Computational Mathematics and Applications
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Thu, 18/01/2007 14:00 |
Prof Toby Driscoll (University of Delaware) |
Computational Mathematics and Applications  |
Comlab |
| Radial basis functions have been used for decades for the interpolation of scattered, high-dimensional data. Recently they have attracted interest as methods for simulating partial differential equations as well. RBFs do not require a grid or triangulation, they offer the possibility of spectral accuracy with local refinement, and their implementation is very straightforward. A number of theoretical and practical breakthroughs in recent years has improved our understanding and application of these methods, and they are currently being tested on real-world applications in shallow water flow on the sphere and tear film evolution in the human eye. | |||
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Thu, 25/01/2007 14:00 |
Dr Mario Arioli (Rutherford Appleton Laboratory) |
Computational Mathematics and Applications |
Rutherford Appleton Laboratory, nr Didcot |
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A strict adherence to threshold pivoting in the direct solution of symmetric indefinite problems can result in substantially more work and storage than forecast by an sparse analysis of the symmetric problem. One way of avoiding this is to use static pivoting where the data structures and pivoting sequence generated by the analysis are respected and pivots that would otherwise be very small are replaced by a user defined quantity. This can give a stable factorization but of a perturbed matrix. The conventional way of solving the sparse linear system is then to use iterative refinement (IR) but there are cases where this fails to converge. We will discuss the use of more robust iterative methods, namely GMRES and its variant FGMRES and their backward stability when the preconditioning is performed by HSL_M57 with a static pivot option. Several examples under Matlab will be presented. |
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Thu, 01/02/2007 14:00 |
Prof Patrick Amestoy (ENSEEIHT, Toulouse) |
Computational Mathematics and Applications |
Comlab |
| We consider the parallel solution of sparse linear systems of equations in a limited memory environment. A preliminary out-of core version of a sparse multifrontal code called MUMPS (MUltifrontal Massively Parallel Solver) has been developed as part of a collaboration between CERFACS, ENSEEIHT and INRIA (ENS-Lyon and Bordeaux). We first briefly describe the current status of the out-of-core factorization phase. We then assume that the factors have been written on the hard disk during the factorization phase and we discuss the design of an efficient solution phase.Two different approaches are presented to read data from the disk, with a discussion on the advantages and the drawbacks of each one. Our work differs and extends the work of Rothberg and Schreiber (1999) and of Rotkin and Toledo (2004) because firstly we consider a parallel out-of-core context, and secondly we also study the performance of the solve phase. This is work on collaboration with E. Agullo, I.S Duff, A. Guermouche, J.-Y. L'Excellent, T. Slavova | |||
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Thu, 08/02/2007 14:00 |
Prof Stefan Vandewalle (KU Leuven) |
Computational Mathematics and Applications |
Comlab |
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Thu, 15/02/2007 14:00 |
Prof Peter Monk (University of Delaware) |
Computational Mathematics and Applications |
Comlab |
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Thu, 22/02/2007 14:00 |
Prof Marlis Hochbruck (University of Dusseldorf) |
Computational Mathematics and Applications |
Comlab |
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Thu, 01/03/2007 14:00 |
Prof Michal Kocvara (University of Birmingham) |
Computational Mathematics and Applications |
Comlab |
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Several formulations of structural optimization problems based on linear and nonlinear semidefinite programming will be presented. SDP allows us to formulate and solve problems with difficult constraints that could hardly be solved before. We will show that sometimes it is advantageous to prefer a nonlinear formulation to a linear one. All the presented formulations result in large-scale sparse (nonlinear) SDPs. In the second part of the talk we will show how these problems can be solved by our augmented Lagrangian code PENNON. Numerical examples will illustrate the talk. Joint work with Michael Stingl. |
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Thu, 08/03/2007 14:00 |
Prof Christian Lubich (University of Tuebingen) |
Computational Mathematics and Applications |
Comlab |
