FSAI preconditioned CG algorithm combined with GPU technique for the finite element analysis of electromagnetic scattering problems

In order to efficiently solve the large sparse complex linear system arising from the vector finite element method (vector FEM) in electromagnetic scattering problems, the factorized sparse approximate inverse (FSAI) algorithm and the programmable graphics processing unit (GPU) are employed in the context of the conjugate gradient (CG) iterative method. The combination of the FSAI with the GPU technique has two advantages. Firstly, the convergence rate of the CG algorithm is significantly accelerated. Secondly, the calculation of the sparse matrix vector product (SMVP) in the FSAI preconditioned CG algorithm is accelerated by harnessing the tremendous parallel processing capacity of the GPU. Numerical experiments indicate that the FSAI preconditioned CG algorithm enhanced by the GPU technique is very effective and can reduce both the number of iterations and the computational time significantly.