Kynthia Stavrakakis

Linearization of Parametric FIT-Discretized Systems for Model Order Reduction

Electrodynamic field simulations typically require the solution of large linear systems which may depend on several variables. Model Order Reduction Techniques offer an approach to solve these multivariate problems in a reasonable time. This paper presents an Order Reduction Method and the required system equation linearization for structures discretized by the Finite Integration Technique (FIT) depending on frequency and length variation.

Parametric Model Order Reduction by Neighbouring Subspaces

Electrodynamic field simulations in the frequency domain typically require the solution of large linear systems. Model Order Reduction (MOR) techniques offer a fast approach to approximate the system impedance with respect to the frequency parameter. Most commonly, MOR via projection is applied associated with certain Krylov projection matrices. During the design process it is desirable to vary specified parameters like the frequency, geometry details as well as material parameters, giving rise to multivariate dynamical systems. In this work, a multivariate MOR method is presented for parameterized systems based on the Finite Integration Technique (FIT). It utilizes the observation, that for small parameter variations the matrices associated with the univariate MOR differ only slightly. Thus, the multivariate MOR method is deduced from the usage of specified univariate subspaces.

Model order reduction methods for multivariate parameterized dynamical systems obtained by the finite integration theory

In electrodynamic field computations the continuous Maxwell equations are typically discretized in the space variables, i. e the continuous space is mapped onto a finite set of discrete elements leading to a system of differential equations constituting the Maxwell grid equations. These dynamical systems can be very large. Due to limited computational, accuracy and storage capabilities, simplified models, obtained by means of model order reduction (MOR) methods, which capture the main features of the original model are then successfully used instead of the original models. Most commonly MOR via projection is used. Variation of model parameters like geometrical or material parameters give rise to multivariate dynamical systems. It is aimed that also the simplified models keep this parameter dependence. In this work, MOR methods are presented for multivariate systems based on the finite integration technique (FIT). The methods are applied to numerical examples with both geometrical and material variations.

Threedimensional geometry variations of FIT systems for Model Order Reduction

Electrodynamic field simulations in the frequency domain typically require the solution of large linear systems. During the design process it is desirable to vary specified parameters like the frequency, geometry details as well as material parameters. Initializing an individual calculation to consider all parameter changes is not efficient. Model Order Reduction (MOR) techniques offer an approach to approximate the transfer function of these multivariate problems in reasonable time. Existing schemes for multivariate MOR require a linearization of the underlying system for systems based on the Finite Integration Technique (FIT). This paper focuses on the linearization for FIT-discretized systems, that depend on frequency and threedimensional rectilinear geometry variations and briefly discusses the utilized MOR techniques.

Fast parameter sweeps for the calculation of S-parameters in electromagnetic field simulations

The Maxwell equations have in general no analytical solution and are therefore often discretized in the space variables leading to a system of differential equations constituting the Maxwell Grid Equations. The discretization method used here is the Finite Integration Theory (FIT). In electromagnetic field computations a model often needs to be simulated many times with varying parameters. As the systems consisting of the Maxwell Grid Equations can be very large, simplified models which capture the main features of the original model are then successfully used instead of the original models. These models are obtained by means of model order reduction (MOR) methods. Parametric MOR (PMOR) methods respect also parametric variations.