### Abstract

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

Article number | 10.1016/j.laa.2008.12.036 |

Pages (from-to) | 300-317 |

Number of pages | 26 |

Journal | Linear algebra and its applications |

Volume | 431 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - Jul 2009 |

### Keywords

- EWI-17315
- MSC-65L05
- MSC-65L20
- MSC-65M12
- MSC-65M20
- IR-69760
- Krylov subspace iteration
- exponential integration
- implicit integration
- conjugate gradient iteration
- METIS-264501
- Maxwell's equations

### Cite this

*Linear algebra and its applications*,

*431*(3-4), 300-317. [10.1016/j.laa.2008.12.036]. https://doi.org/10.1016/j.laa.2008.12.036

}

*Linear algebra and its applications*, vol. 431, no. 3-4, 10.1016/j.laa.2008.12.036, pp. 300-317. https://doi.org/10.1016/j.laa.2008.12.036

**Unconditionally stable integration of Maxwell's equations.** / Verwer, J.G.; Bochev, Mikhail A.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Unconditionally stable integration of Maxwell's equations

AU - Verwer, J.G.

AU - Bochev, Mikhail A.

N1 - Please note different possible spellings of the first author name: "Botchev" or "Bochev".

PY - 2009/7

Y1 - 2009/7

N2 - Numerical integration of Maxwell's equations is often based on explicit methods accepting a stability step size restriction. In literature evidence is given that there is also a need for unconditionally stable methods, as exemplified by the successful alternating direction implicit finite difference time domain scheme. In this paper we discuss unconditionally stable integration for a general semi-discrete Maxwell system allowing non-Cartesian space grids as encountered in finite element discretizations. Such grids exclude the alternating direction implicit approach. Particular attention is given to the second-order trapezoidal rule implemented with preconditioned conjugate gradient iteration and to second-order exponential integration using Krylov subspace iteration for evaluating the arising phi-functions. A three-space dimensional test problem is used for numerical assessment and comparison with an economical second order implicit-explicit integrator. We further pay attention to the Chebyshev series expansion for computing the exponential operator for skew-symmetric matrices.

AB - Numerical integration of Maxwell's equations is often based on explicit methods accepting a stability step size restriction. In literature evidence is given that there is also a need for unconditionally stable methods, as exemplified by the successful alternating direction implicit finite difference time domain scheme. In this paper we discuss unconditionally stable integration for a general semi-discrete Maxwell system allowing non-Cartesian space grids as encountered in finite element discretizations. Such grids exclude the alternating direction implicit approach. Particular attention is given to the second-order trapezoidal rule implemented with preconditioned conjugate gradient iteration and to second-order exponential integration using Krylov subspace iteration for evaluating the arising phi-functions. A three-space dimensional test problem is used for numerical assessment and comparison with an economical second order implicit-explicit integrator. We further pay attention to the Chebyshev series expansion for computing the exponential operator for skew-symmetric matrices.

KW - EWI-17315

KW - MSC-65L05

KW - MSC-65L20

KW - MSC-65M12

KW - MSC-65M20

KW - IR-69760

KW - Krylov subspace iteration

KW - exponential integration

KW - implicit integration

KW - conjugate gradient iteration

KW - METIS-264501

KW - Maxwell's equations

U2 - 10.1016/j.laa.2008.12.036

DO - 10.1016/j.laa.2008.12.036

M3 - Article

VL - 431

SP - 300

EP - 317

JO - Linear algebra and its applications

JF - Linear algebra and its applications

SN - 0024-3795

IS - 3-4

M1 - 10.1016/j.laa.2008.12.036

ER -