Convergence Analysis of a Non-overlapping DDM for Optimal Absorbing Boundary Control Problems Governed by Wave Equations
Keying Ma *
School of Mathematics, Shandong University, Jinan 250100, P.R. China.
Wenyue Liu
School of Mathematics, Shandong University, Jinan 250100, P.R. China.
*Author to whom correspondence should be addressed.
Abstract
A non-overlapping domain decomposition method (DDM) is described to solve optimal boundary control problems governed by wave equations with absorbing boundary condition. The whole domain is divided into non-overlapping subdomains, and the global optimal boundary control problem is decomposed into local problems in these subdomains. An integral mean method is utilized to present an explicit flux calculation on the inter-domain boundary in order to communicate the local problems on the interfaces between subdomains. We establish the full parallel and discrete schemes for solving these local problems, and prove the stability of the schemes. A priori error estimates in suitable natural norms are derived for the state, co-state and control variables.
Keywords: Wave equations, optimal absorbing boundary control problems, non-overlapping DDM, integral mean method, error estimates.