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 an extension of the composite programmable graph grammar (CP-graph grammar) suitable for modeling the parallel direct solver algorithm utilized by the hp finite element method (hp-FEM). In the proposed graph grammar model, the computational mesh is represented by a CP-graph. The presented graph grammar models the solver algorithm by a set of graph grammar productions. The graph grammar model makes it possible to examine the concurrency of the algorithm by analyzing the interdependence between the atomic tasks, tasks and super-tasks. The atomic tasks correspond to the graph grammar productions, representing basic undividable parts of the algorithms. The level of atomic tasks models the concurrency for the shared memory architectures. On the other hand, the tasks correspond to the groups of atomic tasks with predefined inter-task communication channels. They constitute the grain for the decomposition of the parallel algorithm for the distributed memory architecture. Finally, the super-tasks correspond to a group of tasks resulting from the execution of load balancing algorithm. The solver algorithm is tested on distributed memory linux cluster for up to 192 processors. Copyright © 2009 John Wiley & Sons, Ltd.