An Augmented Lagrangian Uzawa Iterative Method for Solving Double Saddle-Point Systems with Semidefinite (2,2) Block and Its Application to DLM/FD Method for Elliptic Interface Problems
Document Type
Article
Publication Date
4-1-2021
Publication Title
Communications in Computational Physics
Volume
30
First page number:
124
Last page number:
143
Abstract
In this paper, an augmented Lagrangian Uzawa iterative method is developed and analyzed for solving a class of double saddle-point systems with semidefinite (2,2) block. Convergence of the iterative method is proved under the assumption that the double saddle-point problem exists a unique solution. An application of the iterative method to the double saddle-point systems arising from the distributed Lagrange multiplier/fictitious domain (DLM/FD) finite element method for solving elliptic interface problems is also presented, in which the existence and uniqueness of the double saddle-point system is guaranteed by the analysis of the DLM/FD finite element method. Numerical experiments are conducted to validate the theoretical results and to study the performance of the proposed iterative method.
Keywords
Double saddle-point problem; Augmented Lagrangian Uzawa method; Elliptic interface problem; Distributed Lagrange multiplier/Fictitious domain (DLM/FD) Method
Disciplines
Mathematics
Language
English
Repository Citation
Wang, C.,
Sun, P.
(2021).
An Augmented Lagrangian Uzawa Iterative Method for Solving Double Saddle-Point Systems with Semidefinite (2,2) Block and Its Application to DLM/FD Method for Elliptic Interface Problems.
Communications in Computational Physics, 30
124-143.
http://dx.doi.org/10.4208/cicp.OA-2020-0084