Taking advantage of symmetry in the automatic generation of numerical programs for finite element analysis

Abstract

The automatic generation of FORTRAN code for finite element analysis is described. A software system running under the VAXIMA system is constructed to perform the analytical derivation and the FORTRAN code generation. Techniques for generating efficient code based on symmetries in the given problem are presented. Symmetry must be extracted and preserved in the analytical derivation phase. One such derivation for the isoparametric formulation in finite element analysis is presented. To gain more control over the code generated, mathematical derivation is interleaved with code generation actions. The ability to automatically generate functions and subroutines is important. An example is given to show how FORTRAN functions and function calls are generated under program control. Techniques discussed should be useful in other applications when a symbolic computation system is used to derive and generate code for numerical computation.

Work reported herein has been supported in part by the US National Aeronautics and Space Administration under Grant NAG 3-298 and in part by the Department of Energy under Grant DE-AC02-ER7602075-A013.