Li Zhao

Electromagnetic model order reduction for system-level modeling

Reduced-order modeling of an electromagnetic system is understood as the approximation of a continuous or discrete model of the system by one of substantially lower order, yet capable of capturing the electromagnetic behavior of the original one with sufficient engineering accuracy. Specific methodologies for model order reduction of distributed electromagnetic systems are discussed in this paper. It is shown that electromagnetic model order reduction enhances computational efficiency and, thus, facilitates system-level modeling and computer simulation of multifunctional systems. The proposed methodologies are demonstrated through applications to the reduced-order modeling of high-speed interconnects, electromagnetic waveguides, and microstrip antennas.

A general approach for the development of unsplit-field time-domain implementations of perfectly matched layers for FDTD grid truncation

It is shown that the anisotropic perfectly matched medium, proposed recently for the construction of reflectionless absorbing boundaries for differential equation-based electromagnetic simulations in unbounded domains, can be made equivalent to the Chew-Weedon perfectly matched medium developed from a modified Maxwells system with coordinate stretching. Consequently, despite the apparently nonphysical coordinate stretching, Chew-Weedons formulation, with an appropriate definition of the involved electric and magnetic fields, is merely an alternative mathematical form of Maxwells system in an anisotropic medium. Finally, a more convenient time-domain implementation of the perfectly matched layer without splitting of the field components is derived.

Rapid FDTD simulation without time stepping

A numerical methodology is presented for fast broad-band extraction of the electromagnetic properties of passive waveguiding structures. The methodology combines the standard finite-difference time-domain (FDTD) method with a nonsymmetric Lanczos eigenvalue algorithm to extract a reduced-order model of the electromagnetic response over the frequency range of interest. The implementation of the algorithm is such that each iteration is computationally equivalent to the update of the electromagnetic fields in the FDTD algorithm. However, no time stepping is required.

GT-PML: generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids

A new formulation is presented for the systematic development of perfectly matched layers (PML) from Maxwells equations in properly constructed anisotropic media. The proposed formulation has an important advantage over the original Berengers PML in that it can be implemented in the time domain without any splitting of the fields. Results from 3D simulations illustrate the effectiveness of the proposed method.

Passive reduced-order modeling of electromagnetic systems

Rapid electromagnetic field simulation is now being recognized as a critical component of next-generation computer-aided design frameworks that will be used for performance evaluation and design of the information processing and communication systems of the 21st century. Except for very simple systems, computer simulation of electromagnetic interactions is hindered by the very large number of degrees of freedom involved in the discrete model. One potentially useful approach to overcoming this computational bottleneck is model order reduction, where parts of the electromagnetic model are replaced by models of substantially lower order, yet capable of capturing the electromagnetic behavior of the original subsystems with sufficient engineering accuracy. Possible approaches to the development of such model order reduction techniques are the subject of this paper. The potential applications and the benefits from such electromagnetic model order reduction are discussed. The important issue of passivity of the generated reduced model is considered, and a set of constraints on the state representation of the discrete electromagnetic boundary-value problem are identified for the reduced order model to be passive. The paper concludes with a presentation of several numerical examples from the application of model order reduction techniques to the analysis of electromagnetic waveguides and antennas.

Rapid FDTD analysis of shielding enclosures

A numerical methodology is presented for fast broadband analysis of shielding enclosures. The methodology combines the standard finite-difference time-domain (FDTD) method with a non-symmetric Lanczos eigenvalue algorithm to generate directly a Pade approximation of the electromagnetic response of the structure over the frequency range of interest. The numerical implementation is such that each iteration of the Lanczos algorithm is computationally equivalent to the update of the electromagnetic fields in the FDTD algorithm. However, no time stepping is required. Thus, both the time step-imposed numerical stability constraint of the FDTD algorithm and its time step-controlled frequency resolution are relaxed. The proposed methodology generates the continuous response of the system at a fraction of the computational cost required by the FDTD method. The effectiveness of the methodology is demonstrated through several numerical experiments.