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Volume 13, Issue 2
Additive Schwarz Preconditioners with Minimal Overlap for Triangular Spectral Elements

Yuen-Yick Kwan

Commun. Comput. Phys., 13 (2013), pp. 411-427.

Published online: 2013-02

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  • Abstract

The additive Schwarz preconditioner with minimal overlap is extended to triangular spectral elements (TSEM). The method is a generalization of the corresponding method in tensorial quadrilateral spectral elements (QSEM). The proposed preconditioners are based on partitioning the domain into overlapping subdomains, solving local problems on these subdomains and solving an additional coarse problem associated with the subdomain mesh. The results of numerical experiments show that the proposed preconditioner are robust with respect to the number of elements and are more efficient than the preconditioners with generous overlaps.

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@Article{CiCP-13-411, author = {}, title = {Additive Schwarz Preconditioners with Minimal Overlap for Triangular Spectral Elements}, journal = {Communications in Computational Physics}, year = {2013}, volume = {13}, number = {2}, pages = {411--427}, abstract = {

The additive Schwarz preconditioner with minimal overlap is extended to triangular spectral elements (TSEM). The method is a generalization of the corresponding method in tensorial quadrilateral spectral elements (QSEM). The proposed preconditioners are based on partitioning the domain into overlapping subdomains, solving local problems on these subdomains and solving an additional coarse problem associated with the subdomain mesh. The results of numerical experiments show that the proposed preconditioner are robust with respect to the number of elements and are more efficient than the preconditioners with generous overlaps.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.080711.160212a}, url = {http://global-sci.org/intro/article_detail/cicp/7228.html} }
TY - JOUR T1 - Additive Schwarz Preconditioners with Minimal Overlap for Triangular Spectral Elements JO - Communications in Computational Physics VL - 2 SP - 411 EP - 427 PY - 2013 DA - 2013/02 SN - 13 DO - http://doi.org/10.4208/cicp.080711.160212a UR - https://global-sci.org/intro/article_detail/cicp/7228.html KW - AB -

The additive Schwarz preconditioner with minimal overlap is extended to triangular spectral elements (TSEM). The method is a generalization of the corresponding method in tensorial quadrilateral spectral elements (QSEM). The proposed preconditioners are based on partitioning the domain into overlapping subdomains, solving local problems on these subdomains and solving an additional coarse problem associated with the subdomain mesh. The results of numerical experiments show that the proposed preconditioner are robust with respect to the number of elements and are more efficient than the preconditioners with generous overlaps.

Yuen-Yick Kwan. (2020). Additive Schwarz Preconditioners with Minimal Overlap for Triangular Spectral Elements. Communications in Computational Physics. 13 (2). 411-427. doi:10.4208/cicp.080711.160212a
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