Graph Transformations for Modeling Parallel hp-Adaptive Finite Element Method

Abstract

The paper presents composition graph (CP-graph) grammar, which consists of a set of CP-graph transformations, suitable for modeling all aspects of parallel hp adaptive Finite Element Method (FEM) computations. The parallel hp adaptive FEM allows to utilize distributed computational meshes, with finite elements of various size (thus h stands for element diameter) and polynomial orders of approximation varying locally, on finite elements edges and interiors (thus p stands for polynomial order of approximation). The computational mesh is represented by attributed CP-graph. The proposed graph transformations model the initial mesh generation, procedure of h refinement (breaking selected finite elements into son elements), and p refinement (adjusting polynomial orders of approximation on selected element edges and interiors), as well as partitioning of computational mesh into sub-domains and enforcement of mesh regularity rules over the distributed data structure.