ADIF迭代法及其有关问题

§1.引言 本文将考虑二维自共轭二阶椭圆型方程边值问题:其中Ω为有界开域;在闭域Ω上系数P,Q和f Lipschitz连续并有P,Q>0,(x,y)∈Ω。用有限差分法或有限元方法求其数值解,通常导致如下稀疏正定矩阵的线性代数方程组的求解问题:

ON ADIF METHOD AND ITS RELATED PROBLEMS

The Alternating-Direction Incomplete Factorization Method is known as a new ef-ficient method for solving the discrete elliptic problems. But its theoretical analysishas not been completed. In the present paper we study the asymptotic properties ofthis method for the model problem. Several asymptotic estimates obtained are impor-tant for a better understanding of this method. A locally-optimized multi-parametermethod with numerical evidences is included.