### 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) |
---|---|

Pages (from-to) | 935-949 |

Number of pages | 15 |

Journal | Mathematics of Computation |

Volume | 70 |

Issue number | 235 |

DOIs | |

State | Published - Jul 2001 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory
- Applied Mathematics
- Computational Mathematics

### Cite this

*Mathematics of Computation*,

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

**An iterative substructuring method for maxwell's equations in two dimensions.** / Toselli, Andrea; Widlund, Olof B.; Wohlmuth, Barbara I.

Research output: Contribution to journal › Article

*Mathematics of Computation*, vol. 70, no. 235, pp. 935-949. https://doi.org/10.1090/S0025-5718-00-01244-8

}

TY - JOUR

T1 - An iterative substructuring method for maxwell's equations in two dimensions

AU - Toselli, Andrea

AU - Widlund, Olof B.

AU - Wohlmuth, Barbara I.

PY - 2001/7

Y1 - 2001/7

N2 - 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 H1, 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.

AB - 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 H1, 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.

KW - Domain decomposition

KW - Iterative substructuring methods

KW - Maxwell's equations

KW - Nédélec finite elements

UR - http://www.scopus.com/inward/record.url?scp=0039845802&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039845802&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-00-01244-8

DO - 10.1090/S0025-5718-00-01244-8

M3 - Article

VL - 70

SP - 935

EP - 949

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

IS - 235

ER -