This paper presents a parameter-free perfectly matched layer (PML) method for the finite-element-based solution of the Helmholtz equation. We employ one of Bermúdez et al.'s unbounded absorbing functions for the complex coordinate mapping underlying the PML. With this choice, the only free parameter that controls the accuracy of the numerical solution for a fixed numerical cost (characterised by the number of elements in the bulk and the PML regions) is the thickness of the perfectly matched layer, δ PML . We show that, for the case of planar waves, the absorbing function performs best for PMLs whose thickness is much smaller than the wavelength. We then perform extensive numerical experiments to explore its performance for non-planar waves, considering domain shapes with smooth and polygonal boundaries, different solution types (smooth and singular), and a wide range of wavenumbers, k, to identify an optimal range for the normalised PML thickness, kδ PML , such that, within this range, the error introduced by the presence of the PML is consistently small and insensitive to change. This implies that if the PML thickness is chosen from within this range * Corresponding author URL: http://www3.imperial.ac.uk/people/radu.cimpeanu11 (Radu Cimpeanu), http://www.maths.manchester.ac.uk/~mheil/ (Matthias Heil) Preprint submitted to Journal of Computational PhysicsMay 4, 2015 no further PML optimisation is required, i.e. the method is parameter-free. We characterise the dependence of the error on the discretisation parameters and establish the conditions under which the convergence of the solution under mesh refinement is controlled exclusively by the discretisation of the bulk mesh.

We investigate the theoretical foundations of the simulated tempering (ST) method and use our findings to design an efficient accelerated sampling algorithm. Employing a large deviation argument first used for replica exchange molecular dynamics [Nuria et al. J. Chem. Phys. 135:134111 (2011)], we demonstrate that the most efficient approach to simulated tempering is to vary the temperature infinitely rapidly. In this limit, we can replace the equations of motion for the temperature and physical variables by averaged equations for the latter alone, with the forces rescaled according to a position-dependent function defined in terms of temperature weights. The averaged equations are similar to those used in Gao's integrated-over-temperature method, except that we show that it is better to use a continuous rather than a discrete set of temperatures. We give a theoretical argument for the choice of the temperature weights as the reciprocal partition function, thereby relating simulated tempering to Wang-Landau sampling. Finally, we describe a self-consistent algorithm for simultaneously sampling the canonical ensemble and learning the weights during simulation. This infinite switch simulated tempering (ISST) algorithm is tested on three examples of increasing complexity: a system of harmonic oscillators; a continuous variant of the Curie-Weiss model, where ISST is shown to perform better than standard ST and to accurately capture the second-order phase transition observed in this model; and Alanine-12 in vacuum, where ISST also compares favorably with standard ST in its ability to calculate the free energy profiles of the root mean square deviation (RMSD) and radius of gyration of the molecule in the 300-500K tempearture range.

A detailed understanding of wind turbine performance status classification can improve operations and maintenance in the wind energy industry. Due to different engineering properties of wind turbines, the standard supervised learning models used for classification do not generalize across data sets obtained from different wind sites. We propose two methods to deal with the transferability of the trained models: first, data normalization in the form of power curve alignment, and second, a robust method based on convolutional neural networks and feature-space extension. We demonstrate the success of our methods on real-world data sets with industrial applications.

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