Rolf Baltes

Time-domain simulation of electromagnetic fields based on reduced-order models residing in the frequency domain

This work presents a method for constructing compact time-domain models from finite-element simulations in the frequency-domain. To reduce the system dimension and speed up computation times, model-order reduction techniques are applied. The resulting reduced-order system is proven to be passive. The proposed method does not only provide the output of the system, but it also enables the reconstruction of the electromagnetic fields.

Adaptive model order reduction for structures fed by dispersive waveguide modes

This paper presents a self-adaptive reduced-basis method for driven microwave problems which incorporates the frequency-dependent mode patterns and dispersive propagation coefficients of inhomogeneous waveguides. A reduced-order model provides a low-dimensional subspace for approximating the relevant waveguide modes over the considered frequency range. That information is exploited to establish affine parameter-dependence in the three-dimensional driven model, which hereby becomes accessible to projection-based model-order reduction.

A simplified domain-decomposition preconditioner for the finite-element discretization of the time-harmonic maxwell equations

This contribution presents a domain-decomposition preconditioner that achieves higher rates of convergence than comparable methods and is yet simple to implement. Its numerical properties are illustrated by examining the eigenvalue distribution of the preconditioned finite element matrix. The practical usefulness of the proposed method is demonstrated by reference to a large-scale antenna array.

Time-domain simulation of electromagnetic fields based on frequency-domain reduced-order models including Debye materials

This contribution presents a new technique for constructing time-domain models from finite-element based simulation data in the frequency-domain, including frequency-dependent materials of Debye type. In order to reduce computational costs, projection-based model-order reduction techniques are applied. Not only do they provide an accurate input/output description of the system but also allow for reconstructing the electromagnetic fields. The resulting reduced-order model is proven to be passive, which is crucial for preserving causality in time-domain simulations.

Compact time-domain models for drude materials using order-reduction in the frequency-domain

A method for constructing time-domain models including Drude materials from finite-element data in the frequency-domain is presented. To produce a model that is compact, projection-based order-reduction techniques are applied. The time-domain model is based on a state space representation and can be proven to be passive and causal. Moreover, the suggested approach provides an efficient way for reconstructing the transient electromagnetic fields.

An efficient parametric near-field-to-far-field transformation technique

This paper presents an efficient numerical method for computing antenna patterns over broad frequency bands and wide ranges of look angles. The proposed scheme is based on finite-element analysis and the empirical interpolation technique, and employs a new sub-domain approach on the Huygens surfaces to speed-up the offline part of the algorithm. Numerical results demonstrate that computational efforts are reduced by orders of magnitude, compared to conventional methods.

A Finite-Element-Based Fast Frequency Sweep Framework Including Excitation by Frequency-Dependent Waveguide Mode Patterns

This paper presents a frequency-sweep technique based on model-order reduction and finite elements, for the broadband analysis of structures fed by waveguides (WGs) possessing frequency-dependent modal field patterns. Standard order reduction requires the matrices and right-hand sides (RHSs) to exhibit affine frequency parameterization. This precondition is violated when the transverse fields of the WG modes vary with frequency. The proposed solution involves two steps. First, a reduced-order model (ROM) for the WG is constructed. It enables the accurate yet inexpensive computation of propagation characteristics. Second, order reduction is applied to the driven problem, wherein the reduced WG model is utilized to construct affine approximations to the matrices and RHSs. Since this process requires operations on reduced-order matrices only, it is computationally cheap and enables offline/online decomposition. Both impedance and scattering formulations are considered. For the latter, an alternative to the transfinite element method is proposed, which does not employ modal field patterns as shape functions. It avoids interior resonances and computes scattering parameters more efficiently when only a limited set of excitations is of interest. The resulting algebraic system is of somewhat larger dimension but easier to assemble. Its simple structure greatly facilitates the construction of the ROM.

Compact and Passive Time-Domain Models Including Dispersive Materials Based on Order-Reduction in the Frequency Domain

In this paper, compact time-domain (TD) models featuring materials with frequency-dependent electromagnetic (EM) properties are derived. The considered frequency-dependent material models include multiterm Debye and Lorentz models for the electric permittivity and the magnetic permeability and a multiterm Drude model for the electric conductivity. The TD models are based on finite-element systems in the frequency domain (FD). To render the model compact and computationally efficient, the dimension of the FD system is compressed with the help of projection-based model-order reduction. In contrast to older approaches, the TD transformation is performed on the FD model itself rather than on the transfer function. The result is a state-space representation, which may either be solved by custom time integrators or imported into commercial circuit simulators. The advantages of the new approach include provable passivity of the FD model, provable causality of the TD model, and the ability to reconstruct the transient EM fields.

Low-frequency stable model-order reduction of finite-element models featuring lumped ports

A fast frequency sweep method for finite-element models of linear time-invariant structures is presented, which is valid from the static/stationary limit up to the optical range. The key ingredients are a low-frequency stable finite-element formulation and a projection-based method of model-order reduction. The dimension of the reduced model is governed by the complexity of the system dynamics only; it does not depend on the size of the finite-element matrix. A numerical example is presented to demonstrate the efficiency of the suggested approach.

Compact time-domain models including Lorentz materials based on reduced-order models in the frequency-domain

This contribution describes a methodology for computing compact time-domain models of electromagnetic devices containing Lorentz materials from finite-element systems in the frequency domain. The procedure starts with projection-based model-order reduction, to downsize system dimension. The resulting reduced-order model is transformed to the time-domain and leads to a state-space representation. The proposed method is mathematically proved to preserve important system properties including passivity, causality, and reciprocity, and allows for reconstructing the transient electromagnetic fields.