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Parallel processing of finite strain, materially nonlinear and incompressible finite element analysis problems.

机译：并行处理有限应变，材料非线性和不可压缩的有限元分析问题。

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This research addresses the problem of parallel processing of finite strain, materially nonlinear, and incompressible FE analysis problems. The main objective of this research is to develop, implement, and test parallel nonlinear FE analysis algorithms using matrix and data level parallelization tools and Message Passing Interface (MPI) communication protocol in the context of direct equation solution procedures.; As a preliminary study, we first develop and implement a 2-D linear static FE algorithm which employs the Domain Decomposition Method (DDM) as the data level parallelization tool and MPI as the communications protocol. Communications cost due to data exchange between the processors and reduction of the solution time due to multiple processors are evaluated.; To address nonlinear problems, we adopt a distributed memory version of the SuperLU libraries (Demmel, Gilbert, and Li 1997) as the matrix level parallelization tool. Extending an earlier nonlinear Updated Lagrangian FE code developed at the University of Rochester (FRAME), we implement the SuperLU libraries for the solution of the linearized equations step. The remaining steps of this implementation follow the existing serial algorithm. We introduce an algorithm to extract the sparse stiffness matrix to be parsed into the SuperLU libraries from our existing banded stiffness matrix. Results show that while considerable speedup factors can be achieved for the solution of the linearized equations step, the speedup factors for the overall solution time remain low.; Data level parallelization requires partitioning of the FE mesh used for the computation. We implement an automatic domain partitioning algorithm using the McTis libraries (Karypis and Kumar 1998b). Following the partitioning, we renumber the subdomain nodes to separate the interior and the interface nodes. The resultant partitioned domains provide the local data required for the domain decomposition parallel version of our nonlinear FE algorithm.; We develop and implement a data level parallel nonlinear FE algorithm based on FRAME using DDM as the data level parallelization tool and MPI as the communications protocol. We introduce new data structures to store the required parameters for the parallel version. Elemental stiffness computations and stress recovery steps are executed in parallel. The resultant interface system is solved on a single processor. The results show that, for banded storage systems, parallel efficiency greatly depends on the node renumbering algorithm, where the increased bandwidth reduces the overall efficiency. The results also show that substantial speedup factors for the overall solution time can be achieved with optimized node numbering after partitioning.
机译：这项研究解决了有限应变，材料非线性和不可压缩有限元分析的并行处理问题。这项研究的主要目的是在直接方程求解程序的背景下，使用矩阵和数据级并行化工具以及消息传递接口（MPI）通信协议来开发，实施和测试并行非线性有限元分析算法。作为初步研究，我们首先开发和实现一种二维线性静态有限元算法，该算法采用域分解方法（DDM）作为数据级并行化工具，并使用MPI作为通信协议。评估了由于处理器之间的数据交换而导致的通信成本以及由于多个处理器而导致的解决时间的减少。为了解决非线性问题，我们采用SuperLU库的分布式内存版本（Demmel，Gilbert和Li 1997）作为矩阵级并行化工具。扩展由罗切斯特大学（FRAME）开发的较早的非线性更新的Lagrangian FE代码，我们实现了SuperLU库，用于线性方程式步骤的求解。此实现的其余步骤遵循现有的串行算法。我们引入一种算法，从现有的带状刚度矩阵中提取要解析为SuperLU库的稀疏刚度矩阵。结果表明，虽然线性方程组的求解可以达到相当大的加速因子，但总求解时间的加速因子仍然很低。数据级并行化需要对用于计算的FE网格进行分区。我们使用McTis库（Karypis和Kumar 1998b）实现了自动域分区算法。分区之后，我们对子域节点重新编号以分隔内部节点和接口节点。所得的分区域提供了非线性有限元算法的域分解并行版本所需的本地数据。我们使用DDM作为数据级并行化工具，以MPI作为通信协议，开发并实现了基于FRAME的数据级并行非线性有限元算法。我们引入了新的数据结构来存储并行版本所需的参数。单元刚度计算和应力恢复步骤并行执行。最终的接口系统在单个处理器上解决。结果表明，对于带状存储系统，并行效率在很大程度上取决于节点重编号算法，其中增加的带宽会降低整体效率。结果还表明，通过在分区后优化节点编号，可以实现总体解决方案时间的显着提速因子。

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