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Numerical Analysis and Scientific Computing Seminars 2013/14

Semester Two (Spring 2013)

Semester One (Autumn 2013)

  • 27 September 2013 A fast Jacobi-type SVD for the graphics processors
    Vedran Novaković (University of Zagreb)

    3.00 pm - Frank Adams Room 1, Alan Turing Building
    Abstract (click to view)

    Singular value decomposition presents a challenge for the graphics processors and similar massively parallel architectures. We present a hierarchically blocked Jacobi SVD algorithm, for both a single and the multiple GPUs. Unlike common hybrid approaches, our algorithm needs a CPU for the controlling purposes only. The algorithm is noticeably faster than Magma's DGESVD on a Tesla C2070 GPU, while retaining the high relative accuracy. In this talk we shall discuss the key components of the algorithm: the blocking structure that reflects the levels of GPU's memory hierarchy, and some new parallel pivoting strategies. The algorithm, in principle, scales to an arbitrary number of GPU nodes, by adding the appropriate blocking levels. The scalability is demonstrated by more than twofold speedup on a Tesla S2050 system with four GPUs.

  • 11 October 2013 Phase Transitions in Convex Geometry and Optimization
    Dennis Amelunxen (The University of Manchester)

    3.00 pm - Frank Adams Room 1, Alan Turing Building
    Abstract (click to view)

    Convex optimization provides a powerful approach to solving a wide range of problems under structural assumptions on the solutions. Examples include solving linear inverse problems or separating signals with mutually incoherent structures. A curious phenomenon arises when studying such problems; as the underlying parameters in the optimization program shift, the convex relaxation can change quickly from success to failure. We reduce the analysis of these phase transitions to a summary parameter, the statistical dimension, associated to the problem. We prove a new concentration of measure phenomenon for some integral geometric invariants, and deduce from this the existence of phase transitions for a wide range of problems; the phase transition being located at the statistical dimension. We furthermore calculate the statistical dimension in concrete problems of interest, and use it to relate previously existing - but seemingly unrelated - approaches to compressed sensing by Donoho and Rudelson & Vershynin. (joint work with Martin Lotz, Michael B. McCoy, Joel A. Tropp)

  • 25 October 2013 Calculation of the Heat Transfer Coefficient for Quenching Probes
    Saša Singer (University of Zagreb)

    3.00 pm - Frank Adams Room 1, Alan Turing Building
    Abstract (click to view)

    The purpose of the Liscic/Petrofer probe is to determine the cooling intensity during liquid quenching in laboratory and workshop environments. The heat transfer coefficient calculation is based on temperatures measured in time near the surface of the probe, and involves two interesting numerical problems: monotone smoothing of measured temperatures, and solution of (one-dimensional) inverse heat conduction problem to determine the surface temperature and the heat transfer coefficient.

  • 8 November 2013 Sparse multifrontal QR factorization on the GPU
    Tim Davis (University of Florida)

    3.00 pm - Frank Adams Room 1, Alan Turing Building
    Abstract (click to view)

    Sparse matrix factorization involves a mix of regular and irregular computation, which is a particular challenge when trying to obtain high-performance on the highly parallel general-purpose computing cores available on graphics processing units (GPUs). We present a sparse multifrontal QR factorization method that meets this challenge, and is up to ten times faster than a highly optimized method on a multicore CPU. Our method is unique compared with prior methods, since it factorizes many frontal matrices in parallel, and keeps all the data transmitted between frontal matrices on the GPU. A novel bucket scheduler algorithm extends the communication-avoiding QR factorization for dense matrices, by exploiting more parallelism and by exploiting the staircase form present in the frontal matrices of a sparse multifrontal method. This is joint work with Nuri Yeralan and Sanjay Ranka (also both at the Univ. of Florida).

  • 22 November 2013 Extending GMRES to allow multiple preconditioners
    Tyrone Rees (Rutherford Appleton Laboratory)

    3.00 pm - Frank Adams Room 1, Alan Turing Building
    Abstract (click to view)

    The fast solution of linear systems by iterative methods generally requires effective preconditioners, and these preconditioners are usually highly tuned to the problem. However, in many cases there is more than one possible choice of preconditioner, and the different preconditioners often complement each other. In spite of this, existing methods only allow us to use one preconditioner at a time, or at best naively cycle through them. Furthermore, almost all computers available today have multiple cores, allowing us to apply more than one preconditioner to a vector simultaneously for minimal extra time cost. In this talk I will introduce MPGMRES, an extension of GMRES which allows the use of more than one preconditioner. This algorithm is available as the HSL subroutine HSL_MI29 and, as well as describing some of the theory behind the algorithm, I will give some numerical examples to illustrate its applicability and potential.

  • 6 December 2013 Fast Iterative Solution of PDE-Constrained Optimization Problems
    John Pearson (University of Edinburgh)

    3.00 pm - Frank Adams Room 1, Alan Turing Building
    Abstract (click to view)

    The solution of PDE-constrained optimization problems is a topic of much recent interest within the numerical analysis and applied mathematics communities. In this presentation we examine the numerical solution of matrix systems arising from finite element discretizations of these problems, by devising preconditioned iterative methods for the systems. Our methods for these problems utilize the fact that the matrix systems are large, sparse, and of saddle point structure. This enables us to create effective techniques by devising good approximations of the (1,1)-block and Schur complement of the matrices involved. In this talk we investigate a range of PDE-constrained optimization problems, including Poisson control, problems motivated by fluid dynamics, time-dependent formulations, and reaction-diffusion control problems resulting from chemical processes. For each problem we motivate the preconditioners that we employ, and carry out numerical experiments to demonstrate the performance of our methods.


Further information

For further information please contact the seminar organiser Vanni Noferini.

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