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

Promotion of dropwise condensation of ethyl alcohol, methyl alcohol, and acetone by polytetrafluoroethylene

Coating condensing surfaces with thin layer of nonpolar Teflon results in dropwise condensation of polar organic vapor. Greater heat transfer coefficients are produced increasing effectiveness of condensing system. Investigation shows that vapors with strong dipole moment tend to condense dropwise

Preliminary investigation of effects of exposure to sulfur hexafluoride on tensile and yield strengths of aluminum and steel

Effects of sulfur hexafluoride on tensile and yield strengths of aluminum and steel with application to exhaust gases from rocket engine