### Abstract

The iterative substructuring methods, also known as Schur complement methods, form one of two important families of domain decomposition algorithms. They are based on a partitioning of a given region, on which the partial differential equation is defined, into nonoverlapping substructures. The preconditioners of these conjugate gradient methods are then given in terms of local problems, defined on individual substructures and pairs of substructures, and, in addition, a global problem of low dimension. An iterative method of this kind is introduced for the lowest order Raviart-Thomas finite elements in three dimensions and it is shown that the condition number of the relevant operator is independent of the number of substructures and grows only as the square of the logarithm of the number of unknowns associated with an individual substructure. The theoretical bounds are confirmed by a series of numerical experiments.

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

Pages (from-to) | 1657-1676 |

Number of pages | 20 |

Journal | SIAM Journal on Numerical Analysis |

Volume | 37 |

Issue number | 5 |

State | Published - 2000 |

### Fingerprint

### Keywords

- Domain decomposition
- Iterative substructuring methods
- Raviart-Thomas finite elements

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics
- Computational Mathematics

### Cite this

*SIAM Journal on Numerical Analysis*,

*37*(5), 1657-1676.

**An iterative substructuring method for Raviart-Thomas vector fields in three dimensions.** / Wohlmuth, Barbara I.; Toselli, Andrea; Widlund, Olof B.

Research output: Contribution to journal › Article

*SIAM Journal on Numerical Analysis*, vol. 37, no. 5, pp. 1657-1676.

}

TY - JOUR

T1 - An iterative substructuring method for Raviart-Thomas vector fields in three dimensions

AU - Wohlmuth, Barbara I.

AU - Toselli, Andrea

AU - Widlund, Olof B.

PY - 2000

Y1 - 2000

N2 - The iterative substructuring methods, also known as Schur complement methods, form one of two important families of domain decomposition algorithms. They are based on a partitioning of a given region, on which the partial differential equation is defined, into nonoverlapping substructures. The preconditioners of these conjugate gradient methods are then given in terms of local problems, defined on individual substructures and pairs of substructures, and, in addition, a global problem of low dimension. An iterative method of this kind is introduced for the lowest order Raviart-Thomas finite elements in three dimensions and it is shown that the condition number of the relevant operator is independent of the number of substructures and grows only as the square of the logarithm of the number of unknowns associated with an individual substructure. The theoretical bounds are confirmed by a series of numerical experiments.

AB - The iterative substructuring methods, also known as Schur complement methods, form one of two important families of domain decomposition algorithms. They are based on a partitioning of a given region, on which the partial differential equation is defined, into nonoverlapping substructures. The preconditioners of these conjugate gradient methods are then given in terms of local problems, defined on individual substructures and pairs of substructures, and, in addition, a global problem of low dimension. An iterative method of this kind is introduced for the lowest order Raviart-Thomas finite elements in three dimensions and it is shown that the condition number of the relevant operator is independent of the number of substructures and grows only as the square of the logarithm of the number of unknowns associated with an individual substructure. The theoretical bounds are confirmed by a series of numerical experiments.

KW - Domain decomposition

KW - Iterative substructuring methods

KW - Raviart-Thomas finite elements

UR - http://www.scopus.com/inward/record.url?scp=0013174621&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0013174621&partnerID=8YFLogxK

M3 - Article

VL - 37

SP - 1657

EP - 1676

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

IS - 5

ER -