Keywords: object-oriented programming, Java, finite elements, symbolic computation, automatic programming.

The problems occurring today in computational mechanics and related domains are getting more and more complex, and may involve several branches of physics. The use of object-oriented programming, in the 1990s, has probably been the first breakthrough in the design of finite element codes. Since the first works published on the subject (for example Rehak [1], Miller [2], Zimmermann [3] and the references therein), almost every sector of computational mechanics has been targeted. In the same time, the use of algebraic manipulation software has been a point of interest for finite element development. Recently, among the most advanced works, one can find the work of Eyheramendy and Zimmermann [4], Korelc [5] and Logg et al. [6]. The goal of these approaches was to develop software for the automation code generation from the mathematical formulation. The approach proposeed by the authors (for example see Saad [7]) covers the development process of numerical models from the variational statement to the simulation tool. The authors have proposed generic concepts to automate the development of the finite element method. The mathematical formalism is based on the tensor algebra to describe the discretisation of a variational formulation. The generic character of the approach is preserved through the object-oriented approach using Java. A framework based on object-oriented concepts, was proposed, that is capable of handling symbolic developments of elemental contributions for finite element codes. The advantage of this approach is that the generic description can be extended naturally to any discretisation model in space or time. This concept is fully validated for simple linear problems (elasticity, heat convection, etc.), for the treatment of mixed variational formulations (thermo-mechanical, Navier-Stokes for incompressible flows, etc.) and Lagrangian frameworks (elasticity in large transformations, hyperelasticity, etc.)

1

D.R. Rehak, J.W. Baugh Jr., "Alternative Programming Techniques for Finite Element Programming Development", Proceedings IABSE Colloquium on Expert Systems in Civil Engineering, Bergamo, Italy, IABSE, 1989.

2

G.R. Miller, "A LISP-Based Object-Oriented approach to structural analysis", Engr. with Comp., 4, 197-203, 1988. doi:10.1007/BF01213981

3

Th. Zimmermann, Y. Dubois-Pèlerin, P. Bomme, "Object-oriented finite element programming: I. Governing principles", Comput. Methods Appl. Mech. Engrg., 98, 291-303, 1992. doi:10.1016/0045-7825(92)90180-R

4

D. Eyheramendy, Th. Zimmermann, "The Object-oriented finite elements: II. A symbolic environment for automatic programming", Comput. Methods Appl. Mech. Engrg., 32, 259-276, 1996. doi:10.1016/0045-7825(96)01041-9

5

J. Korelc, "Multi-language and Multi-environment Generation of Nonlinear Finite Element Codes", Engineering with Computers, 18, 312-327, 2002. doi:10.1007/s003660200028

6

A. Logg, "Automating the Finite Element Method", Arch Comput Methods Eng., 14, 2007. doi:10.1007/s11831-007-9003-9

7

R. Saad, "Sur une approche à objets generalise pour la mécanique non linéaire", PhD Thesis report, Université de Provence, 2011.

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