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

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.