A Graph Grammar Model of the hp Adaptive Three Dimensional Finite Element Method. Part I

Article type: Research Article

Authors: Paszyńska, Anna | Grabska, Ewa | Paszyński, Maciej

Affiliations: Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, Reymonta 4, 30-059, Krakow, Poland. [email protected]; [email protected] | AGH University of Science and Technology, Krakow, Poland. [email protected]

Note: [] Address for correspondence: AGH, University of Science and Technology, Al.Mickiewicza 30, 30-059, Kraków, Poland

Abstract: The first part of our paper presents a composite programmable graph grammar model for the self-adaptive two dimensional hp Finite Element Method algorithms (2D hp-FEM) with mixed triangular and rectangular finite elements. The two dimensional model is a starting point for the three dimensional model of self-adaptive hp-FEM presented in the second part of this paper. A computational mesh is represented by a composite graph. The operations performed over the mesh are expressed by the graph grammar rules. The three dimensional model is based on the extension of the two dimensional model with rectangular finite elements. In the second part of this paper, we conclude the presentation with numerical examples concerning the generation of the optimal mesh for simulation of the Step-and-Flash Imprint Lithography (SFIL).

Keywords: Graph grammar, Automatic hp adaptivity, Finite Element Method

DOI: 10.3233/FI-2012-622

Journal: Fundamenta Informaticae, vol. 114, no. 2, pp. 149-182, 2012