| Issue |
ESAIM: M2AN
Volume 60, Number 2, March-April 2026
|
|
|---|---|---|
| Page(s) | 981 - 1019 | |
| DOI | https://doi.org/10.1051/m2an/2026024 | |
| Published online | 17 April 2026 | |
Convergence analysis of a balancing domain decomposition method for an elliptic optimal control problem with HDG discretizations
1
Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA, USA
2
Department of Mathematics, The Ohio State University, Columbus, OH, USA
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
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Received:
19
August
2025
Accepted:
23
February
2026
Abstract
In this work, a balancing domain decomposition by constraints (BDDC) algorithm is applied to the nonsymmetric positive definite linear system arising from the hybridizable discontinuous Galerkin (HDG) discretization of an elliptic distributed optimal control problem. Convergence analysis for the BDDC preconditioned generalized minimal residual (GMRES) solver demonstrates that, when the subdomain size is small enough, the algorithm is robust with respect to the regularization parameter, and the number of iterations is independent of the number of subdomains and depends only slightly on the subdomain problem size. Numerical experiments are performed to confirm the theoretical results.
Mathematics Subject Classification: 49J20 / 49M41 / 65N30 / 65N55
© The authors. Published by EDP Sciences, SMAI 2026
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