### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | Department of Applied Mathematics, University of Twente |

Number of pages | 23 |

State | Published - Jul 2006 |

### Publication series

Name | Applied Mathematics Memoranda |
---|---|

Publisher | Department of Applied Mathematics, University of Twente |

No. | 1806 |

ISSN (Print) | 0169-2690 |

### Fingerprint

### Keywords

- METIS-237884
- Nédélec vector finite elements
- MSC-65N30
- MSC-65N22
- EWI-8960
- hierarchical preconditioners
- kernel of the rotor operator
- MSC-65N55
- IR-66839
- Domain decomposition
- multilevel iterative solvers

### Cite this

*Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation*. (Applied Mathematics Memoranda; No. 1806). Enschede: Department of Applied Mathematics, University of Twente.

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*Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation*. Applied Mathematics Memoranda, no. 1806, Department of Applied Mathematics, University of Twente, Enschede.

**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: Professional › Report

TY - BOOK

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 - 2006/7

Y1 - 2006/7

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 [1] 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. [1] R. Hiptmair. Multigrid method for Maxwell's equations. SIAM J. Numer. Anal., 36(1):204-225, 1999.

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 [1] 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. [1] R. Hiptmair. Multigrid method for Maxwell's equations. SIAM J. Numer. Anal., 36(1):204-225, 1999.

KW - METIS-237884

KW - Nédélec vector finite elements

KW - MSC-65N30

KW - MSC-65N22

KW - EWI-8960

KW - hierarchical preconditioners

KW - kernel of the rotor operator

KW - MSC-65N55

KW - IR-66839

KW - Domain decomposition

KW - multilevel iterative solvers

M3 - Report

T3 - Applied Mathematics Memoranda

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

PB - Department of Applied Mathematics, University of Twente

ER -