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 - <p style="text-align: justify;">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.</p>