A rigorous condition number estimate of an immersed finite element method
A rigorous condition number estimate of an immersed finite element method
复制标题
浸入有限元法的严格条件数估计
DOI：
10.1007/s10915-020-01212-1
复制
发表时间：
2020
影响因子：
2.5
通讯作者：
Xu Xuejun
中科院分区：
文献类型：
--
作者：
Wang Saihua;Wang Feng;Xu Xuejun
众所周知，共轭梯度法等传统迭代方法的收敛速度取决于刚度矩阵的条件数。此外，诸如多重网格和域分解方法之类的快速求解器的构造也需要估计刚度矩阵的条件数。本文的主要目的是对高对比度界面问题的线性和双线性浸入式有限元近似产生的刚度矩阵进行严格的条件数估计。结果表明，条件数为C.h -2，其中。是不连续系数的跳跃，h是网格尺寸，与常数C无关。以及三角测量中界面的位置。还给出了数值结果来验证我们的理论发现。
It is known that the convergence rate of the traditional iteration methods like the conjugate gradient method depends on the condition number of the stiffness matrix. Moreover the construction of fast solvers like multigrid and domain decomposition methods also need to estimate the condition number of the stiffness matrix. The main purpose of this paper is to give a rigorous condition number estimate of the stiffness matrix resulting from the linear and bilinear immersed finite element approximations of the high-contrast interface problem. It is shown that the condition number is C.h -2, where. is the jump of the discontinuous coefficients, h is the mesh size, and the constant C is independent of. and the location of the interface on the triangulation. Numerical results are also given to verify our theoretical findings.