### Abstract

Dual-primal FETI methods are nonoverlapping domain decomposition methods where some of the continuity constraints across subdomain boundaries are required to hold throughout the iterations, as in primal iterative substructuring methods, while most of the constraints are enforced by Lagrange multipliers, as in one-level FETI methods. These methods are used to solve the large algebraic systems of equations that arise in elliptic finite element problems. The purpose of this article is to develop strategies for selecting these constraints, which are enforced throughout the iterations, such that good convergence bounds are obtained that are independent of even large changes in the stiffness of the subdomains across the interface between them. The algorithms are described in terms of a change of basis that has proven to be quite robust in practice. A theoretical analysis is provided for the case of linear elasticity, and condition number bounds are established that are uniform with respect to arbitrarily large jumps in the Young's modulus of the material and otherwise depend only polylogarithmically on the number of unknowns of a single subdomain. The strategies have already proven quite successful in large-scale implementations of these iterative methods.

Original language | English (US) |
---|---|

Pages (from-to) | 1523-1572 |

Number of pages | 50 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 59 |

Issue number | 11 |

DOIs | |

State | Published - Nov 2006 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*59*(11), 1523-1572. https://doi.org/10.1002/cpa.20156

**Dual-primal FETI methods for linear elasticity.** / Klawonn, Axel; Widlund, Olof B.

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 59, no. 11, pp. 1523-1572. https://doi.org/10.1002/cpa.20156

}

TY - JOUR

T1 - Dual-primal FETI methods for linear elasticity

AU - Klawonn, Axel

AU - Widlund, Olof B.

PY - 2006/11

Y1 - 2006/11

N2 - Dual-primal FETI methods are nonoverlapping domain decomposition methods where some of the continuity constraints across subdomain boundaries are required to hold throughout the iterations, as in primal iterative substructuring methods, while most of the constraints are enforced by Lagrange multipliers, as in one-level FETI methods. These methods are used to solve the large algebraic systems of equations that arise in elliptic finite element problems. The purpose of this article is to develop strategies for selecting these constraints, which are enforced throughout the iterations, such that good convergence bounds are obtained that are independent of even large changes in the stiffness of the subdomains across the interface between them. The algorithms are described in terms of a change of basis that has proven to be quite robust in practice. A theoretical analysis is provided for the case of linear elasticity, and condition number bounds are established that are uniform with respect to arbitrarily large jumps in the Young's modulus of the material and otherwise depend only polylogarithmically on the number of unknowns of a single subdomain. The strategies have already proven quite successful in large-scale implementations of these iterative methods.

AB - Dual-primal FETI methods are nonoverlapping domain decomposition methods where some of the continuity constraints across subdomain boundaries are required to hold throughout the iterations, as in primal iterative substructuring methods, while most of the constraints are enforced by Lagrange multipliers, as in one-level FETI methods. These methods are used to solve the large algebraic systems of equations that arise in elliptic finite element problems. The purpose of this article is to develop strategies for selecting these constraints, which are enforced throughout the iterations, such that good convergence bounds are obtained that are independent of even large changes in the stiffness of the subdomains across the interface between them. The algorithms are described in terms of a change of basis that has proven to be quite robust in practice. A theoretical analysis is provided for the case of linear elasticity, and condition number bounds are established that are uniform with respect to arbitrarily large jumps in the Young's modulus of the material and otherwise depend only polylogarithmically on the number of unknowns of a single subdomain. The strategies have already proven quite successful in large-scale implementations of these iterative methods.

UR - http://www.scopus.com/inward/record.url?scp=33749368945&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33749368945&partnerID=8YFLogxK

U2 - 10.1002/cpa.20156

DO - 10.1002/cpa.20156

M3 - Article

VL - 59

SP - 1523

EP - 1572

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 11

ER -