Performance Evaluation of the Parallel ES-SC-ILU-BiCGSTAB Method

This study investigates the effectiveness of the Error vector Sampling Subspace Correction (ES-SC) preconditioning method for asymmetric matrices in a standard multi-threaded parallel computation environment. The ES-SC preconditioning is a technique to accelerate the solution processes for a sequence of linear systems having an identical asymmetric coefficient matrix. In the present study, we develop a multi-threaded BiCGSTAB solver preconditioned by the ILU and ES-SC methods. Because the ILU preconditioning cannot be straightforwardly parallelized, the block Jacobi and multi-color ordering methods are employed for its parallelization. We examine the effect of the ES-SC preconditioning when used with the parallel ILU preconditioner for the BiCGSTAB method from the viewpoints of its convergence and solution time. Numerical results confirm the effectiveness of the ES-SC preconditioning in a parallel computation environment.