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

Authors:
Anna Paszyń/ska;Ewa Grabska;Maciej Paszyń/ski
Affiliations:
Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, Reymonta 4, 30-059, Krakow, Poland. anna.paszynska@uj.edu.pl/ ewa.grabska@uj.edu.pl;Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, Reymonta 4, 30-059, Krakow, Poland. anna.paszynska@uj.edu.pl/ ewa.grabska@uj.edu.pl;(Correspd.) AGH University of Science and Technology, Krakow, Poland. Maciej.Paszynski@agh.edu.pl
Venue:
Fundamenta Informaticae
Year:
2012

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Abstract

This paper presents a composite programmable graph grammar model of the three dimensional self-adaptive hp Finite Element Method (hp-FEM) algorithms. The computational mesh composed of hexahedral finite elements is represented by a composite graph. The operations performed over the mesh are expressed by composite graph grammar productions. The three dimensional model is based on the extension of the two dimensional model for rectangular finite elements. This paper is concluded with numerical examples, presenting the generation of the optimal mesh for simulation of the Step-and-Flash Imprint Lithography (SFIL), the modern patterning process.