Parallel Woodbury nonlinear analysis method for large-scale engineering structures based on MPI and OpenMP hybrid programming model
The nonlinear analysis method based on Woodbury formula avoids the repeated updating and factorization of global stiffness matrix during nonlinear analysis for engineering structures.However,existing Woodbury methods can only be applied to nonlinear analysis of small-and medium-scale structures because they are still limited to single-computer calculation.The Woodbury method based on substructure technique(abbreviated as substructure Woodbury method)is improved through a two-level sparse approximation strategy,and a parallel Woodbury nonlinear analysis method is proposed by combining MPI and OpenMP hybrid programming model.In this method,the whole structure is partitioned into several substructures,and the tasks at the substructure level are computed in parallel by MPI programming model,while the tasks at the element level are computed in parallel by nesting OpenMP programming model.The proposed method not only overcomes the limitation that the substructure Woodbury method becomes inefficient when the nonlinear region is large,but also breaks through the single-machine performance bottleneck of existing Woodbury methods.The numerical example analysis shows that the proposed method can fully utilize multiple computational nodes to improve the algorithm efficiency greatly,among which the nonlinear coefficient matrices updating and solution process reduces most computational time,which is the key of improving the efficiency of the overall analysis.
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