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

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 a...

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Published in:International journal for numerical methods in engineering 2022-10, Vol.123 (20), p.4844-4858
Main Author: Sousedík, Bedřich
Format: Article
Language:English
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BDDC
domain decomposition
FETI‐DP
Multilevel
multilevel methods
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description 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.
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subjects BDDC
domain decomposition
FETI‐DP
Multilevel
multilevel methods
title Inexact and primal multilevel FETI‐DP methods: a multilevel extension and interplay with BDDC
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