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An object-oriented symbolic approach for the automated derivation of Finite Element contributions

Roy Saad 1 Dominique Eyheramendy 1 Lei Zhang
1 M&S - Matériaux et Structures
LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
Abstract : 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.
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https://hal.inria.fr/hal-01265414
Contributor : Dominique Eyheramendy <>
Submitted on : Monday, February 1, 2016 - 10:06:07 AM
Last modification on : Thursday, January 23, 2020 - 6:22:15 PM

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  • HAL Id : hal-01265414, version 1

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Roy Saad, Dominique Eyheramendy, Lei Zhang. An object-oriented symbolic approach for the automated derivation of Finite Element contributions. Advances in Engineering Software, Elsevier, 2016. ⟨hal-01265414⟩

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