An Exponentially Convergent Nonpolynomial Finite Element Method for Time-Harmonic Scattering from Polygons

In recent years nonpolynomial finite element methods have received increasing attention for the efficient solution of wave problems. As with their close cousin the method of particular solutions, high efficiency comes from using solutions to the Helmholtz equation as basis functions. We present and analyze such a method for the scattering of two-dimensional scalar waves from a polygonal domain that achieves exponential convergence purely by increasing the number of basis functions in each element. Key ingredients are the use of basis functions that capture the singularities at corners and the representation of the scattered field towards infinity by a combination of fundamental solutions. The solution is obtained by minimizing a least-squares functional, which we discretize in such a way that a matrix least-squares problem is obtained. We give computable exponential bounds on the rate of convergence of the least-squares functional that are in very good agreement with the observed numerical convergence. Challenging numerical examples, including a nonconvex polygon with several corner singularities, and a cavity domain, are solved to around 10 digits of accuracy with a few seconds of CPU time. The examples are implemented concisely with MPSpack, a MATLAB toolbox for wave computations with nonpolynomial basis functions, developed by the authors. A code example is included.

The risk-taking and self-harm inventory for adolescents: Development and psychometric evaluation

In this study, we report on the development and psychometric evaluation of the Risk-Taking (RT) and Self-Harm (SH) Inventory for Adolescents (RTSHIA), a self-report measure designed to assess adolescent RT and SH in community and clinical settings. 651 young people from secondary schools in England ranging in age from 11.6 years to 18.7 years and 71 young people referred to mental health services for SH behavior in London between the ages of 11.9 years and 17.5 years completed the RTSHIA along with standardized measures of adolescent psychopathology. Two factors emerged from the principal axis factoring, and RT and SH were further validated by a confirmatory factor analysis as related, but different, constructs, rather than elements of a single continuum. Inter-item and test–retest reliabilities were high for both components (Cronbach's α = .85, rtt = .90; Cronbach's α .93, rtt = .87), and considerable evidence emerged in support of the measure's convergent, concurrent, and divergent validity. The findings are discussed with regard to potential usefulness of the RTSHIA for research and clinical purposes with adolescents.

Equine anthelmintics: survey of the patterns of use, beliefs and attitudes among horse owners in the UK

An online survey was conducted to establish horse owners' beliefs, attitudes and practices relating to the use of anthelmintic drugs. Out of a total of 574 respondents, 89 per cent described themselves as ‘leisure riders’, most of whom took part in a variety of activities including eventing, show jumping, dressage, hunter trials, hunting, driving, endurance and showing. Overall, respondents were generally aware and concerned about the issue of anthelmintic resistance. Less than 60 per cent of all respondents were comfortable with their existing anthelmintic programme, and 25 per cent would like to reduce the use of anthelmintics in their horses. Of all the respondents, 47 per cent used livery, and 49 per cent of those reported that the livery imposed a common anthelmintic programme for horses kept on the premises; 45 per cent of these respondents were not entirely happy with the livery yard's programme. Less than 50 per cent of all respondents included ‘veterinary surgeon’ among their sources of advice on worming.