### Abstract

Iterative substructuring methods, also known as Schur complement methods, form an important family of domain decomposition algorithms. They are preconditioned conjugate gradient methods where solvers on local subregions and a solver on a coarse mesh are used to construct the preconditioner. For conforming finite element approximations of H^{1}, it is known that the number of conjugate gradient steps required to reduce the residual norm by a fixed factor is independent of the number of substructures, and that it grows only as the logarithm of the dimension of the local problem associated with an individual substructure. In this paper, the same result is established for similar iterative methods for low-order Nédélec finite elements, which approximate H(curl; Ω) in two dimensions. Results of numerical experiments are also provided.

Original language | English (US) |
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Pages (from-to) | 935-949 |

Number of pages | 15 |

Journal | Mathematics of Computation |

Volume | 70 |

Issue number | 235 |

DOIs | |

State | Published - Jul 1 2001 |

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### Keywords

- Domain decomposition
- Iterative substructuring methods
- Maxwell's equations
- Nédélec finite elements

### ASJC Scopus subject areas

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics

### Cite this

*Mathematics of Computation*,

*70*(235), 935-949. https://doi.org/10.1090/S0025-5718-00-01244-8