Approximate Inverse Preconditioning of Finite Element Discretizations of Elliptic Operators with Nonsmooth Coefficients
Approximate Inverse Preconditioning of Finite Element Discretizations of Elliptic Operators with Nonsmooth Coefficients
复制标题
非光滑系数椭圆算子有限元离散的近似逆预处理
DOI：
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发表时间：
2005
影响因子：
1.5
通讯作者：
M. Bebendorf
中科院分区：
文献类型：
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作者：
M. Bebendorf
针对由二阶椭圆型偏微分算子引起的大型有限元刚度矩阵，提出了一类新的近似逆预条件子，它保证了条件数的有界性和问题无关性.由于所提出的预条件是基于层次矩阵，它可以生成，存储，并乘以一个向量几乎线性复杂度。该预条件子可用作黑箱方法，因为它对变系数是鲁棒的，并且因为它可应用于任意准均匀网格。
A new class of approximate inverse preconditioners for large finite element stiffness matrices arising from second order elliptic partial differential operators is introduced which guarantees a bounded, problem-independent condition number. Since the proposed preconditioner is based on hierarchical matrices, it can be generated, stored, and multiplied by a vector with almost linear complexity. This preconditioner may be used as a black-box method, because it is robust with respect to varying coefficients and because it can be applied to arbitrary quasi-uniform grids.