Overlapping Schwarz Methods for Isogeometric Analysis

@article{Veiga2012OverlappingSM,
  title={Overlapping Schwarz Methods for Isogeometric Analysis},
  author={Lourenço Beir{\~a}o da Veiga and Durkbin Cho and Luca F. Pavarino and Simone Scacchi},
  journal={SIAM J. Numer. Anal.},
  year={2012},
  volume={50},
  pages={1394-1416}
}
We construct and analyze an overlapping Schwarz preconditioner for elliptic problems discretized with isogeometric analysis. The preconditioner is based on partitioning the domain of the problem into overlapping subdomains, solving local isogeometric problems on these subdomains, and solving an additional coarse isogeometric problem associated with the subdomain mesh. We develop an $h$-analysis of the preconditioner, showing in particular that the resulting algorithm is scalable and its… 

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