Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Computer methods in applied mechanics and engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be re ected in this document. Changes may have been made to this work since it was submitted for publication. A de nitive version was subsequently published in Computer methods in applied mechanics and engineering, 259, 2013, 10.1016/j.cma.2013.03.016 Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be re ected in this document. Changes may have been made to this work since it was submitted for publication. Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. In this paper, the collocation XIBEM formulation is described and numerical results given. The numerical results are compared against closed-form or converged solutions. Comparisons are made against the conventional boundary element method and the non-enriched isogeometric BEM (IGABEM).When compared to non-enriched boundary element simulations, using XIBEM significantly reduces the number of degrees of freedom required to obtain a solution of a given error; thus, with a fixed computational resource, problems of a shorter wavelength can be solved.

Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. SUMMARYThe boundary element method (BEM) is a popular technique for wave scattering problems given its inherent ability to deal with infinite domains. Recently, the partition of unity BEM, in which the approximation space is enriched with a linear combination of plane waves, has been developed; this significantly reduces the number of degrees of freedom required per wavelength. It has been shown that the element ends are more susceptible to errors in the approximation than the mid-element regions. In this paper the authors propose that this is due to the reduced order of continuity in the Lagrangian shape function component of the basis functions. It is demonstrated, using numerical examples, that choosing trigonometric shapes functions, rather than classical quadratic shape functions, provides accuracy benefits. It is also demonstrated that the somewhat arbitrary choice of collocating at equally spaced points about the surface of a scatterer is, in fact, the optimum choice of collocation scheme.

The current study provides a simple algorithm for finding the optimal ROC curve for a linear discriminant between two point distributions, given only information about the classes' means and covariances. The method makes no assumptions concerning the exact type of distribution and is shown to provide the best possible discrimination for any physically reasonable measure of the classification error. This very general solution is shown to specialise to results obtained in other papers which assumed multi-dimensional Gaussian distributed classes, or minimised the maximum classification error. Some numerical examples are provided which show the improvement in classification of this method over previously used methods.

The equal spacing of N points on a sphere with application to partition-of-unity wave diraction problems.', Engineering analysis with boundary elements., 40. pp. 114-122.