EFFICIENT ITERATIVE SOLVERS FOR ELLIPTIC FINITE-ELEMENT PROBLEMS ON NONMATCHING GRIDS
EFFICIENT ITERATIVE SOLVERS FOR ELLIPTIC FINITE-ELEMENT PROBLEMS ON NONMATCHING GRIDS
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DOI：
10.1515/rnam.1995.10.3.187
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发表时间：
1995-01-01
影响因子：
0.6
通讯作者：
KUZNETSOV, YA
中科院分区：
文献类型：
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作者：
KUZNETSOV, YA
研究了椭圆边值问题的非匹配网格有限元离散所产生的鞍点形式的线性代数方程组迭代方法的构造方法。椭圆问题是基于区域分解的宏观混合形式，在子域之间的交界处带有拉格朗日乘子。提出了一种块对角线预处理器，它与原鞍点矩阵在频谱上是等价的，并且具有最优阶的运算复杂度。预处理器包括用于预条件子域和接口问题的块。结果表明，谱等效常数与系数值、网格步长和子域直径无关。
A new approach to the construction of iterative methods for solving systems of linear algebraic equations in the saddle-point form arising from finite element discretizations with nonmatching grids for elliptic boundary value problems is considered. The elliptic problem is presented in the macro-hybrid form based on domain decomposition with Lagrange multipliers at the interfaces between subdomains. A block diagonal preconditioner is proposed which is spectrally equivalent to the original saddle-point matrix and has the optimal order of arithmetical complexity. The preconditioner includes blocks for preconditioning subdomain and interface problems. It is shown that constants of spectral equivalence are independent of values of coefficients, grid step sizes, and diameters of subdomains.