On the Parallelization of Self-Adaptive hp-Finite Element Methods Part II. Partitioning Communication Agglomeration Mapping (PCAM) Analysis

Abstract

The paper presents a general methodology for an efficient parallelization of the fully automatic hp-adaptive Finite Element Method (hp-FEM). The self-adaptive hp-FEM algorithm expressed in terms of the graph grammar productions is analyzed by utilizing the Partitioning Communication Agglomeration Mapping (PCAM) model. The computational tasks are defined over a graph model of the computational mesh. It is done for all parts of the algorithm: the generation of an initial mesh, direct solver (including the integration and elimination of degrees of freedom), mesh transformations (including the h and p refinements), as well as the selection of the optimal refinements. The computation and communication complexities of the resulting parallel algorithms are analyzed. The paper is concluded with the sequence of massive parallel computations. From the performed tests it implies that the code scales well up to 200 processors.