An object-oriented symbolic approach to the automated derivation of finite element contributions

In this paper, we present a symbolic approach to automating the elaboration of numerical tools for the simulation of physical processes using the finite element method. We aim at developing a generic environment to automate discretization schemes in the context of PDEs. The approach is implemented in a consistent object-oriented tool built in Java. We propose a symbolic environment to automatically build the symbolic forms of elemental contributions corresponding to a variational formulation. These contributions are automatically introduced into a classical simulation tool. The basic object-oriented framework covering the elaboration of the elemental contributions derived from the weak statement is briefly discussed. The approach can be naturally extended to any discretization model in space or time. This approach is illustrated by the example of hyperelasticity.