Dominique Eyheramendy

Advances in Symbolic and Numerical Approaches in Computational Mechanics

In this paper, we give a global overview of the latest advances in computational mechanics code design. We give a brief historical perspective of the evolution of finite element code design since the introduction of object-oriented programming in the 90’s. Then, we try to outline the structure of future computational tools. Besides classical architectures applied to multi-fields and multiphysics problems, we present a tentative example of generalization of the discretization scheme to isogeometric analysis, fully integrated in the same variational framework as finite elements. Following, a meta-level of code is developed to manage the variational formulation framework in a symbolic way. This way of thinking about the design of computational tools is expected to open new tracks in the development of codes, offering the natural and fast extendibility capabilities needed in modern engineering.

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.