Affiliations: [a] Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, Reymonta 4, 30-059, Kraków, Poland | [b] Department of Computer Science, Faculty of Computer Science, Electronics and Telecommunications, AGH University of Science and Technology, Al.Mickiewicza 30, 30-059, Kraków, Poland. maciej.paszynski@agh.edu.pl
Note: [*] Address for correspondence: AGH University of Science and Technology, Department of Computer Science, Faculty of Computer Science, Electronics and Telecommunications, Al.Mickiewicza 30, 30-059, Kraków, Poland.
Abstract: In this paper we present several graph transformation systems modeling three dimensional h-adaptive Finite Element Method (3D h-FEM) algorithms with tetrahedral finite elements. In our approach a computational mesh is represented by a composite graph and mesh operations are expressed by the graph transformation rules. Each graph transformation system is responsible for different kind of operations. In particular, there is a graph transformation system expressing generation of an initial mesh, generating element matrices and elimination trees for interfacing with direct solver algorithm, a graph transformation system deciding which elements have to be further refined, as well as a graph transformation system responsible for execution of mesh refinements. These graph transformation systems are tested using a graph transformation tool (called GRAGRA), which provides a graphical environment for defining graphs, graph transformation rules and graph transformation systems. In this paper we illustrate the concepts by using an exemplary derivation for a three dimensional projection problem, based on a set of graph transformation rules.
Keywords: Graph transformation system, Automatic h adaptivity, Finite Element Method
