Representations of finite element tensors via automated code generation

We examine aspects of the computation of finite element matrices and vectors which are made possible by automated code generation. Given a variational form in a syntax which resembles standard mathematical notation, the low-level computer code for building finite element tensors, typically matrices, vectors and scalars, can be generated automatically via a form compiler. In particular, the generation of code for computing finite element matrices using a quadrature approach is addressed. For quadrature representations, a number of optimisation strategies which are made possible by automated code generation are presented. The relative performance of two different automatically generated representations of finite element matrices is examined, with a particular emphasis on complicated variational forms. It is shown that approaches which perform best for simple forms are not tractable for more complicated problems in terms of run time performance, the time required to generate the code or the size of the generated code. The approach and optimisations elaborated here are effective for a range of variational forms

Unified Framework for Finite Element Assembly

At the heart of any finite element simulation is the assembly of matrices and vectors from discrete variational forms. We propose a general interface between problem-specific and general-purpose components of finite element programs. This interface is called Unified Form-assembly Code (UFC). A wide range of finite element problems is covered, including mixed finite elements and discontinuous Galerkin methods. We discuss how the UFC interface enables implementations of variational form evaluation to be independent of mesh and linear algebra components. UFC does not depend on any external libraries, and is released into the public domain

The non-coplanar baselines effect in radio interferometry: The W-Projection algorithm

We consider a troublesome form of non-isoplanatism in synthesis radio telescopes: non-coplanar baselines. We present a novel interpretation of the non-coplanar baselines effect as being due to differential Fresnel diffraction in the neighborhood of the array antennas. We have developed a new algorithm to deal with this effect. Our new algorithm, which we call "W-projection", has markedly superior performance compared to existing algorithms. At roughly equivalent levels of accuracy, W-projection can be up to an order of magnitude faster than the corresponding facet-based algorithms. Furthermore, the precision of result is not tightly coupled to computing time. W-projection has important consequences for the design and operation of the new generation of radio telescopes operating at centimeter and longer wavelengths.Comment: Accepted for publication in "IEEE Journal of Selected Topics in Signal Processing

Evaluation of lumbar angles and their clinical correlates in a Nigerian population

Background: There is paucity of data on the geometric angles of the lumbosacral spine in Nigeria and other African countries. The objective was to study the lumbar angles in our population and causes of variations if any.Methods: The lateral views of the lumbosacral spine radiographs of 300 Nigerian subjects were studied. The lumbar angles measured were lumbosacral angle (LSA), Lumbar lordosis angle (LLA), Sacral inclination angle (SIA) and lumbosacral disc angle (LSDA). The demographics and anthropometric measurements of the subjects such as weight, height, body mass index (BMI), hip circumference (HC), waist circumference (WC) and waist-hip ratio (WHR) were also recorded.Results: The mean values of the angles were as follows: LSA=37.80±9.20; LLA=40.40±11.20; SIA=38.70±8.90 and LSDA=14.60±3.40. There was a positive correlation between the weight, BMI, HC and WC of the subjects and LSA. A significant association was noted between the height, weight, BMI, HC, WC and WHR of the subjects and LLA. Whereas SIA was significantly affected by sex, weight, BMI, HC and WC of the subjects, LSDA was determined by age, BMI, WC and WHR.Conclusion: The mean values of these angles may form the reference values for the Nigerian population. Overweight and obesity were associated with increased lumbar angles