中文摘要：

基于六面体的高阶叠层基函数,提出了一种新颖的构造预条件矩阵的方法.该方法基于叠层基函数特有的嵌套性质,利用特殊的编号策略,将由有限元方法导致的系数矩阵分成块矩阵的形式,最后由不完全LU分解（ILU）导出近似的预条件矩阵.结合该预条件技术,发展了一种叠层预条件-GMRES算法,并将该预条件算法用于加速三维腔体散射的矢量有限元/边界积分（FE-BI）矩阵方程的迭代求解,讨论了该预条件算法中块矩阵ILU分解截断门限Tdr对算法的影响.

英文摘要：

A preeonditioner is proposed for accelerating solutions of finite element matrix equations. The precondifioner is constructed from a sequence of hierarchical vector spaces spanned by higher order hexahedral basis functions. The preconditioned GMRES algorithm with the precondtioner presented is developed and applied to solve the vector finite element-boundary integral （FE-BI） matrix equations for simulation of scattering from three-dimensional cavities. Numerical results show that the preconditioner for solving the FE-BI systems exhibits superior efficiency and reduced the CPU time significantly.