The Book of Traces
Exploiting Two-Level Parallelism in FEM Applications
HPCN Europe '97 Proceedings of the International Conference and Exhibition on High-Performance Computing and Networking
Graph Transformations for Modeling hp-Adaptive Finite Element Method with Triangular Elements
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part III
ICCS 2009 Proceedings of the 9th International Conference on Computational Science
Computing with Hp-Adaptive Finite Elements, Vol. 2: Frontiers Three Dimensional Elliptic and Maxwell Problems with Applications
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PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
A Graph Grammar Model of the hp Adaptive Three Dimensional Finite Element Method. Part I
Fundamenta Informaticae
A Graph Grammar Model of the hp Adaptive Three Dimensional Finite Element Method. Part II
Fundamenta Informaticae
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The paper presents the Petri nets model describing the process of rectangular finite element mesh generation and h adaptation. This is the first step towards the formal analysis of all the parts of the existing graph grammar based parallel adaptive hp-Finite Element Method algorithms expressed by graph grammar productions. The mesh transformations are expressed as composite programmable graph grammar productions. The transitions on Petri nets correspond to the execution of graph grammar productions. The graph grammar based algorithms modeled as a Petri net can be analyzed for deadlocks, starvation or infinite execution. The parallel adaptive algorithms have many applications in the area of numerical simulations of different engineering problems, including material science, heat transfer, wave propagation and other.