On multipoint constraints in FETI methods

Pavla Hrušková; Zdeněk Dostál; Oldřich Vlach; Petr Vodstrčil

Applications of Mathematics (2025)

  • Issue: 1, page 47-64
  • ISSN: 0862-7940

Abstract

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FETI (finite element tearing and interconnecting) based domain decomposition methods are well-established massively parallel methods for solving huge linear systems arising from discretizing partial differential equations. The first steps of FETI decompose the domain into nonoverlapping subdomains, discretize the subdomains using matching grids, and interconnect the adjacent variables by multipoint constraints. However, the multipoint constraints enforcing identification of the corners' variables do not have a unique representation and their proper choice and modification can improve the performance of FETI. Here, we briefly review the main options, including orthogonal, fully redundant, or localized constraints, and use the basic linear algebra and spectral graph theory to examine the quantitative effect of their choice on the effective control of the feasibility error and rate of convergence of FETI.

How to cite

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Hrušková, Pavla, et al. "On multipoint constraints in FETI methods." Applications of Mathematics (2025): 47-64. <http://eudml.org/doc/299926>.

@article{Hrušková2025,
abstract = {FETI (finite element tearing and interconnecting) based domain decomposition methods are well-established massively parallel methods for solving huge linear systems arising from discretizing partial differential equations. The first steps of FETI decompose the domain into nonoverlapping subdomains, discretize the subdomains using matching grids, and interconnect the adjacent variables by multipoint constraints. However, the multipoint constraints enforcing identification of the corners' variables do not have a unique representation and their proper choice and modification can improve the performance of FETI. Here, we briefly review the main options, including orthogonal, fully redundant, or localized constraints, and use the basic linear algebra and spectral graph theory to examine the quantitative effect of their choice on the effective control of the feasibility error and rate of convergence of FETI.},
author = {Hrušková, Pavla, Dostál, Zdeněk, Vlach, Oldřich, Vodstrčil, Petr},
journal = {Applications of Mathematics},
keywords = {domain decomposition; multipoint constraint; redundant multiplier},
language = {eng},
number = {1},
pages = {47-64},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On multipoint constraints in FETI methods},
url = {http://eudml.org/doc/299926},
year = {2025},
}

TY - JOUR
AU - Hrušková, Pavla
AU - Dostál, Zdeněk
AU - Vlach, Oldřich
AU - Vodstrčil, Petr
TI - On multipoint constraints in FETI methods
JO - Applications of Mathematics
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 47
EP - 64
AB - FETI (finite element tearing and interconnecting) based domain decomposition methods are well-established massively parallel methods for solving huge linear systems arising from discretizing partial differential equations. The first steps of FETI decompose the domain into nonoverlapping subdomains, discretize the subdomains using matching grids, and interconnect the adjacent variables by multipoint constraints. However, the multipoint constraints enforcing identification of the corners' variables do not have a unique representation and their proper choice and modification can improve the performance of FETI. Here, we briefly review the main options, including orthogonal, fully redundant, or localized constraints, and use the basic linear algebra and spectral graph theory to examine the quantitative effect of their choice on the effective control of the feasibility error and rate of convergence of FETI.
LA - eng
KW - domain decomposition; multipoint constraint; redundant multiplier
UR - http://eudml.org/doc/299926
ER -

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