Automatic Generation of Numerical Code

This paper presents a hybrid system for automatic generation of numerical codes using a symbolic approach, with emphasis on finite element formulations where straightforward use of symbolic and algebraic systems leads to exponential growth of derived expressions. The system comprises two major components. The Mathematica package AceGen is used for symbolic derivation of formulae needed in numerical procedures and automatic code generation. An approach implemented in AceGen overcomes the problem of expression growth by combining automatic differentiation, automatic code generation and theorem proving. The second component, named Computational Templates is a collection of prearranged modules for automatic creation of the interface between the finite element code and the finite element environment.