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Finite element parallel computing based on minimal residual-preconditioned conjugate gradient method
FU Chaojiang, CHEN Hongjun
Journal of Computer Applications    2015, 35 (12): 3387-3391.   DOI: 10.11772/j.issn.1001-9081.2015.12.3387
Abstract544)      PDF (700KB)(311)       Save
Finite element analysis for elastic-plastic problem is very time-consuming. A parallel substructure Preconditioned Conjugate Gradient (PCG) algorithm combined with Minimal Residual (MR) smoothing was proposed under the environment of Message Passing Interface (MPI) cluster. The proposed method was based on domain decomposition, and substructure was treated as isolated finite element model via the interface conditions. Throughout the analysis, each processor stored only the information relevant to its substructure and generated the local stiffness matrix. A parallel substructure oriented preconditioned conjugate gradient method was developed, which combined with MR smoothing and diagonal storage scheme. Load balance was discussed and interprocessor communication was optimized in the parallel algorithm. A substepping scheme to integrate elastic-plastic stress-strain relations was used. The errors in the integration process were controlled by adjusting the substep size automatically according to a prescribed tolerance. Numerical example was implemented to validate the performance of the proposed PCG algorithm on workstation cluster. The performance of the proposed PCG algorithm was analyzed and the performance was compared with conventional PCG algorithm. The example results indicate that the proposed algorithm has good speedup and efficiency and is superior in performance to the conventional PCG algorithm. The proposed algorithm is efficient for parallel computing of 3D elastic-plastic problems.
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