Alexander Sommer

A New Method for Accurate and Efficient Residual Computation in Adaptive Model-Order Reduction

Projection-based model-order reduction is a powerful methodology for solving parameter-dependent linear systems of equations. The efficient computation of the residual norm is of paramount importance in adaptive model reduction schemes because it is heavily used in error indicators and a posteriori error bounds. These guide the adaptive selection of expansion points in multi-point methods and serve as stopping criteria for subspace enrichment. This paper demonstrates that the standard algorithm for fast residual norm computation leads to premature stagnation, and it presents a new approach of improved accuracy.

A Posteriori Error Bounds for Krylov-Based Fast Frequency Sweeps of Finite-Element Systems

Projection-based model reduction is a well-established methodology for computing fast frequency sweeps of finite-element (FE) approximations to passive microwave structures. This contribution presents a novel provable error bound for moment-matching reduced-order models of lossless systems. It improves over existing methods by increasing the accuracy of the estimate and by reducing numerical costs. Numerical studies demonstrate the benefits of the suggested approach.

Efficient finite-element computation of far-fields of phased arrays by order reduction

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 c...

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.

Reduced-Order Models of Finite-Element Systems Featuring Shape and Material Parameters

Abstract Since typical finite-element systems are of high dimension, the analysis of parameter-dependent microwave structures over broad frequency bands tends to be very time-consuming. This issue is addressed by parametric order reduction, which provides a systematic methodology for constructing surrogate models that are cheap to evaluate and feature low and controllable levels of error. This article presents an order reduction technique for finite-element models that depends on the operating frequency and features explicit and implicit parameters for material properties and shape, respectively. It uses polynomial interpolation to resolve implicit parameter dependencies and employs parameter-dependent bases defined on sub-domains of parameter space. The resulting reduced-order models are of very small dimension and preserve the structure and frequency dependency of the original finite-element model. Numerical results demonstrate that the proposed method reduces solution times by several orders of magnitude compared to the underlying finite-element model at very low error.

Certified dual-corrected radiation patterns of phased antenna arrays by offline-online order reduction of finite-element models

This paper presents a fast numerical method for computing certified far-field patterns of phased antenna arrays over broad frequency bands as well as wide ranges of steering and look angles. The proposed scheme combines finite-element analysis, dual-corrected model-order reduction, and empirical interpolation. To assure the reliability of the results, improved a posteriori error bounds for the radiated power and directive gain are derived. Both the reduced-order model and the error-bounds algorithm feature offline-online decomposition. A real-world example is provided to demonstrate the efficiency and accuracy of the suggested approach.

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.

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.

A hierarchical greedy strategy for adaptive model-order reduction

Projection-based model-order reduction is a powerful methodology for solving parameter-dependent linear systems of equations. Adaptive multi-point methods commonly employ a greedy strategy for expansion point placement: The location where some error measure is maximum is selected. This requires evaluating an error indicator on a dense sampling of the parameter domain at each iteration of the model generation phase. To reduce runtimes, a hierarchical refinement strategy that reuses information from previous steps is proposed.

An Adaptive Deflation Domain-Decomposition Preconditioner for Fast Frequency Sweeps

An adaptive multi-point model-order reduction is a well-established methodology for computing fast frequency sweeps of finite-element (FE) models. For structures that are electrically large, however, generating the reduced-order system is computationally expensive, because both the size of the FE model and the number of expansion points become large. Thus, a great number of independent large-scale systems of linear equations must be solved by iterative methods. To alleviate this problem, this paper proposes to employ the reduced-order system already available at a given adaptive step for constructing an efficient two-level preconditioner. Two numerical examples demonstrate the benefits of the suggested approach.