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.
Highlights
In applied sciences, such as computational electromagnetics, the solving of partial-differential equation systems is usually touched upon
For testing the new algorithm, some results on the Inspur TS10000 cluster have been given by the new algorithm and order 2 multi-splitting algorithm [2], which is a well-known parallel iterative algorithm
Regardless of the number of processors, the speedup values obtained using the BSOR method, the parameter k (PEk) method, and the multi-splitting algorithm (MPA) algorithm are close, those obtained with the BSOR method and the Figure 2 shows the parallel efficiency performance of the incomplete lower and upper factorization preconditioner (ILUP) algorithm and the other three methods for Example 1 at different central processing unit (CPU) cores
Summary
In applied sciences, such as computational electromagnetics, the solving of partial-differential equation systems is usually touched upon. Many variables need to be sought for solving engineering problems These often need to be transformed into a solution of partial differential equations. Sameh [1] contributed a spike algorithm as a parallel solution to hybrid banded equations. Methods for block-tridiagonal linear equations contain iterative algorithms such as the multi-splitting algorithm [2,3]. The multi-splitting algorithm (MPA) [2] can be used to solve large band linear systems of equations; it sometimes has lower parallel efficiency. In [6], a parallel direct algorithm is used on multi-computers. In [7], a parallel direct method for large banded equations is presented
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