2,160 research outputs found
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
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