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Volume 8, Issue 3
A Robin-Robin Non-Overlapping Domain Decomposition Method for an Elliptic Boundary Control Problem

L. S. Hou & J. Lee

Int. J. Numer. Anal. Mod., 8 (2011), pp. 443-465.

Published online: 2011-08

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  • Abstract

A Robin-Robin non-overlapping domain decomposition method for an optimal boundary control problem associated with an elliptic boundary value problem is presented. The existence of the whole domain and subdomain optimal solutions is proven. The convergence of the subdomain optimal solutions to the whole domain optimal solution is shown. The optimality system is derived and a gradient-type method is defined for finding the optimal solution. A theoretic convergence result for the gradient method is established. The finite element version of the Robin-Robin non-overlapping domain decomposition method is analyzed and some numerical results by the method on both serial and parallel computers (using MPI) are presented.

  • Keywords

Nonoverlapping domain decomposition method, elliptic boundary control problem, elliptic boundary value problem, MPI.

  • AMS Subject Headings

65N55, 65N30, 65Y10, 35J20, 65K10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-8-443, author = {Hou , L. S. and Lee , J.}, title = {A Robin-Robin Non-Overlapping Domain Decomposition Method for an Elliptic Boundary Control Problem}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {3}, pages = {443--465}, abstract = {

A Robin-Robin non-overlapping domain decomposition method for an optimal boundary control problem associated with an elliptic boundary value problem is presented. The existence of the whole domain and subdomain optimal solutions is proven. The convergence of the subdomain optimal solutions to the whole domain optimal solution is shown. The optimality system is derived and a gradient-type method is defined for finding the optimal solution. A theoretic convergence result for the gradient method is established. The finite element version of the Robin-Robin non-overlapping domain decomposition method is analyzed and some numerical results by the method on both serial and parallel computers (using MPI) are presented.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/695.html} }
TY - JOUR T1 - A Robin-Robin Non-Overlapping Domain Decomposition Method for an Elliptic Boundary Control Problem AU - Hou , L. S. AU - Lee , J. JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 443 EP - 465 PY - 2011 DA - 2011/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/695.html KW - Nonoverlapping domain decomposition method, elliptic boundary control problem, elliptic boundary value problem, MPI. AB -

A Robin-Robin non-overlapping domain decomposition method for an optimal boundary control problem associated with an elliptic boundary value problem is presented. The existence of the whole domain and subdomain optimal solutions is proven. The convergence of the subdomain optimal solutions to the whole domain optimal solution is shown. The optimality system is derived and a gradient-type method is defined for finding the optimal solution. A theoretic convergence result for the gradient method is established. The finite element version of the Robin-Robin non-overlapping domain decomposition method is analyzed and some numerical results by the method on both serial and parallel computers (using MPI) are presented.

Hou , L. S. and Lee , J.. (2011). A Robin-Robin Non-Overlapping Domain Decomposition Method for an Elliptic Boundary Control Problem. International Journal of Numerical Analysis and Modeling. 8 (3). 443-465. doi:
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