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 introduce formal definitions for several graph transformation systems modeling three dimensional h-adaptive Finite Element Method (3D h-FEM) algorithms with tetrahedral finite elements. We introduce a composite graph representation of the computational mesh and graph transformation rules expressing the mesh operations. In particular, there are graph transformation rules expressing the generation of the initial mesh consisting with tetrahedral finite elements, graph transformation rules expressing the construction of an elimination tree for interfacing with multi-frontal direct solver algorithm, graph transformation rules selecting sub-graph representing finite elements for further refinements, graph transformation rules responsible for execution of mesh refinements. We also discuss several benefits of using graph transformation system instead of classical FEM approach, including the benefits from the viewpoint of multi-frontal direct solvers.
Keywords: Graph transformation system, Automatic h adaptivity, Finite Element Method
