Convergence analysis of optimization-based domain decomposition methods for a bonded structure

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• 作者：Jonas Koko
• 关键词：Domain decomposition ; Bonded structure ; Steklov– ; Poincaré ; operator ; Conjugate gradient
• 刊名：Applied Numerical Mathematics
• 出版年：2008
• 期刊代码：8_01689274
• 类别：cp
• 出版时间：January 2008
• 卷：58
• 期：1
• 页码：69-87
• 文件大小：327 K

摘要

We study two optimization-based domain decomposition methods for a bonded structure: the least squares conjugate gradient method and the Uzawa conjugate gradient method. Using the Steklov–Poincaré operator, we show that both methods solve the same underlying linear equation with a symmetric and coercive operator. The convergence analysis is developed using the properties of the trace operator associated to the coupled problem. Numerical experiments show that the Lagrange multiplier approach is more efficient unless a suitable norm is used in the least squares formulation.