Computational Mathematics and Applications
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Thu, 22/01/2004 14:00 |
Prof Simon Chandler-Wilde (University of Reading) |
Computational Mathematics and Applications  |
Rutherford Appleton Laboratory, nr Didcot |
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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.
This is joint work with Claire Lines (Brunel University). |
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Thu, 29/01/2004 14:00 |
Prof John Hinch (University of Cambridge) |
Computational Mathematics and Applications |
Comlab |
While the average settling velocity of particles in a suspension has been successfully predicted, we are still unsuccessful with the r.m.s velocity, with theories suggesting a divergence with the size of
the container and experiments finding no such dependence. A possible resolution involves stratification originating from the spreading of the front between the clear liquid above and the suspension below. One theory describes the spreading front by a nonlinear diffusion equation
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Experiments and computer simulations find differently. |
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Thu, 05/02/2004 14:00 |
Prof Marco Picasso (Ecole Polytechnique Federale de Lausanne) |
Computational Mathematics and Applications |
Comlab |
| Following the framework of Formaggia and Perotto (Numer. Math. 2001 and 2003), anisotropic a posteriori error estimates have been proposed for various elliptic and parabolic problems. The error in the energy norm is bounded above by an error indicator involving the matrix of the error gradient, the constant being independent of the mesh aspect ratio. The matrix of the error gradient is approached using Zienkiewicz-Zhu error estimator. Numerical experiments show that the error indicator is sharp. An adaptive finite element algorithm which aims at producing successive triangulations with high aspect ratio is proposed. Numerical results will be presented on various problems such as diffusion-convection, Stokes problem, dendritic growth. | |||
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Thu, 12/02/2004 14:00 |
Dr Markus Melenk (Max-Planck-Institute for Mathematics in the Sciences, Leipzig) |
Computational Mathematics and Applications |
Comlab |
It is known for elliptic problems with smooth coefficients
that the solution is smooth in the interior of the domain;
low regularity is only possible near the boundary.
The  -version of the FEM allows us to exploit this
property if we use meshes where the element size grows
porportionally to the element's distance to the boundary
and the approximation order is suitably linked to the
element size. In this way most degrees of freedom are
concentrated near the boundary.
In this talk, we will discuss convergence and complexity issues of the boundary concentrated FEM. We will show that it is comparable to the classical boundary element method (BEM) in that it leads to the same convergence rate (error versus degrees of freedom). Additionally, it generalizes the classical FEM since it does not require explicit knowledge of the fundamental solution so that it is also applicable to problems with (smooth) variable coefficients. |
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Thu, 19/02/2004 14:00 |
Dr Ken Badcock (Dept of Aerospace Engineering, University of Glasgow) |
Computational Mathematics and Applications |
Comlab |
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The standard airframe industry tool for flutter analysis is based
on linear potential predictions of the aerodynamics. Despite the
limitations of the modelling this is even true in the transonic
range. There has been a heavy research effort in the past decade to
use CFD to generate the aerodynamics for flutter simulations, to
improve the reliability of predictions and thereby reduce the risk
and cost of flight testing. The first part of the talk will describe
efforts at Glasgow to couple CFD with structural codes to produce
a time domain simulation and an example calculation will be described for
the BAE SYSTEMS Hawk aircraft.
A drawback with time domain simulations is that unsteady CFD is still costly and parametric searches to determine stability through the growth or decay of responses can quickly become impractical. This has motivated another active research effort in developing ways of encapsulating the CFD level aerodynamic predictions in models which are more affordable for routine application. A number of these approaches are being developed (eg POD, system identification...) but none have as yet reached maturity. At Glasgow effort has been put into developing a method based on the behaviour of the eigenspectrum of the discrete operator Jacobian, using Hopf Bifurcation conditions to formulate an augmented system of steady state equations which can be used to calculate flutter speeds directly. The talk will give the first three dimensional example of such a calculation. For background reports on these topics see http://www.aero.gla.ac.uk/Research/CFD/projects/aeroelastics/pubs/menu.htm |
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Fri, 20/02/2004 14:00 |
Dr Peter Bastian (University of Heidelberg) |
Computational Mathematics and Applications |
Comlab |
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Discontinuous Galerkin methods (DG) use trial and test functions that are continuous within
elements and discontinuous at element boundaries. Although DG methods have been invented
in the early 1970s they have become very popular only recently.
DG methods are very attractive for flow and transport problems in porous media since they can be used to solve hyperbolic as well as elliptic/parabolic problems, (potentially) offer high-order convergence combined with local mass balance and can be applied to unstructured, non-matching grids. In this talk we present a discontinuous Galerkin method based on the non-symmetric interior penalty formulation introduced by Wheeler and Rivière for an elliptic equation coupled to a nonlinear parabolic/hyperbolic equation. The equations cover models for groundwater flow and solute transport as well as two-phase flow in porous media. We show that the method is comparable in efficiency with the mixed finite element method for elliptic problems with discontinuous coefficients. In the case of two-phase flow the method can outperform standard finite volume schemes by a factor of ten for a five-spot problem and also for problems with dominating capillary pressure. |
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Thu, 26/02/2004 14:00 |
Prof Pablo Parrilo (ETH Zurich) |
Computational Mathematics and Applications |
Comlab |
| Semidefinite programming (SDP) techniques have been extremely successful in many practical engineering design questions. In several of these applications, the problem structure is invariant under the action of some symmetry group, and this property is naturally inherited by the underlying optimization. A natural question, therefore, is how to exploit this information for faster, better conditioned, and more reliable algorithms. To this effect, we study the associative algebra associated with a given SDP, and show the striking advantages of a careful use of symmetries. The results are motivated and illustrated through applications of SDP and sum of squares techniques from networked control theory, analysis and design of Markov chains, and quantum information theory. | |||
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Thu, 04/03/2004 14:00 |
Dr Peter Kohl (University of Oxford) |
Computational Mathematics and Applications |
Comlab |
| The heart can be described as an electrically driven mechanical pump. This pump couldn't adapt to beat-by-beat changes in circulatory demand if there was no feedback from the mechanical environment to the electrical control processes. Cardiac mechano-electric feedback has been studied at various levels of functional integration, from stretch-activated ion channels, through mechanically induced changes in cardiac cells and tissue, to clinically relevant observations in man, where mechanical stimulation of the heart may either disturb or reinstate cardiac rhythmicity. The seminar will illustrate the patho-physiological relevance of cardiac mechano-electric feedback, introduce underlying mechanisms, and show the utility of iterating between experimental research and mathematical modelling in studying this phenomenon. | |||
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Thu, 11/03/2004 14:00 |
Dr Francoise Tisseur |
Computational Mathematics and Applications |
Rutherford Appleton Laboratory, nr Didcot |
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We consider matrix groups defined in terms of scalar products. Examples of interest include the groups of
matrices. We
This talk is based on recent joint work with N. Mackey, D. S. Mackey, and N. J. Higham. |
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