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

Additive Schwarz Preconditioners with Minimal Overlap for Triangular Spectral Elements

Yuen-Yick Kwan 1*

1 Center for Computational Science, Tulane University, New Orleans, LA 70118, USA.

Received 8 July 2011; Accepted (in revised version) 16 February 2012
Available online 28 June 2012


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.

AMS subject classifications: 65F08, 65N35

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Key words: Spectral elements, additive Schwarz.

*Corresponding author.
Email: (Y.-Y. Kwan)

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