Gibson Grd floor SR

Many continuum models have been derived in recent years which describe the self-assembly of industrially utilisable crystalline films to a level of detail that allows qualitative comparisons with experiments. For thin-film problems, where the characteristic length scales in vertical and horizontal directions differ significantly, the governing surface diffusion equations can be reduced to simpler PDEs by making use of asymptotic expansions. Many mathematical problems and solutions emerge from such new evolution equations and many of them remind of Cahn-Hilliard type equations. The surface diffusion models are of high, of fourth or even sixth, order.

We present the modeling, model reduction and simulation results for heteroepitaxial growth as for Ge/Si quantum dot self-assembly. The numerical methods we are using are based on trigonometric interpolation. These kind of pseudospectral methods seem very well suited for simulating the coarsening of large quantum dot arrays. When the anisotropy of the growing crystalline film is strong, it might become necessary to add a corner regularisation to the model. Then the transition region between neighboring facets is still smooth, but its scale is rather small. In this case it might be useful to think about an adaptive extension of the existing method.

Figure 1: Ostwald ripening process of quantum dots depicted at consecutive time points. One fourth of the whole, periodic, simulated domain is shown.

Joint work with Peter Evans and Barbara Wagner

Please note that this is a short notice change from the originally advertised talk by Dr Shahrokh Shahpar (Rolls-Royce plc.)

The new talk "Multilevel Monte Carlo method" is given by Mike Giles, Oxford-Man Institute of Quantitative Finance, Mathematical Institute, University of Oxford.

Joint work with Rob Scheichl, Aretha Teckentrup (Bath) and Andrew Cliffe (Nottingham)

Over the last several decades, many mesh generation methods and a plethora of adaptive methods for solving differential equations have been developed.  In this talk, we take a general approach for describing the mesh generation problem, which can be considered as being in some sense equivalent to determining a coordinate transformation between physical space and a computational space.  Our description provides some new theoretical insights into precisely what is accomplished from mesh equidistribution (which is a standard adaptivity tool used in practice) and mesh alignment.  We show how variational mesh generation algorithms, which have historically been the most common and important ones, can generally be compared using these mesh generation principles.  Lastly, we relate these to a variety of moving mesh methods for solving time-dependent PDEs.

This is joint work with Weizhang Huang, Kansas University

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.

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

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/

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.