*Article* **Investigation of High-E**ffi**ciency Iterative ILU Preconditioner Algorithm for Partial-Di**ff**erential Equation Systems**

**Yan-Hong Fan <sup>1</sup> , Ling-Hui Wang 1,\*, You Jia 1, Xing-Guo Li 1, Xue-Xia Yang <sup>1</sup> and Chih-Cheng Chen 2,\***


Received: 14 October 2019; Accepted: 21 November 2019; Published: 28 November 2019

**Abstract:** In this paper, we investigate an iterative incomplete lower and upper (ILU) factorization preconditioner for partial-differential equation systems. We discretize the partial-differential equations into linear equation systems. An iterative scheme of linear systems is used. The ILU preconditioners of linear systems are performed on the different computation nodes of multi-central processing unit (CPU) cores. Firstly, the preconditioner of general tridiagonal matrix equations is tested on supercomputers. Then, the effects of partial-differential equation systems on the speedup of parallel multiprocessors are examined. The numerical results estimate that the parallel efficiency is higher than in other algorithms.

**Keywords:** iterative ILU; preconditioner; partial-differential equations; parallel computation
