Fine-grained heterogeneous parallel direct solver for finite element problems

Abstract

The improvement of computational effectiveness is a vital issue in the field of large-scale finite element analysis. The performance is fundamentally determined by the efficiency of solving sparse linear system equations using the implicit finite element method. This paper presents a direct linear solver based on heterogeneous hybrid parallel computing on CPUs and GPUs. This can efficiently utilize computing resources of multiple devices to achieve performance improvement. Initially, we partition the elimination tree into several subtrees to accomplish the task decomposition. Based on this, we build a dynamic programming mathematical model to balance the computational load of the various devices. Then, we develop a numerical decomposition strategy by combining node parallelism and tree parallelism for the CPUs. In addition, efficient numerical decomposition is achieved on the GPU through batch processing and maximizing the overlap between computations and data transfers. Numerical experiments show that, compared with MKL PARDISO, the performance of numerical factorization can be improved by up to 10 times by using CPU and dual-path GPU hybrid calculations, and the computation time of simulation can be reduced by one-third for the multicondition analysis of Body In White and by 20% for the large-scale nonlinear finite element deformation analysis.