### Abstract

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

Place of Publication | Enschede |

Publisher | Department of Applied Mathematics, University of Twente |

Number of pages | 25 |

State | Published - Feb 2012 |

### Publication series

Name | Memorandum / Department of Applied Mathematics |
---|---|

Publisher | University of Twente, Department of Applied Mathematics |

No. | 1975 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### Fingerprint

### Keywords

- Second-order damped Maxwell wave equation
- High-order numerical time integration
- H(curl)-conforming finite element method
- IR-79682
- METIS-285242
- Discontinuous Galerkin finite element method
- MSC-65M60
- MSC-65M20
- MSC-65L20
- MSC-65L06
- EWI-21520

### Cite this

*Time-integration methods for finite element discretisations of the second-order Maxwell equation*. (Memorandum / Department of Applied Mathematics; No. 1975). Enschede: Department of Applied Mathematics, University of Twente.

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*Time-integration methods for finite element discretisations of the second-order Maxwell equation*. Memorandum / Department of Applied Mathematics, no. 1975, Department of Applied Mathematics, University of Twente, Enschede.

**Time-integration methods for finite element discretisations of the second-order Maxwell equation.** / Sarmany, D.; Bochev, Mikhail A.; van der Vegt, Jacobus J.W.

Research output: Professional › Report

TY - BOOK

T1 - Time-integration methods for finite element discretisations of the second-order Maxwell equation

AU - Sarmany,D.

AU - Bochev,Mikhail A.

AU - van der Vegt,Jacobus J.W.

N1 - Devoted to the memory of Jan Verwer. Second author's surname can also be spelled as "Bochev".

PY - 2012/2

Y1 - 2012/2

N2 - This article deals with time integration for the second-order Maxwell equations with possibly non-zero conductivity in the context of the discontinuous Galerkin finite element method DG-FEM) and the $H(\mathrm{curl})$-conforming FEM. For the spatial discretisation, hierarchic $H(\mathrm{curl})$-conforming basis functions are used up to polynomial order $p=3$ over tetrahedral meshes, meaning fourth-order convergence rate. A high-order polynomial basis often warrants the use of high-order time-integration schemes, but many well-known high-order schemes may suffer from a severe time-step stability restriction owing to the conductivity term. We investigate several possible time-integration methods from the point of view of accuracy, stability and computational work. We also carry out a numerical Fourier analysis to study the dispersion and dissipation properties of the semi-discrete DG-FEM scheme as well as the fully-discrete schemes with several of the time-integration methods. The dispersion and dissipation properties of the spatial discretisation and those of the time-integration methods are investigated separately, providing additional insight into the two discretisation steps.

AB - This article deals with time integration for the second-order Maxwell equations with possibly non-zero conductivity in the context of the discontinuous Galerkin finite element method DG-FEM) and the $H(\mathrm{curl})$-conforming FEM. For the spatial discretisation, hierarchic $H(\mathrm{curl})$-conforming basis functions are used up to polynomial order $p=3$ over tetrahedral meshes, meaning fourth-order convergence rate. A high-order polynomial basis often warrants the use of high-order time-integration schemes, but many well-known high-order schemes may suffer from a severe time-step stability restriction owing to the conductivity term. We investigate several possible time-integration methods from the point of view of accuracy, stability and computational work. We also carry out a numerical Fourier analysis to study the dispersion and dissipation properties of the semi-discrete DG-FEM scheme as well as the fully-discrete schemes with several of the time-integration methods. The dispersion and dissipation properties of the spatial discretisation and those of the time-integration methods are investigated separately, providing additional insight into the two discretisation steps.

KW - Second-order damped Maxwell wave equation

KW - High-order numerical time integration

KW - H(curl)-conforming finite element method

KW - IR-79682

KW - METIS-285242

KW - Discontinuous Galerkin finite element method

KW - MSC-65M60

KW - MSC-65M20

KW - MSC-65L20

KW - MSC-65L06

KW - EWI-21520

M3 - Report

T3 - Memorandum / Department of Applied Mathematics

BT - Time-integration methods for finite element discretisations of the second-order Maxwell equation

PB - Department of Applied Mathematics, University of Twente

ER -