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

Aerodynamic Characteristics of Propeller-Driven VTOL Aircraft

This paper discusses the two major configurations that are usually considered for achieving VTOL while keeping the fuselage essentially horizontal - that is, the tilt-wing and the deflected-slipstream configurations. Because of the high turning losses incurred by deflected-slipstream configurations in hovering and because of the wing-stalling problem of the pure tilt-wing configurations during the transition, it appears that a combination of the two principles should be used. This tilt-wing and flap configuration should make use of a programmed extensible-chord slotted flap together with a leading-edge high-lift device in order to avoid the performance and handling qualities problems associated with wing stalling during the transition while keeping the wing area as low as possible for efficiency in cruising flight