A robust two-level overlapping preconditioner for Darcy flow in high-contrast media
arxiv(2024)
摘要
In this article, a two-level overlapping domain decomposition preconditioner
is developed for solving linear algebraic systems obtained from simulating
Darcy flow in high-contrast media. Our preconditioner starts at a mixed finite
element method for discretizing the partial differential equation by Darcy's
law with the no-flux boundary condition and is then followed by a velocity
elimination technique to yield a linear algebraic system with only unknowns of
pressure. Then, our main objective is to design a robust and efficient domain
decomposition preconditioner for this system, which is accomplished by
engineering a multiscale coarse space that is capable of characterizing
high-contrast features of the permeability field. A generalized eigenvalue
problem is solved in each non-overlapping coarse element in a
communication-free manner to form the global solver, which is accompanied by
local solvers originated from additive Schwarz methods but with a non-Galerkin
discretization to derive the two-level preconditioner. We provide a rigorous
analysis that indicates that the condition number of the preconditioned system
could be bounded above with several assumptions. Extensive numerical
experiments with various types of three-dimensional high-contrast models are
exhibited. In particular, we study the robustness against the contrast of the
media as well as the influences of numbers of eigenfunctions, oversampling
sizes, and subdomain partitions on the efficiency of the proposed
preconditioner. Besides, strong and weak scalability performances are also
examined.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要