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Volume 30, Issue 1
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

Cheng Wang & Pengtao Sun

DOI: 10.4208/cicp.OA-2020-0084

Commun. Comput. Phys., 30 (2021), pp. 124-143.

Published online: 2021-04

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  • 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.

  • AMS Subject Headings

65F10, 65F50, 65N30, 65N85

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-30-124, author = {Wang , Cheng and Sun , Pengtao}, title = {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}, journal = {Communications in Computational Physics}, year = {2021}, volume = {30}, number = {1}, pages = {124--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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0084}, url = {http://global-sci.org/intro/article_detail/cicp/18876.html} }
TY - JOUR T1 - 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 AU - Wang , Cheng AU - Sun , Pengtao JO - Communications in Computational Physics VL - 1 SP - 124 EP - 143 PY - 2021 DA - 2021/04 SN - 30 DO - http://doi.org/10.4208/cicp.OA-2020-0084 UR - https://global-sci.org/intro/article_detail/cicp/18876.html KW - Double saddle-point problem, augmented Lagrangian Uzawa method, elliptic interface problem, distributed Lagrange multiplier/fictitious domain (DLM/FD) method. AB -

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.

Cheng Wang & Pengtao Sun. (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 (1). 124-143. doi:10.4208/cicp.OA-2020-0084
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