Fine-grained GPU implementation of assembly-free iterative solver for finite element problems

• Fine-grained GPU instance of matrix-free CG solver for FEM is proposed.
• The parallelization potential of SIMD architectures is exploited.
• The workload is well-balanced for all the threads of the GPU architecture.
• The factors affecting to the proposal are studied using diverse GPU instances.

This paper proposes a fine-grained implementation of matrix-free Conjugate Gradient (CG) solver for Finite Element Analysis (FEA) using Graphics Processing Unit (GPU) architectures. The use of GPU computing in FEA is today an active research field. This is primary due to current GPU sparse solvers are partially parallelizable and can hardly make use of Data-Level Parallelism (DLP) for which GPU architectures are designed. The proposed GPU instance takes advantage of Massively Parallel Processing (MPP) architectures performing well-balanced parallel calculations at the Degree-of-Freedom (DoF) level of finite elements. The numerical experiments evaluate and analyze the performance of diverse GPU instances of the matrix-free CG solver.