planar substrate is considered. We derive the parametric solution for any generalized Newtonian fluid whose viscosity is specified as a function of the shear rate, and the explicit solution for any generalised Newtonian fluid whose viscosity is specified as a function of the shear stress. We use these solutions to describe rivulet flow of a Carreau fluid and of an Ellis fluid, highlighting the similarities and differences between the behaviour of these two fluids.*

**Khulud Alayyash (Cardiff University)**

Optimal Material Density of Cellular Bodies under Large Elastic Deformation

Optimal Material Density of Cellular Bodies under Large Elastic Deformation

*In this thesis, for hyperelastic cellular bodies, several main factors determine the magnitude of the stress level in the cellular material, including the cell geometry, the cell wall thickness, and the presence of cell inclusions. To achieve this, we identify two non-standard mechanical parameters, namely a non-linear elastic modulus and a non-linear Poisson’s ratio defined in terms of the large stresses and strains in the elastic cell walls. For the numerical investigation, finite element simulations of honeycomb-like structures with a non-linear hyperelastic material are presented.*

**Scott Bagwell (Swansea University)**

Acousto-Magneto-Mechanical simulation using hp finite elements for MRI scanner design [view online]

Acousto-Magneto-Mechanical simulation using hp finite elements for MRI scanner design [view online]

*This poster presents a hp finite element framework for accurately resolving the physical phenomena present in an MRI scanner environment. The framework poses solutions to a monolithic multi physics system of equations for acousto-magneto-mechanical effects.*

**Michał Bosy (University of Strathclyde)**

A hybrid discontinuous Galerkin inspired preconditioner for the Stokes equation with non-standard boundary conditions [view online]

A hybrid discontinuous Galerkin inspired preconditioner for the Stokes equation with non-standard boundary conditions [view online]

*We consider the Stokes problem with non-standard boundary conditions. Specifically, we consider a Stokes problem with an imposed tangential velocity and a normal flux on the boundary. The discretisation is carried out using a hybrid discontinuous Galerkin method. Moreover, we introduce a new domain decomposition preconditioner that is easy to parallelise. Finally, we present convergence validation of the problem and we later compare the proposed preconditioner with standard Restricted Additive Schwarz preconditioners.*

**Andrew Croudace (University of Strathclyde)**

Unsteady Flow of a Thixotropic Fluid in a Slowly Varying Pipe

Unsteady Flow of a Thixotropic Fluid in a Slowly Varying Pipe

*We use lubrication theory to study the axisymmetric flow of thixotropic fluid in a slowly varying pipe. In regimes of weak thixotropy, the strength of thixotropy is similar to the aspect ratio of the pipe. We follow the expansion method of Pritchard et al., who showed that in a widening channel, thixotropy increases the velocity near the centre of the pipe, while antithixotropy has the opposite effect. We show that these results are generic for steady pipe flow, but not for unsteady flow, so we may not be able to make generic statements about the effects of antithixotropy on lubrication flow.*

**Francisco de Melo Virissimo (University of Bath)**

Three Layered Flows and the Non-Boussinesq Case

Three Layered Flows and the Non-Boussinesq Case

*In this work, we will study a variety of configurations and limits of the equations for long waves in three-layered stratified flows. We will present results on the transition between hyperbolic (wave-like) and elliptic (unstable) behaviour, on the limiting rigid lid and Boussinesq cases, on the conserved quantities, together with numerical investigations of the dynamics. (Joint work with Paul Milewski)*

**Massimiliano Fasi (The University of Manchester)**

Computing the matrix logarithm at higher precision

Computing the matrix logarithm at higher precision

*We present a multiprecision algorithm to compute the principal logarithm of a matrix to arbitrary precision, given multiprecision arithmetic. Our approach combines the well established inverse scaling and squaring method with an improved version of the classical bound for the error of Padé approximation of Kenney and Laub, which is sharper for highly nonnormal matrices. We compare the behaviour in high precision of truncated Taylor series and diagonal Padé approximants.*

**Matthew Gwynne (The University of Manchester)**

The Quadratic Eigenvalue Problem in Structural Analysis

The Quadratic Eigenvalue Problem in Structural Analysis

*In structural analysis, we use the eigenpairs of a quadratic eigenvalue problem (QEP) to study the behaviour of a given structure under periodic forcing, such as that caused by earthquakes. Most of the engineering software available already contains tools to solve the QEPs with the assumption of simple damping, but obtaining the solution to these with more realistic, and hence more complex, damping is currently too computationally expensive. We explore methods that can efficiently solve the QEPs where a realistic and more complex damping model is used.*

**Xiaokai Huo (Tsinghua University, China)**

Importance of compatibility conditions in establishing global existence for equations for viscoelastic fluids

Importance of compatibility conditions in establishing global existence for equations for viscoelastic fluids

*We show the importance of compatibility condition in continuum mechanics in proving the global existence of system of partial differential equations from viscoelastic fluids. The breaking of Kawashima condition is compensated by these conditions, and we will demonstrate the reasons. What is more, these conditions have different influences in the 1d, 2d and higher dimensions. The global existence theorem is thus proved in a unified way and it sheld light upon on the importance of these physically motivated compatibility conditions.*

**Pallav Kant (The University of Manchester)**

Spreading of a droplet on topographical features

Spreading of a droplet on topographical features

*Controlled spreading of liquid is of crucial importance to many industrial processes. For the current study we concentrate on the spreading of a single droplet on the surfaces with topographical features. We investigate, how topographical can be used to control or enhance spreading of the liquid. We also demonstrate that a thin-film model combined with an experimentally measured spreading law which relates the speed of the contact line to the contact angle, provides excellent predictions of the evolving liquid morphologies.*

**Nicolas Loizou (University of Edinburgh)**

A New Perspective on Randomized Gossip Algorithms [view online]

A New Perspective on Randomized Gossip Algorithms [view online]

*We propose a new approach for the design and analysis of randomized gossip algorithms which can be used to solve the average consensus problem. We show how the Randomized Block Kaczmarz (RBK) method—a method for solving linear systems—works as gossip algorithm when applied to a special system encoding the underlying network.*

**John McGowan (University of Strathclyde)**

Linking Physiologically Based Pharmacokinetics, Mathematical Modelling and Systems Biology

Linking Physiologically Based Pharmacokinetics, Mathematical Modelling and Systems Biology

*Physiologically Based Pharmacokinetics (PBPK) is the study of what the body does to a drug after it has been administered, by considering physical, chemical and physiological factors. We aim to see how mathematics can be used to model the concentration of a general drug solute as it moves through organs within the body. Once we know how to model the organs individually, we can then integrate these models into a larger systems model that can be implemented using PBPK software. Simulations are run to make predictions regarding the behaviour of the drug which helps the drug development process.*

**Christopher Miles (University of Nottingham)**

Phase-Field Model for Surface Coverage of Thin Films

Phase-Field Model for Surface Coverage of Thin Films

*We propose a non-linear PDE model describing surface coverage of thin films deposited onto a substrate. The equations are derived from energy minimisation using phase-field modelling techniques. This is an important consideration in fabricating efficient thin film solar cells. The model is discretized using finite elements and a third order IMEX Runge-Kutta method and used to simulate post-deposition morphological changes. This is joint work with M. Hubbard, R. MacKenzie and K.G. van der Zee.*

**Charles Murray (Durham University)**

Adaptive Stencil Computations

Adaptive Stencil Computations

*Subsurface fluids often comprise solving non-homogeneous, anisotropic, elliptic problems. It requires accurate material handling which yields large memory footprints and costly setup phases. In-situ meshing can create dynamically adaptive Cartesian Grids via geometric grid hierarchies. Dynamic adaptivity refines meshes using current solution values. Both techniques plus iterative solvers imply accurate stencils are not required immediately. Numerical integration ran as a background task can iteratively update stencils and limit accurate stencil calculation to specific areas to aid memory use.*

**Andrea Natale (Imperial College London)**

Multiscale energy-conserving finite elements for atmospheric flows

Multiscale energy-conserving finite elements for atmospheric flows

*We introduce a novel finite element discretisation of the incompressible Euler equations. We derive the scheme by applying Hamilton's principle of stationary action to a Lagrangian functional, representing the total kinetic energy. The resulting discretisation conserves the Lagrangian by construction and it can be easily generalised to other Hamiltonian fluid models. Moreover, the variational derivation defines a form of upwind stabilisation that induces an energy transfer from small to large scales, reproducing in this way the characteristic behaviour of two-dimensional turbulent flows.*

**Alberto Paganini (University of Oxford)**

Shape optimization of microlenses [view online]

Shape optimization of microlenses [view online]

*Microlenses are optical structures exhibiting interesting effects caused by internal resonances. These effects cannot be computed with geometric optics because microlenses are not much larger than the wavelength of the incident light. For this reason, optimizing their design is a challenging task. We apply a shape optimization algorithm tailored for finite element simulations to improve the optical properties of an initial design. The algorithm allows for arbitrarily high resolution of shapes by employing B-spline based representations of the deformation diffeomorphism.*

**Pranjal Pranjal (The University of Manchester)**

Balanced Solvers for Nonsymmetric Linear Systems With Stochastic PDE Origins

Balanced Solvers for Nonsymmetric Linear Systems With Stochastic PDE Origins

*This poster discusses the design and implementation of efficient solution algorithms for nonsymmetric linear systems arising from FEM approximation of convection-diffusion problems. The novel feature of our preconditioned GMRES and BICGSTAB(L) solvers is the incorporation of error control in the ‘natural’ norm in combination with a reliable and efficient a posteriori estimator for the PDE approximation error. This leads to a robust and optimally efficient inbuilt stopping criterion: the iteration is terminated as soon as the algebraic error is insignificant compared to the approximation error.*

**Sarah Roggendorf (University of Nottingham)**

Eliminating oscillations using a non-linear Petrov-Galerkin method in Banach spaces

Eliminating oscillations using a non-linear Petrov-Galerkin method in Banach spaces

*Rough solutions to PDEs, having thin layers or even discontinuities, are notoriously difficult to approximate numerically. In order to eliminate oscillations that occur in the standard Galerkin FEM approximation near sharp features, we consider the approximation problem as a residual minimisation problem in Lp-type Sobolev spaces with p<2. Applying a non-standard, non-linear Petrov-Galerkin method based on employing optimal test functions, we demonstrate for some numerical examples that the oscillations vanish as p tends to 1. This is joint work with P. Houston, I. Muga and K.G. van der Zee.*

**Alex Safar (Cardiff University)**

Gap Openings in Shearing Cellular Tissues: Two-Step Method to Improve FEA

Gap Openings in Shearing Cellular Tissues: Two-Step Method to Improve FEA

*Cellular tissues subject to shear deformation are studied using large strain elasticity and contact mechanics. Diagonal openings are obtained within the tissue and grow with the applied deformation. A Successive Decomposition Procedure (SDP) is employed to decrease FEA computation time and increase reliability. Surface pressure is then used to successfully model intercellular cohesion.*

**Josh Walton (University of Strathclyde)**

Surface anchoring effects in confined liquid crystals

Surface anchoring effects in confined liquid crystals

*A liquid crystal is an intermediate state of matter between a solid crystal and an isotropic liquid. The continuum theory of liquid crystals employs a unit vector called the director to describe the mean molecular alignment at a point. We consider a liquid crystal confined in a rectangle. We examine the effects of surface anchoring on a liquid crystal, where an additional surface energy models the misalignment of the director at the boundaries. By solving for the director angle, we are then able to examine the relationship between the energy and the anchoring asymptotically and numerically.*

**Mante Zemaityte (The University of Manchester)**

A Shift-and-Invert Lanczos Algorithm for the Dynamic Analysis of Structures

A Shift-and-Invert Lanczos Algorithm for the Dynamic Analysis of Structures

*To accurately describe the behaviour of a structure under dynamic loading, engineers require the smallest number of eigenvectors of the corresponding generalized eigenvalue problem that contribute by 90% to its total response. Usually only a few eigenvectors are required to achieve the 90% target, however, since the eigenvalues corresponding to the dominant eigenvectors are not known in advance, this may require the computation of a large number of eigenpairs. We present a method for estimating frequency intervals corresponding to dominant eigenvectors, which improves upon existing methods.*

**Weijian Zhang (The University of Manchester)**

Building a New Search Engine for Researchers

Building a New Search Engine for Researchers

*In this poster, we present Ethimo, a new graphic search engine for researchers. It is available at http://ethimo.io The challenge is to visualize millions of papers on a map in less than a second. We will illustrate our approach to the problem and how different components of the engine work together. Dimensionality reduction is crucial for visualizing high-dimensional data. We compare and contrast different methods such as self-organizing map (SOP) and t-distributed stochastic neighbor embedding (t-SNE). We show how we can exploit temporal network information to get more accurate results.*