【摘要】 提出了一种MAINV稀疏近似逆预条件算法,用于改善电磁场边值问题的有限元分析所产生的的线性系统的迭代求解。该预条件子是在基本AINV算法基础上,在分解过程中对可能导致算法崩溃的极小主元进行实时补偿,从而获得高质量的预条件子。数值结果表明,MAINV预条件子对SQMR以及若干经典迭代法的加速效果十分明显;此外,与其他常规预条件子相比较,MAINV具有更好的求解性能。更多还原

【Abstract】 A new modified sparse approximate inverse preconditioning algorithm,MAINV,is proposed to improve the iterative solution of the linear system which is arised from the finite element method for analyzing the electromagnetic boundary problem.The proposed preconditioner is constructed by adding pivots compensation strategy to the very small pivots which may cause breakdowns during the basic AINV process.Therefore the high quality preconditioner can be achieved.Numerical examples show that the MAINV can dramatically accelerate the iteration of SQMR and other typical iterative methods.Moreover,MAINV is proved to achieve better performance by comparison with some standard preconditioners.更多还原