### Abstract

Original language | English |
---|---|

Pages (from-to) | 2346-2362 |

Number of pages | 23 |

Journal | Computers and mathematics with applications |

Volume | 55 |

Issue number | 274/10 |

DOIs | |

State | Published - 2008 |

### Fingerprint

### Keywords

- EWI-12880
- MSC-65N22
- MSC-65N30
- MSC-65N55
- Domain decomposition
- IR-62360
- Nédélec vector finite elements
- kernel of the rotor operator
- hierarchical preconditioners
- METIS-251009
- multilevel iterative solvers

### Cite this

*Computers and mathematics with applications*,

*55*(274/10), 2346-2362. DOI: 10.1016/j.camwa.2007.11.003

}

*Computers and mathematics with applications*, vol 55, no. 274/10, pp. 2346-2362. DOI: 10.1016/j.camwa.2007.11.003

**Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation.** / Nechaev, O.V.; Shurina, E.P.; Bochev, Mikhail A.

Research output: Scientific - peer-review › Article

TY - JOUR

T1 - Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation

AU - Nechaev,O.V.

AU - Shurina,E.P.

AU - Bochev,Mikhail A.

N1 - Please note different possible spellings of the last author's name: "Botchev" or "Bochev"

PY - 2008

Y1 - 2008

N2 - In the edge vector finite element solution of the frequency domain Maxwell equations, the presence of a large kernel of the discrete rotor operator is known to ruin convergence of standard iterative solvers. We extend the approach of [R. Hiptmair, Multigrid method for Maxwell’s equations, SIAM J. Numer. Anal. 36 (1) (1999) 204–225] and, using domain decomposition ideas, construct a multilevel iterative solver where the projection with respect to the kernel is combined with the use of a hierarchical representation of the vector finite elements. The new iterative scheme appears to be an efficient solver for the edge finite element solution of the frequency domain Maxwell equations. The solver can be seen as a variable preconditioner and, thus, accelerated by Krylov subspace techniques (e.g. GCR or FGMRES). We demonstrate the efficiency of our approach on a test problem with strong jumps in the conductivity.

AB - In the edge vector finite element solution of the frequency domain Maxwell equations, the presence of a large kernel of the discrete rotor operator is known to ruin convergence of standard iterative solvers. We extend the approach of [R. Hiptmair, Multigrid method for Maxwell’s equations, SIAM J. Numer. Anal. 36 (1) (1999) 204–225] and, using domain decomposition ideas, construct a multilevel iterative solver where the projection with respect to the kernel is combined with the use of a hierarchical representation of the vector finite elements. The new iterative scheme appears to be an efficient solver for the edge finite element solution of the frequency domain Maxwell equations. The solver can be seen as a variable preconditioner and, thus, accelerated by Krylov subspace techniques (e.g. GCR or FGMRES). We demonstrate the efficiency of our approach on a test problem with strong jumps in the conductivity.

KW - EWI-12880

KW - MSC-65N22

KW - MSC-65N30

KW - MSC-65N55

KW - Domain decomposition

KW - IR-62360

KW - Nédélec vector finite elements

KW - kernel of the rotor operator

KW - hierarchical preconditioners

KW - METIS-251009

KW - multilevel iterative solvers

U2 - 10.1016/j.camwa.2007.11.003

DO - 10.1016/j.camwa.2007.11.003

M3 - Article

VL - 55

SP - 2346

EP - 2362

JO - Computers and mathematics with applications

T2 - Computers and mathematics with applications

JF - Computers and mathematics with applications

SN - 0898-1221

IS - 274/10

ER -