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Volume 8, Issue 1
Inexact Solvers for Saddle-Point System Arising from Domain Decomposition of Linear Elasticity Problems in Three Dimensions

X. Chen & Q. Hu

Int. J. Numer. Anal. Mod., 8 (2011), pp. 156-173.

Published online: 2011-08

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  • Abstract

In this paper, we propose a domain decomposition method with Lagrange multipliers for three-dimensional linear elasticity, based on geometrically non-conforming subdomain partitions. Some appropriate multiplier spaces are presented to deal with the geometrically non-conforming partitions, resulting in a discrete saddle-point system. An augmented technique is introduced, such that the resulting new saddle-point system can be solved by the existing iterative methods. Two simple inexact preconditioners are constructed for the saddle-point system, one for the displacement variable, and the other for the Schur complement associated with the multiplier variable. It is shown that the global preconditioned system has a nearly optimal condition number, which is independent of the large variations of the material parameters across the local interfaces.

  • Keywords

Domain decomposition, geometrically non-conforming, Lagrange multiplier, saddle-point system, preconditioners, condition number.

  • AMS Subject Headings

65F10, 65N30, 65N55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-8-156, author = {X. Chen and Q. Hu}, title = {Inexact Solvers for Saddle-Point System Arising from Domain Decomposition of Linear Elasticity Problems in Three Dimensions}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {1}, pages = {156--173}, abstract = {

In this paper, we propose a domain decomposition method with Lagrange multipliers for three-dimensional linear elasticity, based on geometrically non-conforming subdomain partitions. Some appropriate multiplier spaces are presented to deal with the geometrically non-conforming partitions, resulting in a discrete saddle-point system. An augmented technique is introduced, such that the resulting new saddle-point system can be solved by the existing iterative methods. Two simple inexact preconditioners are constructed for the saddle-point system, one for the displacement variable, and the other for the Schur complement associated with the multiplier variable. It is shown that the global preconditioned system has a nearly optimal condition number, which is independent of the large variations of the material parameters across the local interfaces.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/679.html} }
TY - JOUR T1 - Inexact Solvers for Saddle-Point System Arising from Domain Decomposition of Linear Elasticity Problems in Three Dimensions AU - X. Chen & Q. Hu JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 156 EP - 173 PY - 2011 DA - 2011/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/679.html KW - Domain decomposition, geometrically non-conforming, Lagrange multiplier, saddle-point system, preconditioners, condition number. AB -

In this paper, we propose a domain decomposition method with Lagrange multipliers for three-dimensional linear elasticity, based on geometrically non-conforming subdomain partitions. Some appropriate multiplier spaces are presented to deal with the geometrically non-conforming partitions, resulting in a discrete saddle-point system. An augmented technique is introduced, such that the resulting new saddle-point system can be solved by the existing iterative methods. Two simple inexact preconditioners are constructed for the saddle-point system, one for the displacement variable, and the other for the Schur complement associated with the multiplier variable. It is shown that the global preconditioned system has a nearly optimal condition number, which is independent of the large variations of the material parameters across the local interfaces.

X. Chen and Q. Hu. (2011). Inexact Solvers for Saddle-Point System Arising from Domain Decomposition of Linear Elasticity Problems in Three Dimensions. International Journal of Numerical Analysis and Modeling. 8 (1). 156-173. doi:
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