Stefan Burgard, Ortwin Farle and Romanus Dyczij-Edlinger
The goal is to derive a numerical method for computing parametric reduced-order models (PROMs) from finite-element (FE) models of microwave structures that feature geometrical…
Abstract
Purpose
The goal is to derive a numerical method for computing parametric reduced-order models (PROMs) from finite-element (FE) models of microwave structures that feature geometrical parameters.
Design/methodology/approach
First, a parameter-dependent FE mesh is constructed by a topology-preserving mesh-morphing algorithm. Then, multivariate polynomial interpolation is employed to achieve explicit geometrical parameterization of all FE matrices. Finally, a PROM based on parameter-dependent projection matrices is constructed by means of interpolation and state transformation techniques.
Findings
The resulting PROMs are of low dimension and fast to evaluate. Moreover, the method features high rates of convergence, and the number of FE solutions required for constructing the PROM is small. The accuracy of the PROM is only limited by that of the underlying FE model and can be controlled by varying the PROM dimension.
Research limitations/implications
Since the method uses topology-preserving mesh-morphing algorithms to instantiate FE models at a number of interpolation points in geometrical parameter space, there are limitations to the amount of deformation that can be handled.
Practical implications
PROM evaluations are computationally cheap. In many cases they can be evaluated hundreds or even thousands of times per second. Therefore, PROMs are very well-suited for parametric studies or numerical optimization.
Originality/value
The presented methodology employs a new way of constructing parameter-dependent interpolation matrices, based on interpolation and space transformations. The proposed methodology yields better accuracy and higher rates of convergence than previous approaches.
Details
Keywords
Yves Konkel, Ortwin Farle, Andreas Köhler, Alwin Schultschik and Romanus Dyczij‐Edlinger
The purpose of this paper is to compare competing adaptive strategies for fast frequency sweeps for driven and waveguide‐mode problems and give recommendations for practical…
Abstract
Purpose
The purpose of this paper is to compare competing adaptive strategies for fast frequency sweeps for driven and waveguide‐mode problems and give recommendations for practical implementations.
Design/methodology/approach
The paper first summarizes the theory of adaptive strategies for multi‐point (MP) sweeps and then evaluates the efficiency of such methods by means of numerical examples.
Findings
The authors' numerical tests give clear evidence for exponential convergence. In the driven case, highly resonant structures lead to pronounced pre‐asymptotic regions, followed by almost immediate convergence. Bisection and greedy point‐placement methods behave similarly. Incremental indicators are trivial to implement and perform similarly well as residual‐based methods.
Research limitations/implications
While the underlying reduction methods can be extended to any kind of affine parameter‐dependence, the numerical tests of this paper are for polynomial parameter‐dependence only.
Practical implications
The present paper describes self‐adaptive point‐placement methods and termination criteria to make MP frequency sweeps more efficient and fully automatic.
Originality/value
The paper provides a self‐adaptive strategy that is efficient and easy to implement. Moreover, it demonstrates that exponential convergence rates can be reached in practice.
Details
Keywords
Daniel Klis, Stefan Burgard, Ortwin Farle and Romanus Dyczij-Edlinger
– The purpose of this paper is to determine the broadband frequency response of the impedance matrix of wireless power transfer (WPT) systems comprising litz wire coils.
Abstract
Purpose
The purpose of this paper is to determine the broadband frequency response of the impedance matrix of wireless power transfer (WPT) systems comprising litz wire coils.
Design/methodology/approach
A finite-element (FE)-based method is proposed which treats the microstructure of litz wires by an auxiliary cell problem. In the macroscopic model, litz wires are represented by a block with a homogeneous, artificial material whose properties are derived from the cell problem. As the frequency characteristics of the material closely resemble a Debye relaxation, it is possible to convert the macroscopic model to polynomial form, which enables the application of model reduction techniques of moment-matching type.
Findings
FE-based model-order reduction using litz wire homogenization provides an efficient approach to the broadband analysis of WPT systems. The error of the reduced-order model (ROM) is comparable to that of the underlying original model and can be controlled by varying the ROM dimension.
Research limitations/implications
Since the present model does not account for displacement currents, the operating frequency of the system must lie well below its first self-resonance frequency.
Practical implications
The proposed method is well-suited for the computer-aided design of WPT systems. It outperforms traditional FE analysis in computational efficiency.
Originality/value
The presented homogenization method employs a new formulation for the cell problem which combines the benefits of several existing approaches. Its incorporation into an order-reduction method enables the fast computation of broadband frequency sweeps.
Details
Keywords
Alexander Sommer, Ortwin Farle and Romanus Dyczij-Edlinger
The article aims to present an efficient numerical method for computing the far-fields of phased antenna arrays over broad frequency bands as well as wide ranges of steering and…
Abstract
Purpose
The article aims to present an efficient numerical method for computing the far-fields of phased antenna arrays over broad frequency bands as well as wide ranges of steering and look angles.
Design/methodology/approach
The suggested approach combines finite-element analysis, projection-based model-order reduction, and empirical interpolation.
Findings
The reduced-order models are highly accurate but significantly smaller than the underlying finite-element models. Thus, they enable a highly efficient numerical far-field computation of phased antenna arrays. The frequency-slicing greedy method proposed in this paper greatly reduces the computational costs for constructing the reduced-order models, compared to state-of-the-art methods.
Research limitations/implications
The frequency-slicing greedy method is intended for use with matrix factorization methods. It is not applicable when the underlying finite-element system is solved by iterative methods.
Practical implications
In contrast to conventional finite-element models of phased antenna arrays, reduced-order models are very cheap to evaluate. Hence, they provide an enabling technology for computing radiation patterns over broad frequency bands and wide ranges of steering angles.
Originality/value
The paper presents a two-step model-order reduction method for efficiently computing the far-field patterns of phased antenna arrays. The suggested frequency-slicing greedy method constructs the reduced-order models in a systematic fashion and improves computing times, compared to existing methods.