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A dual substructuring method with a penalty term was introduced in the previous works by the authors, which is a variant of the \fetidp \ method. The proposed method imposes the continuity not only by using Lagrange multipliers but also by adding a penalty term which consists of a positive penalty parameter $\eta$ and a measure of the jump across the interface. Due to the penalty term, the proposed iterative method has a better convergence property than the standard \fetidp \ method in the sense that the condition number of the resulting dual problem is bounded by a constant independent of the subdomain size and the mesh size. In this paper, a further study for a dual iterative substructuring method with a penalty term is discussed in terms of its convergence analysis. We provide an improved estimate of the condition number which shows the relationship between the condition number and $\eta$ as well as a close spectral connection of the proposed method with the \fetidp \ method. As a result, a choice of a moderately small penalty parameter is guaranteed.
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참고문헌 (16)
참고문헌 신청
A. Iserles / 1996 / A First Course in the Numerical Analysis of Differential Equations / Cam-bridge University Press
A. Klawonn / 2002 / Dual-primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients / SIAM J. Numer. Anal 40 (1) : 159 ~ 179
A. Toselli / 2005 / Domain Decomposition Methods?Algorithms and Theory / Springer-Verlag
C. Farhat / 1991 / A method of finite element tearing and interconnecting and its parallel solution algorithm / Internat. J. Numer. Methods Engrg 32 : 1205 ~ 1227
C. Farhat / 2000 / A scalable dual-primal domain decomposition method / Numer. Linear Algebra Appl 7 (7-8) : 687 ~ 714
A. Klawonn / 2002 / Dual-primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients / SIAM J. Numer. Anal 40 (1) : 159 ~ 179
A. Toselli / 2005 / Domain Decomposition Methods?Algorithms and Theory / Springer-Verlag
C. Farhat / 1991 / A method of finite element tearing and interconnecting and its parallel solution algorithm / Internat. J. Numer. Methods Engrg 32 : 1205 ~ 1227
C. Farhat / 2000 / A scalable dual-primal domain decomposition method / Numer. Linear Algebra Appl 7 (7-8) : 687 ~ 714
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