【摘要】 <正> ξ1.引言本文考虑对不同介质交接面问题作有限元离散后所得的大型稀疏矩阵问题的求解.为便于讨论,仅考虑两种常介质ρ₁、ρ₂的交接线问题,设其有限元离散方程为A（η）U=F.（1.1）其中U和F为N维向量,η=ρ₂/ρ₁,为介质比,A（η）为与η有关的N×N稀疏矩阵,且A的条件数Cond（A）=∥A∥·∥A^-1∥随η趋于零而无限增大. 在η很小时,因A的条件数太大引起（1.1）严重病态,使得通常的直接法(如Gauss更多还原

【Abstract】 In this paper, an new multigrid algorithm—MG-BGS iteration for solving the algebraic equation which arises from the finite element approximation of interface problems with small media ratio is presented and analysed. As an important development of MG-BGS iteration, we finally obtain another algorithm for the same problems—MG-IBGS iteration whose work estimation is proportional to the number of unknowns.更多还原