论文标题
用$ \ mathcal {h} $ - 矩阵近似于非均匀网格上的逆FEM矩阵 - 矩阵
Approximating inverse FEM matrices on non-uniform meshes with $\mathcal{H}$-matrices
论文作者
论文摘要
我们考虑数据稀疏$ \ MATHCAL {H} $ - 矩阵格式中有限元刚度矩阵的倒数的近似值。对于一大批形状的常规但可能是不均匀的网格，包括分级网格，我们证明刚度矩阵的倒数可以在$ \ nathcal {h} $ - 矩阵格式中以块等级的指数速率近似。由于层次矩阵的存储复杂性是对数线性的，并且仅在块级中线性增长，因此我们获得了可以使用的有效近似值，例如，作为迭代求解器的近似直接求解器或预处理。
We consider the approximation of the inverse of the finite element stiffness matrix in the data sparse $\mathcal{H}$-matrix format. For a large class of shape regular but possibly non-uniform meshes including graded meshes, we prove that the inverse of the stiffness matrix can be approximated in the $\mathcal{H}$-matrix format at an exponential rate in the block rank. Since the storage complexity of the hierarchical matrix is logarithmic-linear and only grows linearly in the block-rank, we obtain an efficient approximation that can be used, e.g., as an approximate direct solver or preconditioner for iterative solvers.
