Minisymposia
A number of minisymposia will be scheduled during the parallel sessions. Each minisymposium should consist of a multiple of three 20 minute talks.If you are interested in organising a minisymposium, in any branch of Numerical Analysis or a cognate area, please contact the conference committee at naconf@maths.strath.ac.uk. Please supply the title of your proposed minisymposium along with a brief abstract and a tentative list of speakers. Organisers are encouraged to ensure that the speakers represent a broad spectrum of research experience. Authors will advised of acceptance of proposals by email shortly after submission. The deadline for submission of minisymposium abstracts is 30th April 2009.
Stabilised finite element methods
| Organiser | Gabriel Barrenechea (Strathclyde) |
| Speakers | Linda El Alaoui, Martin Stynes, Volker John, Lutz Tobiska, Gabriel Barrenechea, Benjamin Tews, Maicon Correa |
Abstract
The finite element solution of problems in fluid mechanics usually poses two basic problems. On one hand, the satisfaction of the discrete inf-sup (or Babuska-Brezzi) condition relating the finite element spaces for velocity and pressure, and on the other hand the spurious oscillations arising from the convection-dominated regime. To overcome these problems different solutions have been proposed in the last two decades. The main common point to these stabilised formulations is the addition of new terms to the formulation. These terms aim to correct the instabilities of the classical Galerkin method, without compromising the consistency of the method (or at least, not violating the consistency too much). In this minisymposium new developments and new applications of stabilized finite element methods will be discussed.
Partition of unity enrichment for moving boundary problems
| Organiser | Stephane Bordas (Glasgow) |
| Speakers |
Stephane Bordas, Ulrich Hoppe, Alexander Menk, Natarajan Sundararajan, Garth Wells |
Abstract
With the seminal contribution of Melenk and Babuska in 1995, a new era started for partition of unity based methods, where the approximation may be enriched locally with special functions, including a priori knowledge about the solution. The partition of unity finite element method (PUFEM), the generalized finite element method (GFEM) and the extended finite element method (XFEM) are such methods.
Because of the possibility to add any function to the approximation space, partition of unity enrichment has led to an increased flexibility in modelling, without meshing nor remeshing, moving boundary problems where one or more fields or their derivatives are discontinuous through a moving boundary: crack propagation, multi-phase flows, solidification problems, composite materials, biofilm growth, fluid structure interaction among others.
With the freedom provided by the absence of remeshing come several difficulties that recent research has been attempting to alleviate: implicit description of the moving boundary; numerical integration; eventual lack of optimal convergence; ill-conditioning; stability in constrained settings (incompressibility); error estimation; constraint enforcement on moving boundaries described implicitly; blending between enriched and non-enriched zones, etc.
The objective of this symposium is to bring together applied mathematicians and computational mechanicians, in an effort to bridge the gap and facilitate further communications, beyond the NACONF event.
The QR Algorithm: 50 Years later, its Genesis by John Francis, and
Subsequent Developments
| Organiser | Frank Uhlig (Auburn) |
| Speakers |
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Matrix Computations for Complex Networks
| Organisers | Des Higham (Strathclyde) and Alastair Spence (Bath) |
| Speakers | Jonathan Crofts, Ernesto Estrada, David Gleich, Gabriela Kalna, Zhivko Stoyanov, Keith Vass |
Abstract
The study of large, sparse networks that describe complex interactions is throwing up new challenges in numerical linear algebra. Cleve Moler (MATLAB News & Notes - October 2002) described Google's monthly PageRank operation as `The World's Largest Matrix Computation'. Beyond the world wide web, interaction data is rife in genomics, neuroscience, sociology, telecommunication, energy and business. Typical pairwise interactions lie somewhere between the structured connectivity matrices arising from discretized PDEs and the totally random networks studied by pure mathematicians.
Numerical analysts can contribute to this area in several ways. Standard data mining and visualisation tasks reduce to linear system or eigenvalue computations with these partially structured interaction matrices, so there is a need to understand how existing algorithms perform in this context. Moreover, experimental data comes with built-in uncertainty, for example, it has been estimated that a typical protein-protein interaction network has at least a 50% rate of false positives and false negatives. Hence, we need algorithms that are robust in the presence of noise, and, ideally, can pinpoint spurious and missing information. Finally, discovering specific network features, such as approximately bi-partite subgraphs, over-represented network motifs and nodes with unusually high `betweenness' or `centrality' indices, requires customized algorithms to be developed and analyzed.
Numerical methods for singularly perturbed problems
| Organisers | Natalia Kopteva (Limerick) and Eugene O'Riordan (Dublin City) |
| Speakers | Naresh Chadha, Carmelo Clavero, Sebastian Franz, Alan Hegarty, Natalia Kopteva, Niall Madden, Eugene O'Riordan, Maria Pickett, Jason Quinn, Martin Viscor |
Abstract
Classical numerical methods do not produce informative approximations to the solutions of singularly perturbed differential equations. The essential nature of the boundary or interior layers, that typically occur in the solutions, can be captured by invoking appropriate a priori or a posteriori layer-adapted numerical methods. As the presence of steep gradients in the layer regions can result in the error constants in classical error estimates becoming arbitrarily large, the numerical analysis of singularly perturbed problems requires specialized analytical techniques that reveal explicit dependence on the singular perturbation parameter(s). This mini-symposium will bring together people who have particular interests in the development and applications of layer-adapted numerical methods for various classes of singularly perturbed differential equations.
Approximation theory
| Organisers | Oleg Davydov (Strathclyde) |
| Speakers (tbc) | Brad Baxter, Kirill Kopotun, Tom Lyche, Gerhard Opfer, Manfred Sommer, Joe Ward |
Abstract
The minisymposium will represent several directions of modern approximation theory, including approximation with splines and radial basis functions, shape preserving approximation, approximation on the sphere.
Meshfree Methods for Partial Differential Equations
| Organisers | Stephane Bordas (Glasgow), Oleg Davydov (Strathclyde) and Holger Wendland (Sussex) |
| Speakers (tbc) | Uday Banerjee, Francesco Chinesta, Oleg Davydov, Greg Fasshauer, Elisabeth Larsson, Hennadiy Netuzhylov, Holger Wendland |
Abstract
The numerical approximation of partial differential equations by meshfree discretization techniques has been a very active and flourishing research area in recent years. Meshfree methods are a flexible tool to build high-order approximation spaces in arbitrary space dimensions. They have the capability to cope with changing geometries efficiently and can be defined in such a way that certain physical requirements like incompressibility can be incorporated analytically. Typical meshfree methods comprise Radial Basis Functions, Moving Least Squares, Kernel-Based Methods, Partition of Unity Methods, Generalized Finite Element Methods, Particle and Vortex Methods.
The goal of this minisymposium is to promote collaboration amongst mathematicians, computer scientists, engineers and industrial researchers. It will cover the development; mathematical, numerical, and algorithmic analysis; and application of meshfree methods.
Numerical Methods and Solvers for PDEs with Random Data
| Organiser | Catherine Powell (Manchester) |
| Speakers | Catherine Powell, Andrew Gordon, Eveline Rosseel, Par Hakansson, Antoine Tambue, Elisabeth Ullmann |
Abstract
In deterministic modelling, inputs to PDEs (boundary data, source terms, material parameters etc) are assumed to be known exactly. Such simplifications lead to tractable computations but the results are of limited use. In the real-world, inputs for PDEs arising in engineering applications are subject to uncertainty, either because they are truely random in nature, or because we have limited resources for recording deterministic quantities. For example, in the modelling of fluid flow in porous media, the porosity coefficients can never be measured at every point in the computational domain. Probabilistic models are more fitting and we need numerical techniques that allow us to quantify uncertainty in quantities of interest and robust solvers for the resulting high dimensional linear systems of equations.
The talks in this mini-symposium survey some of the popular numerical techniques for solving stochastic PDEs arising in en gineering applications, including Monte Carlo methods, stochastic Galerkin and stochastic collocation schemes, as well as appropriate iterative methods and preconditioners for solving the resulting linear systems.
Chebfun Computation
| Organisers | Ricardo Pachon, Rodrigo Platte and Lloyd N. Trefethen (Oxford) |
| Speakers | Ricardo Pachon, Rodrigo Platte and Lloyd N. Trefethen |
Abstract
Chebfun is a Matlab-based system for computing with functions and solving differential equations much as Matlab computes with vectors and solves matrix problems. The mathematical basis is Chebyshev interpolants and series. This minisymposium will discuss three recent developments in the chebfun system, with online demonstrations throughout. Close collaborators in this work are Folkmar Bornemann, Toby Driscoll and Nicholas Hale.
PDE constrained optimization
| Organisers | Andy Wathen and Martin Stoll (Oxford) |
| Speakers | Karl Kunisch, Matthias Heinkenschloss, Amos Lawless, Luise Blank, Tyrone Rees, Martin Stoll |
Abstract
Optimization problems with constraints which require the solution of a partial differential equation arise widely in many areas of the sciences and engineering, in particular in problems of design. The size and complexity of the discretized PDE constraints often pose significant challenges for contemporary optimization methods. This makes the solution of such PDE constrained optimization problems a major computational task. The aim of this minisymposium is to address recent developments in the analysis of such problems as well as the construction of robust and efficient numerical algorithms.
Contemporary Issues in Teaching and Learning
| Organisers | Michael Grove and Joe Kyle (MSOR Network) |
Abstract
We will offer three presentations followed by a discussion. Each of the presentations will explore issues and raise some questions for the later discussion.
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The Skills Agenda - The Place of Numerical Analysis
Our title is prompted by the following, taken from a UK mathematics Department module description: "Students will acquire skill in using numerical analysis software, work effectively in a team, and have acquired wider IT skills." In this presentaion we will examine recent data from a survey of employers, look at how one university in England has moved to address these findings.
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Spreadsheets: More useful than you might think, or more useless than you could imagine?
A means to meet the (reluctant) student halfway, or a barrier to series engagement? Packages such as MATLAB offer accurate and robust numerical procedures for numerical integration, and if such packages are available, it is probably better to encourage students to use them. However, the use of a spreadsheet is not without its advantages. Students have a great deal of familiarity with e.g. MS Excel, and generally have ready access to it. Any subsequent processing and the graphical display of the solution is aided by this familiarity. We look at current examples of this practice in UK HE.
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What Makes a Good Exam Question?
The question is often asked within Mathematics Departments generally. Are there special considerations within Numerical Analysis that raise separate issues? Taking assessment more widely, what are the features that we should be building into our design strategies? Some colleagues report success with a "little-and-often" approach. Is this appropriate for Numerical Analysis? Participants are invited to submit examples of good practice in the assessment of Numerical Analysis or, if this happens to be easier, examples of bad practice!
Algorithms for Multi-core Systems
| Organiser | Lawrence Mulholland (NAG Ltd) |
| Speakers |
Lawrence Mulholland, Robert Tong, Yiqi Qi, Yuhe Ren, Cliff Addison, Geoff Curtiss |
Abstract
The general trend in processor development has been first to multi-core and now towards many-core processors. Additionally multi-core chips are incorporating features such as simultaneous multi-threading, extra hierarchies of memory and special "heterogeneous" cores such as GPGPUs. If exploited correctly these ought to provide further significant performance gains.
The challenge to the numerical analysis community is to develop and adapt algorithms to fully exploit these architectures. NAG recognises that it must address this challenge and is currently and actively tackling this on several fronts; these include (in addition to re-engineering its core products):
- NAG is developing software to run on GPUs, initially implementing algorithms for Monte Carlo simulations on the nVidia Tesla card.
- In providing Computational Science and Engineering (CSE) support for HECToR, NAG has experience of adapting User application algorithms to improve their performance on that multi-core platform (including using mixed-mode programming) and, more recently, in the upgrade from a dual-core to a quad-core system
- NAG has helped AMD develop its Math Core Library (ACML) which provides a broad spectrum of functionality with high levels of single core performance and multi-core parallelism.
This mini-symposium will discuss the above experiences at NAG in addressing the challenge presented by the move toward multi-core and heterogeneous core platforms. In addition we expect to introduce some work undertaken by other developers in providing efficient algorithms for modern architectures.
Continuous Optimisation: Methods and Models
| Organisers | Nick Gould (RAL), Tibor Illés (Strathclyde), Michal Kočvara (Birmingham) |
| Speakers | Coralia Cartis, Sue Dollar, Jan Fiala, Jaroslav Fowkes, Michal Kočvara, Daniel Robinson, Jared Tanner, Andrew Thompson, George Tzallas-Regas |
Abstract
Optimisation problems from real-world applications usually lead to highly-structured, large-scale mathematical models. However, such models often suffer from
- a lack of convexity,
- badly-conditioned or even ill-posed formulations, and
- expensive objective and/or constraint functions.
The real-life applications discussed in this mini-symposium vary from structural optimisation problems with nonlinear stability constraints to the problem of optimising oil production for an oil reservoir; the methods discussed include many of the main algorithm families, from interior-point and SQP algorithms to trust region and regularisation methods. The aim of this mini-symposium is to address recent developments in both modelling and solving large scale, structured, nonlinear optimisation problems.