A2ILU: Auto-accelerated ILU Preconditioner for Sparse Linear Systems

The ILU-based preconditioning methods in previous work have their own parameters to improve their performances. Although the parameters may degrade the performance, their determination is left to users. Thus, these previous methods are not reliable in practical computer-aided engineering use. This paper proposes a novel ILU-based preconditioner called the auto-accelerated ILU, or AILU. In order to improve the convergence, AILU introduces acceleration parameters which modify the ILU factorized preconditioning matrix. AILU needs no more operations than the original ILU because the acceleration parameters are optimized automatically by AILU itself. Numerical tests reveal the performance of AILU is superior to previous ILU-based methods with manually optimized parameters. The numerical tests also demonstrate the ability to apply autoacceleration to ILU-based methods to improve their performances and robustness of parameter sensitivities.