Abstract
The paper presents composition graph (CP-graph) grammar, which consists of a set of CP-graph transformations, suitable for modeling triangular finite element mesh transformations utilized by the self-adaptive hp Finite Element Method (FEM). The hp adaptive FEM allows to utilize distributed computational meshes, with finite elements of various size (thus h stands for element diameter) and polynomial orders of approximation varying locally, on finite elements edges and interiors (thus p stands for polynomial order of approximation). The computational triangular mesh is represented by attributed CP-graph. The proposed graph transformations model the initial mesh generation, procedure of h refinement (breaking selected finite elements into son elements), and p refinement (adjusting polynomial orders of approximation on selected element edges and interiors). The graph grammar has been defined and verified by implemented graph grammar transformation software tool.
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© 2008 Springer-Verlag Berlin Heidelberg
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Paszyńska, A., Paszyński, M., Grabska, E. (2008). Graph Transformations for Modeling hp-Adaptive Finite Element Method with Triangular Elements. In: Bubak, M., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds) Computational Science – ICCS 2008. ICCS 2008. Lecture Notes in Computer Science, vol 5103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69389-5_68
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DOI: https://doi.org/10.1007/978-3-540-69389-5_68
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69388-8
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