A2ILU: Auto-accelerated ILU Preconditioner for Sparse Linear Systems

Abstract

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 A2ILU. In order to improve the convergence, A2ILU introduces acceleration parameters which modify the ILU factorized preconditioning matrix. A$^2$ILU needs no more operations than the original ILU because the acceleration parameters are optimized automatically by A2ILU itself. Numerical tests reveal the performance of A2ILU is superior to previous ILU-based methods with manually optimized parameters. The numerical tests also demonstrate the ability to apply auto-acceleration to ILU-based methods to improve their performances and robustness of parameter sensitivities.