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Volume 8, Issue 6
Restricted Additive Schwarz Preconditioner for Elliptic Equations with Jump Coefficients

Zhiyong Liu & Yinnian He

DOI: 10.4208/aamm.2014.m669

Adv. Appl. Math. Mech., 8 (2016), pp. 1072-1083.

Published online: 2018-05

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  • Abstract

This paper provides a proof of robustness of the restricted additive Schwarz preconditioner with harmonic overlap (RASHO) for the second order elliptic problems with jump coefficients. By analyzing the eigenvalue distribution of the RASHO preconditioner, we prove that the convergence rate of preconditioned conjugate gradient method with RASHO preconditioner is uniform with respect to the large jump and mesh size.

  • Keywords

Jump coefficients, conjugate gradient, effective condition number, domain decomposition, restricted additive Schwarz.

  • AMS Subject Headings

65N30, 65N55, 65F10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-8-1072, author = {Liu , Zhiyong and He , Yinnian}, title = {Restricted Additive Schwarz Preconditioner for Elliptic Equations with Jump Coefficients}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {6}, pages = {1072--1083}, abstract = {

This paper provides a proof of robustness of the restricted additive Schwarz preconditioner with harmonic overlap (RASHO) for the second order elliptic problems with jump coefficients. By analyzing the eigenvalue distribution of the RASHO preconditioner, we prove that the convergence rate of preconditioned conjugate gradient method with RASHO preconditioner is uniform with respect to the large jump and mesh size.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m669}, url = {http://global-sci.org/intro/article_detail/aamm/12132.html} }
TY - JOUR T1 - Restricted Additive Schwarz Preconditioner for Elliptic Equations with Jump Coefficients AU - Liu , Zhiyong AU - He , Yinnian JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1072 EP - 1083 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2014.m669 UR - https://global-sci.org/intro/article_detail/aamm/12132.html KW - Jump coefficients, conjugate gradient, effective condition number, domain decomposition, restricted additive Schwarz. AB -

This paper provides a proof of robustness of the restricted additive Schwarz preconditioner with harmonic overlap (RASHO) for the second order elliptic problems with jump coefficients. By analyzing the eigenvalue distribution of the RASHO preconditioner, we prove that the convergence rate of preconditioned conjugate gradient method with RASHO preconditioner is uniform with respect to the large jump and mesh size.

Liu , Zhiyong and He , Yinnian. (2018). Restricted Additive Schwarz Preconditioner for Elliptic Equations with Jump Coefficients. Advances in Applied Mathematics and Mechanics. 8 (6). 1072-1083. doi:10.4208/aamm.2014.m669
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