Inexact and primal multilevel FETI-DP methods: a multilevel extension and interplay with BDDC

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https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.7057

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https://doi.org/10.1002/nme.7057
 http://hdl.handle.net/11603/25145

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UMBC Mathematics and Statistics Department
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https://orcid.org/0000-0002-8053-8956

Date

2022-06-07

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journal articles
preprints
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Citation of Original Publication

Sousedík, B. Inexact and primal multilevel FETI-DP methods: a multilevel extension and interplay with BDDC. Int J Numer Methods Eng. 2022; 1- 15. doi:10.1002/nme.7057

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This is the pre-peer reviewed version of the following article: Sousedík, B. Inexact and primal multilevel FETI-DP methods: a multilevel extension and interplay with BDDC. Int J Numer Methods Eng. 2022; 1- 15. doi:10.1002/nme.7057, which has been published in final form at https://doi.org/10.1002/nme.7057. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions

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Abstract

We study a framework that allows to solve the coarse problem in the FETI-DP method approximately. It is based on the saddle-point formulation of the FETI-DP system with a block-triangular preconditioner. One of the blocks approximates the coarse problem, for which we use the multilevel BDDC method as the main tool. This strategy then naturally leads to a version of multilevel FETI-DP method, and we show that the spectra of the multilevel FETI-DP and BDDC preconditioned operators are essentially the same. The theory is illustrated by a set of numerical experiments, and we also present a few experiments when the coarse solve is approximated by algebraic multigrid.