Efficient Compilation of a Class of Variational Forms

We investigate the compilation of general multilinear variational forms over affines simplices and prove a representation theorem for the representation of the element tensor (element stiffness matrix) as the contraction of a constant reference tensor and a geometry tensor that accounts for geometry and variable coefficients. Based on this representation theorem, we design an algorithm for efficient pretabulation of the reference tensor. The new algorithm has been implemented in the FEniCS Form Compiler (FFC) and improves on a previous loop-based implementation by several orders of magnitude, thus shortening compile-times and development cycles for users of FFC.Comment: ACM Transactions on Mathematical Software 33(3), 20 pages (2007

A general approach to transforming finite elements

The use of a reference element on which a finite element basis is constructed once and mapped to each cell in a mesh greatly expedites the structure and efficiency of finite element codes. However, many famous finite elements such as Hermite, Morley, Argyris, and Bell, do not possess the kind of equivalence needed to work with a reference element in the standard way. This paper gives a generalizated approach to mapping bases for such finite elements by means of studying relationships between the finite element nodes under push-forward.Comment: 28 page

In-flight measurement of ice growth on an airfoil using an array of ultrasonic transducers

Results of preliminary tests to measure ice growth on an airfoil during flight icing conditions are presented. Ultrasonic pulse echo measurements of ice thickness are obtained from an array of eight ultrasonic transducers mounted flush with the leading edge of the airfoil. These thickness measurements are used to document the evolution of the ice shape during the encounter in the form of successive ice profiles. Results from 3 research flights are presented and discussed. The accuracy of the ultrasonic measurements is found to be within 0.5 mm of mechanical and stereo photograph measurements of the ice accretion