## Abstract

In this paper an efficient algorithm is presented for the development or compact and passive macro-models of electromagnetic devices through the systematic reduction of the order of discrete models for these devices obtained through the use of finite elements. The proposed methodology is founded on a new finite element formulation that casts Maxwell's curl equations in a state-space form. Such state-space representations are very compatible with a class of robust model order reduction techniques based on Krylov subspaces. However, the advantage of this compatibility appears to be hindered by the fact that the state matrix of the discretized Maxwellian system is of dimension almost twice that obtained from the finite element approximation of the electromagnetic vector wave equation. It is shown in this paper that the apparent penalty in both memory and computation efficiency can be avoided by a proper selection of the finite element expansion functions used for the discretization of the electromagnetic fields. More specifically, it is shown that the proper selection of expansion functions renders the state-space form of the Maxwellian system equivalent to the discrete problem obtained from the approximation of the vector wave equation using tangentially continuous vector finite elements. This equivalence is then used to effect Krylov-based model order reduction directly from the finite element approximation of the vector wave equation. In particular, a passive model order reduction algorithm is used for this purpose. The proposed reduced order macro-modelling algorithm is demonstrated through its application to a variety of microwave passive components.

Original language | English (US) |
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Pages (from-to) | 73-92 |

Number of pages | 20 |

Journal | International Journal of Numerical Modelling: Electronic Networks, Devices and Fields |

Volume | 15 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2002 |

## ASJC Scopus subject areas

- Modeling and Simulation
- Computer Science Applications
- Electrical and Electronic Engineering