An octree pattern-based massively parallel PCG solver for elasto-static and dynamic problems

Abstract

In this paper, an octree pattern-based massively parallel preconditioned conjugate gradient (PCG) solver is developed for large-scale elastostatic and implicit elastodynamic applications. The problem domain is discretised using octree cells to enable a fully automatic mesh generation. The compatibility between neighbouring octree cells of different sizes is satisfied by employing polyhedral elements. Matrix operations within the solver are carried out by adopting an octree pattern-based pre-computation approach. Here, a limited number of master cells in a balanced octree mesh is exploited to reduce memory requirements and perform highly efficient matrix product computations. The parallelism is achieved by employing a mesh-partitioning strategy and message-passing-interface (MPI) directives. The results show that the developed PCG solver attains a significant parallel speed-up and efficiency with an increasing number of cores on distributed memory systems. The practical applications of the proposed framework are demonstrated using large-scale examples for both CAD and image-based analyses.