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A posteriori error analysis for Schwarz overlapping domain decomposition methods

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Abstract

Domain decomposition methods are widely used for the numerical solution of partial differential equations on high performance computers. We develop an adjoint-based a posteriori error analysis for both multiplicative and additive overlapping Schwarz domain decomposition methods. The numerical error in a user-specified functional of the solution (quantity of interest) is decomposed into contributions that arise as a result of the finite iteration between the subdomains and from the spatial discretization. The spatial discretization contribution is further decomposed into contributions arising from each subdomain. This decomposition of the numerical error is used to construct a two stage solution strategy that efficiently reduces the error in the quantity of interest by adjusting the relative contributions to the error.

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Acknowledgements

J. Chaudhry’s work is supported by the NSF-DMS 1720402. S. Tavener’s work is supported by NSF-DMS 1720473. D. Estep’s work is supported by NSF-DMS 1720473.

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Authors and Affiliations

  1. The University of New Mexico, Albuquerque, NM, 87131, USA

    Jehanzeb H. Chaudhry

  2. Simon Fraser University, Burnaby, BC, V5A 1S6, Canada

    Donald Estep

  3. Colorado State University, Fort Collins, CO, 80523, USA

    Simon J. Tavener

Authors
  1. Jehanzeb H. Chaudhry
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  2. Donald Estep
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  3. Simon J. Tavener
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Correspondence to Simon J. Tavener.

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Communicated by Axel Målqvist.

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Chaudhry, J.H., Estep, D. & Tavener, S.J. A posteriori error analysis for Schwarz overlapping domain decomposition methods. Bit Numer Math 61, 1153–1191 (2021). https://doi.org/10.1007/s10543-021-00864-1

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