Computational Mathematics and Applications
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Thu, 22/01/2009 14:00 |
Dr Fred Wubs (University of Groningen) |
Computational Mathematics and Applications  |
Rutherford Appleton Laboratory, nr Didcot |
| The climate is largely determined by the ocean flow, which in itself is driven by wind and by gradients in temperature and salinity. Nowadays numerical models exist that are able to describe the occurring phenomena not only qualitatively but also quantitatively. At the Institute for Marine and Atmospheric research Utrecht (IMAU) a so-called thermohaline circulation model is developed in which methods of dynamical systems theory are used to study the stability of ocean flows. Here bifurcation diagrams are constructed by varying the strength of the forcing, for instance the amount of fresh water coming in from the north due to melting. For every value of the strength we have to solve a nonlinear system, which is handled by a Newton-type method. This produces many linear systems to be solved. In the talk the following will be addressed: the form of the system of equations, a special purpose method which uses Trilinos and MRILU. The latter is a multilevel ILU preconditioner developed at Groningen University. Results of the approach obtained on the Dutch national supercomputer will be shown. | |||
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Thu, 29/01/2009 14:00 |
Dr Martin Lotz (Oxford University and City University of Hong Kong) |
Computational Mathematics and Applications |
Comlab |
| This talk is concerned with the probabilistic behaviour of a condition number C(A) for the problem of deciding whether a system of n homogeneous linear inequalities in m unknowns has a non-zero solution. In the case where the input system is feasible, the exact probability distribution of the condition number for random inputs is determined, and a sharp bound for the general case. In particular, for the expected value of the logarithm log C(A), an upper bound of order O(log m) (m the number of variables) is presented which does not depend on the number of inequalities. The probability distribution of the condition number C(A) is closely related to the probability of covering the m-sphere with n spherical caps of a given radius. As a corollary, we obtain bounds on the probability of covering the sphere with random caps. | |||
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Thu, 05/02/2009 14:00 |
Dr Robert Nürnberg (Imperial College London) |
Computational Mathematics and Applications |
Comlab |
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Thu, 12/02/2009 14:00 |
Dr Raphael Hauser (Computing Laboratory, Oxford) |
Computational Mathematics and Applications |
Comlab |
| The aim of this talk is to render the power of (short-step) interior-point methods for linear programming (and by extension, convex programming) intuitively understandable to those who have a basic training in numerical methods for dynamical systems solving. The connection between the two areas is made by interpreting line-search methods in a forward Euler framework, and by analysing the algorithmic complexity in terms of the stiffness of the vector field of search directions. Our analysis cannot replicate the best complexity bounds, but due to its weak assumptions it also applies to inexactly computed search directions and has explanatory power for a wide class of algorithms. Co-Author: Coralia Cartis, Edinburgh University School of Mathematics. | |||
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Thu, 19/02/2009 14:00 |
Dr Christian Mehl (University of Birmingham) |
Computational Mathematics and Applications |
Comlab |
| We discuss numerical methods for the solution of the palindromic eigenvalue problem Ax=λ ATx, where A is a complex matrix. Such eigenvalue problems occur, for example, in the vibration analysis of rail tracks. The structure of palindromic eigenvalue problems leads to a symmetry in the spectrum: all eigenvalues occur in reciprocal pairs. The need for preservation of this symmetry in finite precision arithmetic requires the use of structure-preserving numerical methods. In this talk, we explain how such methods can be derived. | |||
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Thu, 26/02/2009 14:00 |
Dr Richard Katz (Department of Earth Sciences, University of Oxford) |
Computational Mathematics and Applications |
Comlab |
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Thu, 05/03/2009 14:00 |
Prof Reinout Quispel (Latrobe University Melbourne) |
Computational Mathematics and Applications |
Comlab |
| Geometric integration is the numerical integration of a differential equation, while preserving one or more of its geometric/physical properties exactly, i.e. to within round-off error. Many of these geometric properties are of crucial importance in physical applications: preservation of energy, momentum, angular momentum, phase-space volume, symmetries, time-reversal symmetry, symplectic structure and dissipation are examples. The field has tantalizing connections to dynamical systems, as well as to Lie groups. In this talk we first present a survey of geometric numerical integration methods for differential equations, and then exemplify this by discussing symplectic vs energy-preserving integrators for ODEs as well as for PDEs. | |||
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Thu, 12/03/2009 14:00 |
Prof Ke Chen (The University of Liverpool) |
Computational Mathematics and Applications |
Rutherford Appleton Laboratory, nr Didcot |
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In recent years, the interdisciplinary field of imaging science has been experiencing an explosive growth in research activities including more models being developed, more publications generated, and above all wider applications attempted. |
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