Efficient implementation of total FETI solver for graphic processing units using Schur complement

Abstract

This paper presents a new approach developed for acceleration of FETI solvers by Graphic Processing Units (GPU) using the Schur complement (SC) technique. By using the SCs FETI solvers can avoid working with sparse Cholesky decomposition of the stiffness matrices. Instead a dense structure in form of SC is computed and used by conjugate gradient (CG) solver. In every iteration of CG solver a forward and backward substitution which are sequential are replaced by highly parallel General Matrix Vector Multiplication (GEMV) routine. This results in 4.1 times speedup when the Tesla K20X GPU accelerator is used and its performance is compared to a single 16-core AMD Opteron 6274 (Interlagos) CPU. The main bottleneck of this method is computation of the Schur complements of the stiffness matrices. This bottleneck is significantly reduced by using new PARDISO-SC sparse direct solver. This paper also presents the performance evaluation of SC computations for three-dimensional elasticity stiffness matrices. We present the performance evaluation of the proposed approach using our implementation in the ESPRESO solver package.