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ACMS Abstracts: Fall 2014

Agisilaos Athanasoulis (Leicester)

Semiclassical regularization for ill-posed classical flows: microlocal coarse-graining beyond Wigner measures

Wigner measures (WMs) have been successfully used as a parameter-free tool to provide homogenised descriptions of wave problems. Notable applications are the efficient simulation of large linear wave fields, and the painless resolution of linear caustics. However, their applicability to non-linear problems has been very limited.

In this talk we discuss the role of smoothness of the underlying flow as a limiting factor in the applicability of WMs. Non-smooth flows are ill-posed for measures, and new phenomena are possible in that regime. For example, single wavepackets may be "split" cleanly into several new wavepackets. We introduce a modification of the WM approach, and show that it can capture successfully some of these new phenomena. These results include joint work with T. Paul, I. Kyza and Th. Katsaounis.

The main idea behind this regularised scheme can be used to setup a unifying framework for several different approaches developed in the last few years. Some ideas about the extension of this framework to non-linear problems are also discussed.

Dongbin Xiu (Utah)

Uncertainty quantification algorithms for large-scale systems

Abstract: The field of uncertainty quantification (UQ) has received an increasing amount of attention recently. Extensive research efforts have been devoted to it and many novel numerical techniques have been developed. These techniques aim to conduct stochastic simulations for very large­-scale complex systems. Although remarkable progresses have been made, UQ simulations remains challenging due to their exceedingly high simulation cost for problems at extreme scales. In this talk I will discuss some of the recent developed UQ algorithms that are particularly suitable for extreme-­scale simulations. These methods are (1) collocation­ based, such that they can be directly applied to systems with legacy simulation codes; and (2) capacity­ based, such that they deliver the (near) optimal simulation accuracy based on the available simulation capacity. In another word, these methods deliver the best UQ simulation results based on any given computational resource one can afford, which is often very limited at the extreme scales.