Computational Mathematics and Applications
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Thu, 20/01/2011 14:00 |
Dr Sebastien Loisel (Heriot-Watt University) |
Computational Mathematics and Applications  |
Gibson Grd floor SR |
| In various fields of application, one must solve very large scale boundary value problems using parallel solvers and supercomputers. The domain decomposition approach partitions the large computational domain into smaller computational subdomains. In order to speed up the convergence, we have several “optimized” algorithm that use Robin transmission conditions across the artificial interfaces (FETI-2LM). It is known that this approach alone is not sufficient: as the number of subdomains increases, the number of iterations required for convergence also increases and hence the parallel speedup is lost. A known solution for classical Schwarz methods as well as FETI algorithms is to incorporate a “coarse grid correction”, which is able to transmit low-frequency information more quickly across the whole domain. Such algorithms are known to “scale weakly” to large supercomputers. A coarse grid correction is also necessary for FETI-2LM methods. In this talk, we will introduce and analyze coarse grid correction algorithms for FETI-2LM domain decomposition methods. | |||
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Thu, 27/01/2011 14:00 |
Dr David Titley-Peloquin (University of Oxford) |
Computational Mathematics and Applications |
Rutherford Appleton Laboratory, nr Didcot |
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We consider the iterative solution of large sparse linear least squares (LS) problems. Specifically, we focus on the design and implementation of reliable stopping criteria for the widely-used algorithm LSQR of Paige and Saunders. First we perform a backward perturbation analysis of the LS problem. We show why certain projections of the residual vector are good measures of convergence, and we propose stopping criteria that use these quantities. These projections are too expensive to compute to be used directly in practice. We show how to estimate them efficiently at every iteration of the algorithm LSQR. Our proposed stopping criteria can therefore be used in practice. This talk is based on joint work with Xiao-Wen Chang, Chris Paige, Pavel Jiranek, and Serge Gratton. |
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Thu, 03/02/2011 14:00 |
Prof Des Higham (University of Strathclyde) |
Computational Mathematics and Applications |
Gibson Grd floor SR |
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Thu, 10/02/2011 14:00 |
Prof Mike Giles (University of Oxford) |
Computational Mathematics and Applications |
Gibson Grd floor SR |
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Based on an MPI library written over 10 years ago, OP2 is a new open-source library which is aimed at application developers using unstructured grids. Using a single API, it targets a variety of HPC architectures, including both manycore GPUs and multicore CPUs with vector units. The talk will cover the API design, key aspects of the parallel implementation on the different platforms, and preliminary performance results on a small but representative CFD test code. Project homepage: http://people.maths.ox.ac.uk/gilesm/op2/ |
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Thu, 17/02/2011 14:00 |
Prof Raymond Spiteri (University of Saskatchewan) |
Computational Mathematics and Applications |
Gibson Grd floor SR |
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Thu, 24/02/2011 14:00 |
Dr Juan Vera (Tilburg University) |
Computational Mathematics and Applications |
Gibson Grd floor SR |
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Polynomial Programs are ussually solved by using hierarchies of convex relaxations. This scheme rapidly becomes computationally expensive and is often tractable only for problems of small sizes. We propose an iterative scheme that improves an initial relaxation without incurring exponential growth in size. The key ingredient is a dynamic scheme for generating valid polynomial inequalities for general polynomial programs. These valid inequalities are then used to construct better approximations of the original problem. As a result, the proposed scheme is in principle scalable to large general combinatorial optimization problems. Joint work with Bissan Ghaddar and Miguel Anjos |
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Thu, 03/03/2011 14:00 |
Dr Selin Damla Ahipasaoglu (London School of Economics) |
Computational Mathematics and Applications |
Gibson Grd floor SR |
| In this talk, we focus on the analytical properties of a decentralized auction, namely the PAUSE Auction Procedure. We prove that the revenue of the auctioneer from PAUSE is greater than or equal to the profit from the well-known VCG auction when there are only two bidders and provide lower bounds on the profit for arbitrary number of bidders. Based on these bounds and observations from auctions with few items, we propose a modification of the procedure that increases the profit. We believe that this study, which is still in progress, will be a milestone in designing better decentralized auctions since it is the first analytical study on such auctions with promising results. | |||
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Thu, 10/03/2011 14:00 |
Prof David Silvester (University of Manchester) |
Computational Mathematics and Applications |
Rutherford Appleton Laboratory, nr Didcot |
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In this talk we discuss the design of efficient numerical methods for solving symmetric indefinite linear systems arising from mixed approximation of elliptic PDE problems with associated constraints. Examples include linear elasticity (Navier-Lame equations), steady fluid flow (Stokes' equations) and electromagnetism (Maxwell's equations). The novel feature of our iterative solution approach is the incorporation of error control in the natural "energy" norm in combination with an a posteriori estimator for the PDE approximation error. This leads to a robust and optimally efficient stopping criterion: the iteration is terminated as soon as the algebraic error is insignificant compared to the approximation error. We describe a "proof of concept" MATLAB implementation of this algorithm, which we call EST_MINRES, and we illustrate its effectiveness when integrated into our Incompressible Flow Iterative Solution Software (IFISS) package (http://www.manchester.ac.uk/ifiss/). |
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