Graph Grammar Based Petri Nets Model of Concurrency for Self-adaptive hp-Finite Element Method with Triangular Elements

Abstract

The paper presents the model of concurrency for the self-adaptive hp -Finite Element Method (hp -FEM) with triangular elements. The model concerns the process of an initial mesh generation as well as mesh adaptation. The model is obtained by defining CP-graph grammar productions as basic undivided tasks for both mesh generation and adaptation algorithms. The order of execution of graph grammar productions is set by control diagrams. Finally, the Petri nets are created based on the control diagrams. The self-adaptive hp -FEM algorithm modeled as a Petri net can be analyzed for deadlocks, starvation or infinite execution.