Rutherford Appleton Laboratory, nr Didcot

A method for computing periodic orbits for the Navier-Stokes

equations will be presented. The method uses a finite-element Galerkin

discretisation for the spatial part of the problem and a spectral

Galerkin method for the temporal part of the problem. The method will

be illustrated by calculations of the periodic flow behind a circular

cylinder in a channel. The problem has a simple reflectional symmetry

and it will be explained how this can be exploited to reduce the cost

of the computations.

Traditional optimisation theory and -methods on the basis of the

Lagrangian function do not apply to objective or constraint functions

which are defined by means of a combinatorial selection structure. Such

selection structures can be explicit, for example in the case of "min",

"max" or "if" statements in function evaluations, or implicit as in the

case of inverse optimisation problems where the combinatorial structure is

induced by the possible selections of active constraints. The resulting

optimisation problems are typically neither convex nor smooth and do not

fit into the standard framework of nonlinear optimisation. Users typically

treat these problems either through a mixed-integer reformulation, which

drastically reduces the size of tractable problems, or by employing

nonsmooth optimisation methods, such as bundle methods, which are

typically based on convex models and therefore only allow for weak

convergence results. In this talk we argue that the classical Lagrangian

theory and SQP methodology can be extended to a fairly general class of

nonlinear programs with combinatorial constraints. The paper is available

at http://www.eng.cam.ac.uk/~ss248/publications.

Dynamic optimisation is a tool that enables the process industries to

compute optimal control strategies for important chemical processes.

Aspen DynamicsTM is a well-established commercial engineering software

package containing a dynamic optimisation tool. Its intuitive graphical

user interface and library of robust dynamic models enables engineers to

quickly and easily define a dynamic optimisation problem including

objectives, control vector parameterisations and constraints. However,

this is only one part of the story. The combination of dynamics and

non-linear optimisation can create a problem that can be very difficult

to solve due to a number of reasons, including non-linearities, poor

initial guesses, discontinuities and accuracy and speed of dynamic

integration. In this talk I will begin with an introduction to process

modelling and outline the algorithms and techniques used in dynamic

optimisation. I will move on to discuss the numerical issues that can

give us so much trouble in practice and outline some solutions we have

created to overcome some of them.

A new filter method will be presented that attempts to find a feasible

point for sets of nonlinear sets of equalities and inequalities. The

method is intended to work for problems where the number of variables

or the number of (in)equalities is large, or both. No assumption is

made about convexity. The technique used is that of maintaining a list

of multidimensional "filter entries", a recent development of ideas

introduced by Fletcher and Leyffer. The method will be described, as

well as large scale numerical experiments with the corresponding

Fortran 90 module, FILTRANE.

The seminar will focus on mathematical modelling of physics phenomena,

with applications in e.g. mass and heat transfer, fluid flow, and

electromagnetic wave propagation. Simultaneous solutions of several

physics phenomena described by PDEs - multiphysics - will also be

presented and discussed.

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All models will be realised through the use of the MATLAB based finite

element package FEMLAB. FEMLAB is a multiphysics modelling environment

with built-in PDE solvers for linear, non-linear, time dependent and

eigenvalue problems. For ease-of-use, it comprises ready-to-use applications

for various physics phenomena, and tailored applications for Structural

Mechanics, Electromagnetics, and Chemical Engineering. But in addition,

FEMLAB facilitates straightforward implementation of arbitrary coupled

non-linear PDEs, which brings about a great deal of flexibility in problem

definition. Please see http://ww.uk.comsol.com for more info.

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FEMLAB is developed by the COMSOL Group, a Swedish headquartered spin-off

from the Royal Institute of Technology (KTH) in Stockholm, with offices

around the world. Its UK office is situated in The Oxford Science Park.

The process industries are one of the UK's major sectors and include

petrochemicals, pharmaceuticals, water, energy and the food industry,

amongst others. The design of a processing plant is a difficult task. This

is due to both the need to cater for multiple criteria (such as economics,

environmental and safety) and the use highly complex nonlinear models to

describe the behaviour of individual unit operations in the process. Early

in the design stages, an engineer may wish to use automated design tools to

generate conceptual plant designs which have potentially positive attributes

with respect to the main criteria. Such automated tools typically rely on

optimization for solving large mixed integer nonlinear programming models.

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This talk presents an overview of some of the work done in the Computer

Aided Process Engineering group at UCL. Primary emphasis will be given to

recent developments in hybrid optimization methods, including the use of

graphical interfaces based on problem specific visualization techniques to

allow the engineer to interact with embedded optimization procedures. Case

studies from petrochemical and water industries will be presented to

demonstrate the complexities involved and illustrate the potential benefits

of hybrid approaches.

We consider matrix groups defined in terms of scalar products. Examples of interest include the groups of

• complex orthogonal,
• real, complex, and conjugate symplectic,
• real perplectic,
• real and complex pseudo-orthogonal,
• pseudo-unitary

matrices. We

• Construct a variety of transformations belonging to these groups that imitate the actions of Givens rotations, Householder reflectors, and Gauss transformations.
• Describe applications for these structured transformations, including to generating random matrices in the groups.
• Show how to exploit group structure when computing the polar decomposition, the matrix sign function and the matrix square root on these matrix groups.

This talk is based on recent joint work with N. Mackey, D. S. Mackey, and N. J. Higham.

We consider the problem of recovering the position of a scattering surface

from measurements of the scattered field on a finite line above the surface.

A point source algorithm is proposed, based on earlier work by Potthast,

which reconstructs, in the first instance, the scattered field in the whole

region above the scattering surface. This information is used in a second

stage to locate the scatterer. We summarise the theoretical results that can

be obtained (error bounds on the reconstructed field as a function of the

noise level in the original measurements). For the case of a point source of

the incident field we present numerical experiments for both a steady source

(time harmonic excitation) and a pulse source typical of an antenna in

ground penetrating radar applications.

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This is joint work with Claire Lines (Brunel University).

The talk will start with an introduction to recent development in Mathematica, with emphasis on numerical computing. This will be followed by a discussion of graph drawing algorithms for the display of relational information, in particular force directed algorithms. The talk will show that by employing multilevel approach and octree data structure, it is possible to achieve fast display of very large relational information, without compromising the quality.