Graph Transformation Systems for Modeling Three Dimensional Finite Element Method. Part II

Abstract

In this paper we present several graph transformation systems modeling three dimen- sional 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 g raph 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 responsibl e 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 con cepts by using an exemplary derivation for a three dimensional projection problem, based on a set of graph transformation rules.