### Abstract

The vector finite element method (VFEM) is formulated for the time-harmonic Maxwell's equations to model microwave integrated circuits and electronic packages at high frequencies. A number of computational challenges often appear during the formulation of these problems ranging from proper excitation of the input ports and reflection-free truncation of the unbounded infinite domain to accurate modeling of material interfaces and anisotropies. To deal with the challenge of proper excitation/termination of the ports, a generalized eigenvalue problem is formulated at each of the ports in order to obtain the dispersive propagation characteristics and governing modes of the 2-D structure; these modal characteristics are subsequently used to properly excite and terminate the input and output ports of the 3-D structure under investigation. In the case where scattering is involved, the unbounded infinite domain is properly truncated using first-, second-, or even higher-order absorbing boundary conditions (ABCs), a perfectly matched layer (PML), or an exact radiation condition based on a boundary-integral (BI) method. Numerical results on a number of practical engineering applications illustrate the power and effectiveness of the VFEM in solving complex electromagnetic problems.

Original language | English |
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Title of host publication | Application of Mathematics in Technical and Natural Sciences - Proceedings of the 2nd International Conference, AMiTaNS'10 |

Pages | 37-48 |

Number of pages | 12 |

Volume | 1301 |

DOIs | |

Publication status | Published - 2010 |

Event | 2nd International Conference on Application of Mathematics in Technical and Natural Sciences, AMiTaNS'10 - Sozopol, Bulgaria Duration: 21 Jun 2010 → 26 Jun 2010 |

### Other

Other | 2nd International Conference on Application of Mathematics in Technical and Natural Sciences, AMiTaNS'10 |
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Country | Bulgaria |

City | Sozopol |

Period | 21/06/10 → 26/06/10 |

### Keywords

- eigenvalue problems
- electromagnetics
- Finite element method
- microwave circuits
- time-harmonic Maxwell's equations

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## Cite this

*Application of Mathematics in Technical and Natural Sciences - Proceedings of the 2nd International Conference, AMiTaNS'10*(Vol. 1301, pp. 37-48) https://doi.org/10.1063/1.3526636