December 5, 2014 (Friday)       Informatics Forum, Edinburgh
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Assyr Abdulle (EPFL)

Reduced order modeling techniques for multiscale methods

Abstract: In this talk we will review the use of reduced order modeling techniques in the design of multiscale methods for partial differential equations with multiple scales. Applications to linear and nonlinear problems will be discussed. The talk is based upon a series of joint works with various collaborators [AbB12, AbB14, ABV14, AbB13, AbH14].

[AbB12] A. Abdulle and Y. Bai, Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems, J. Comput. Phys., 2012.

[AbB14] A. Abdulle and Y. Bai, Reduced order modelling numerical homogenization, Philosophical Transactions of the Royal Society A, vol. 372, num. 2021, 2014.

[ABV14] A. Abdulle, Y. Bai and G. Vilmart, Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems, Discrete Contin. Dyn. Syst. vol. 8, num. 1, 2015.

[AbB13] A. Abdulle and O. Budac, An adaptive finite element heterogeneous multiscale method for Stokes flow in porous media, to appear in SIAM MMS.

[AbH14] A. Abdulle and P. Henning, A reduced basis localized orthogonal decomposition, preprint submitted for publication.

Doug Carson (Keysignt)

Systolic Processing and Software Defined Compute Architectures

Abstract: Systolic processing architectures apply a stream of data to instructions as opposed to von Neuman processing architectures which apply a stream of instructions to data. Although systolic processing predates von Neuman processing as a result of its use in Colussus Mark II at Bletchley Park in 1944; its use has been confined to research and VLSI signal processing devices. Recent advances in FPGA capacity and high level synthesis techniques have enabled the construction of reconfigurable systolic processing arrays and resulted in a renewal of interest in this highly parallel and efficient compute architecture. In this talk we will cover the earliest practical examples of systolic processors and programming and highlight UK innovations in this field such as the transputer and CSP. Recent developments in software and hardware synthesis that make systolic processing a practical proposition will be covered and will include research findings from Keysight Technologies. Finally, possible high performance processing applications enabled by future devices and tooling will be considered.

Des Higham (University of Strathclyde)

Computational Complexity of Large-Scale Gillespie Style Simulations

Abstract: I will analyze and compare the computational complexity of different simulation strategies for continuous time Markov chains. I consider the task of approximating the expected value of some functional of the state of the system over a compact time interval. This task is the computational bottleneck in many large-scale computations arising in biochemical kinetics and cell biology. In this context, the terms 'Gillespie's method', 'The Stochastic Simulation Algorithm' and 'The Next Reaction Method' are widely used to describe exact simulation methods. For example, Google Scholar records more than 5,500 citations to Gillespie's seminal 1977 paper. I will look at the use of standard Monte Carlo when samples are produced by exact simulation and by approximation with tau-leaping or an Euler-Maruyama discretization of a diffusion approximation. Appropriate modifications of recently proposed multi-level Monte Carlo algorithms will also be studied for the tau-leaping and Euler-Maruyama approaches. I will pay particular attention to a parameterization of the problem that, in the mass action chemical kinetics setting, corresponds to the classical system size scaling.