求解波导问题FEM线性系统的RIC预条件算法

RIC Preconditioning Algorithm for Solving Waveguide Problem FEM Linear System

摘要:

提出了一种新型RIC预条件COCG迭代技术，用于改善有限元法仿真分析光电工程问题所产生的高度非正定的线性系统的迭代求解。提出的RIC预条件子是针对基本IC算法可能出现的分解崩溃问题，通过对主元进行加强来获得稳定的分解过程，进而产生高效的预条件子。数值试验表明，提出的RIC预条件子不仅能有效避免COCG迭代等方性崩溃，而且比常用的预条件子更高效；此外，RIC对其他若干Krylov子空间迭代法求解性能的改善作用也相当明显。

Abstract:

A new RIC preconditioned conjugate orthogonal conjugate gradient(COCG) iterative method is presented for solving the highly indefinite linear equations, which is arised from the finite element method(FEM) for analyzing optical and electrical engineering problems. The proposed RIC preconditioner is based on the basic IC algorithm and aiming at solving the breakdowns during the factorizing process. By adding compensation to the pivots, RIC process can be more stable thus generating the more effective preconditioner. Numerical examples show that, the proposed RIC preconditioner can not only avoid the isotropic breakdown of COCG, but also can be more effective than other typical ones; moreover, RIC can dramatically improve the performance of several other Krylov subspace iterative methods.