Automatic generation of finite-element code by simultaneous optimization of expressions

AbstractThe paper presents a MATHEMATICA package SMS (Symbolic Mechanics System) for the automatic derivation of formulas needed in nonlinear finite element analysis. Symbolic generation of the characteristic arrays of nonlinear finite elements (e.g. nodal force vectors, stiffness matrices, sensitivity vectors) leads to exponential behavior, both in time and space. A new approach, implemented in SMS, avoids this problem by combining several techniques: symbolic capabilities of Mathematica, automatic differentiation technique, simultaneous optimization of expressions and a stochastic evaluation of the formulas instead of a conventional pattern matching technique. SMS translates the derived symbolic formulas into an efficient compiled language (FORTRAN or C). The generated code is then incorporated into an existing finite element analysis environment. SMS was already used to developed several new, geometrically and materially nonlinear finite elements with up to 72 degrees of freedom. The design and implementation of SMS are presented. Efficiency of the new approach is compared with the efficiency of the manually written code on an example

Numerical analysis of finite difference schemes in automatically generated mathematical modeling software

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.Includes bibliographical references (leaves 64-65).by Shuk-Han Ada Yau.M.S

HPCCP/CAS Workshop Proceedings 1998

This publication is a collection of extended abstracts of presentations given at the HPCCP/CAS (High Performance Computing and Communications Program/Computational Aerosciences Project) Workshop held on August 24-26, 1998, at NASA Ames Research Center, Moffett Field, California. The objective of the Workshop was to bring together the aerospace high performance computing community, consisting of airframe and propulsion companies, independent software vendors, university researchers, and government scientists and engineers. The Workshop was sponsored by the HPCCP Office at NASA Ames Research Center. The Workshop consisted of over 40 presentations, including an overview of NASA's High Performance Computing and Communications Program and the Computational Aerosciences Project; ten sessions of papers representative of the high performance computing research conducted within the Program by the aerospace industry, academia, NASA, and other government laboratories; two panel sessions; and a special presentation by Mr. James Bailey