### Abstract

In this paper, we develop several two-grid methods for the Nédélec edge finite element approximation of the time-harmonic Maxwell equations. We first present a two-grid method that uses a coarse space to solve the original problem and then use a fine space to solve a corresponding symmetric positive definite problem. Then, we present two types of iterative two-grid methods, one is to add the kernel of the curl-operator in the fine space to a coarse mesh space to solve the original problem and the other is to use an inner iterative method for dealing with the kernel of the curl-operator in the fine space and the coarse space, separately. We provide the error estimates for the first two methods and present numerical experiments to show the efficiency of our methods.

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

Pages (from-to) | 93-111 |

Number of pages | 19 |

Journal | Numerical Linear Algebra with Applications |

Volume | 20 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2013 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Applied Mathematics

### Cite this

*Numerical Linear Algebra with Applications*,

*20*(1), 93-111. https://doi.org/10.1002/nla.1827

}

*Numerical Linear Algebra with Applications*, vol. 20, no. 1, pp. 93-111. https://doi.org/10.1002/nla.1827

**Two-grid methods for time-harmonic Maxwell equations.** / Zhong, Liuqiang; Shu, Shi; Wang, Junxian; Xu, J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Two-grid methods for time-harmonic Maxwell equations

AU - Zhong, Liuqiang

AU - Shu, Shi

AU - Wang, Junxian

AU - Xu, J.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - In this paper, we develop several two-grid methods for the Nédélec edge finite element approximation of the time-harmonic Maxwell equations. We first present a two-grid method that uses a coarse space to solve the original problem and then use a fine space to solve a corresponding symmetric positive definite problem. Then, we present two types of iterative two-grid methods, one is to add the kernel of the curl-operator in the fine space to a coarse mesh space to solve the original problem and the other is to use an inner iterative method for dealing with the kernel of the curl-operator in the fine space and the coarse space, separately. We provide the error estimates for the first two methods and present numerical experiments to show the efficiency of our methods.

AB - In this paper, we develop several two-grid methods for the Nédélec edge finite element approximation of the time-harmonic Maxwell equations. We first present a two-grid method that uses a coarse space to solve the original problem and then use a fine space to solve a corresponding symmetric positive definite problem. Then, we present two types of iterative two-grid methods, one is to add the kernel of the curl-operator in the fine space to a coarse mesh space to solve the original problem and the other is to use an inner iterative method for dealing with the kernel of the curl-operator in the fine space and the coarse space, separately. We provide the error estimates for the first two methods and present numerical experiments to show the efficiency of our methods.

UR - http://www.scopus.com/inward/record.url?scp=84870955426&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870955426&partnerID=8YFLogxK

U2 - 10.1002/nla.1827

DO - 10.1002/nla.1827

M3 - Article

AN - SCOPUS:84870955426

VL - 20

SP - 93

EP - 111

JO - Numerical Linear Algebra with Applications

JF - Numerical Linear Algebra with Applications

SN - 1070-5325

IS - 1

ER -