MPI-based parallel finite element approaches for implicit nonlinear dynamic analysis employing sparse PCG solvers

This paper presents three formulations combining domain decomposition based finite element method with linear preconditioned conjugate gradient (LPCG) technique for solving large-scale problems in structural mechanics on parallel processing machines. In the first formulation called the Global Interface Formulation (GIF), the PCG algorithm is applied on the assembled interface stiffness coefficient matrices of all submeshes. The second formulation called Local Submesh Formulation (LSF) operates on the local unassembled submesh matrices and the preconditioner is constructed using the local submesh information. In the third formulation called Local Interface Formulation (LIF), the sparse PCG algorithm is formulated using the unassembled local schur complement matrices of submeshes. Both diagonal and incomplete Cholesky preconditioners have been employed. These domain decomposition based PCG algorithms have been implemented within a finite element code for nonlinear implicit transient dynamic analysis. Time integration is performed using Newmark-β constant average acceleration method. The parallel finite element code uses an MPI-based message passing approach to provide portable parallel execution on shared, distributed and distributed shared memory computers. Numerical experiments have been conducted on PARAM-10000, an Indian parallel supercomputer to evaluate the performance of the implicit parallel nonlinear finite element code employing the three proposed PCG formulations. Numerical studies indicate that the proposed parallel PCG formulations are highly adaptive for parallel computing and superior in performance when compared to the conventional domain decomposition algorithm with parallel direct solver. The LSF formulation, which is amenable for efficient implementation of communications by way of overlapping with computations found to be superior in performance compared to other two PCG formulations.