Conformally mapped polynomial chaos expansions for Maxwell's source problem with random input data

Georg, Niklas

doi:10.1002/jnm.2776

Cited by 4 publications

(11 citation statements)

References 32 publications

(114 reference statements)

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“…In [ 24 ], a framework was established to incorporate conformal maps into the gPC algorithm for enlarging the Bernstein ellipse, based on earlier research from [ 25 ]. Consider a map g that is conformal in an open region

with subdomain

, with

and

.…”

Section: Methodsmentioning

confidence: 99%

“…Being based on polynomials, however, gPC has its own drawbacks, one of the most important ones being slow convergence in the presence of function singularities [ 22 , 23 ]. Conformal maps can alleviate these problems, as demonstrated on Maxwell’s source problem in [ 24 ]. Conformal maps were used previously in [ 25 ] to compute more accurate quadrature rules for integrands with similar non-polynomial behavior, inspired by [ 26 , 27 ].…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we extend the techniques described in [ 24 ] by introducing a novel map that compensates for (apparent) singularities on the real axis. We illustrate the effectiveness of this new conformal map by characterizing the effects of elliptical array deformations on root-Multiple Signal Classification for uniform circular arrays (UCA root-MUSIC) [ 28 ], as it is a well-established and efficient DOA estimation algorithm.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A New Conformal Map for Polynomial Chaos Applied to Direction-of-Arrival Estimation via UCA Root-MUSIC

Brandt

Verhaevert

Hecke

et al. 2022

Sensors

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The effects of random array deformations on Direction-of-Arrival (DOA) estimation with root-Multiple Signal Classification for uniform circular arrays (UCA root-MUSIC) are characterized by a conformally mapped generalized Polynomial Chaos (gPC) algorithm. The studied random deformations of the array are elliptical and are described by different Beta distributions. To successfully capture the erratic deviations in DOA estimates that occur at larger deformations, specifically at the edges of the distributions, a novel conformal map is introduced, based on the hyperbolic tangent function. The application of this new map is compared to regular gPC and Monte Carlo sampling as a reference. A significant increase in convergence rate is observed. The numerical experiments show that the UCA root-MUSIC algorithm is robust to the considered array deformations, since the resulting errors on the DOA estimates are limited to only 2 to 3 degrees in most cases.

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with subdomain

, with

and

.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A New Conformal Map for Polynomial Chaos Applied to Direction-of-Arrival Estimation via UCA Root-MUSIC

Brandt

Verhaevert

Hecke

et al. 2022

Sensors

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“…It is worth mentioning that Conformable Chaotic Maps (CCM)-based lightweight schemes are highly coveted to support the security of critical user information transmitted over 5G WSNs channels. However, the works [39][40][41] did not consider the application of conformable chaotic maps in the design of secure lightweight subtree-based online/offline signature procedure for massive devices in 5G WSNs as in the current paper.…”

Section: Related Workmentioning

confidence: 99%

SBOOSP for Massive Devices in 5G WSNs Using Conformable Chaotic Maps

Meshram¹,

Imoize²,

Jamal³

et al. 2022

Computers, Materials &Amp; Continua

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The commercialization of the fifth-generation (5G) wireless network has begun. Massive devices are being integrated into 5G-enabled wireless sensor networks (5G WSNs) to deliver a variety of valuable services to network users. However, there are rising fears that 5G WSNs will expose sensitive user data to new security vulnerabilities. For secure end-to-end communication, key agreement and user authentication have been proposed. However, when billions of massive devices are networked to collect and analyze complex user data, more stringent security approaches are required. Data integrity, nonrepudiation, and authentication necessitate special-purpose subtree-based signature mechanisms that are pretty difficult to create in practice. To address this issue, this work provides an efficient, provably secure, lightweight subtreebased online/offline signature procedure (SBOOSP) and its aggregation (Agg-SBOOSP) for massive devices in 5G WSNs using conformable chaotic maps. The SBOOSP enables multi-time offline storage access while reducing processing time. As a result, the signer can utilize the pre-stored offline information in polynomial time. This feature distinguishes our presented SBOOSP from previous online/offline-signing procedures that only allow for one signature. Furthermore, the new procedure supports a secret key during the pre-registration process, but no secret key is necessary during the offline stage. The suggested SBOOSP is secure in the logic of unforgeability on the chosen message attack in the random oracle. Additionally, SBOOSP and Agg-SBOOSP had the lowest computing costs compared to other contending schemes. Overall, the suggested SBOOSP outperforms several preliminary security schemes in terms of performance and computational overhead.

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“…Koziel and Pietrenko‐Dabrowska 2 describe the developments of performance‐driven surrogate modeling methods, which is one of the approaches recently proposed to address the dimensionality and parameter range issues in high‐frequency modeling. Loukreziz et al 3 propose a novel algorithm for sparse least squares‐based polynomial chaos expansion models involving sequential experimental designs, whereas Georg and Römer 4 discuss the utilization of conformal maps to construct basis functions for generalized polynomial chaos (gPC) as a way of enhancing its convergence properties. The advantages of the method are demonstrated using optical components.…”

mentioning

confidence: 99%

Editorial for the special issue on advances in forward and inverse surrogate modeling for high‐frequency design

Koziel

Pietrenko‐Dabrowska

2020

Int J Numerical Modelling

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The design of modern-day high-frequency devices and circuits, including microwave/RF, antenna and photonic components, historically has relied on full-wave electromagnetic (EM) simulation tools. Initially used for design verification, EM simulations are nowadays used in the design process itself, for example, for finding optimum values of geometry and/or material parameters of the structures of interest. In a growing number of cases, EM-driven design closure is mandatory because alternative ways of evaluating the circuit performance (such as through equivalent network modeling) are grossly inaccurate and unable to account for cross-coupling effects (eg, in densely arranged layouts of compact circuits or antenna arrays), or various environmental components that affect the circuit performance (eg, connectors or housing for antenna structures). Despite being imperative, simulation-based design poses significant challenges, mostly due to the high computational cost of accurate, high-fidelity analysis. Repetitive simulations entailed by conventional optimization routines and even more by uncertainty quantification procedures (eg, Monte Carlo analysis) or toleranceaware design tasks may generate the costs that are unmanageable or at least impractical. The availability of massive computational resources does not always translate into design speedup due to the need to account for interactions between devices and their surroundings as well as multiphysics (eg, EM-thermal) effects. Not surprisingly, traditional design procedures that directly utilize EM-simulated responses often fail or are impractical. Alternatives to full-wave simulation tools, therefore, are increasingly popular among EM designers. Among the many available options, fast surrogate models that accurately capture the electrical characteristics of the components of interest, recently have received significant attention. Replacing or supplementing EM analysis by the surrogates enables execution of simulation-based design tasks at low computational cost. This is especially the case for data-driven (approximation) models, which are by far the most popular ones due to their versatility and widespread availability. Some broadly used methods include polynomial regression, kriging, radial basis function, neural networks, and polynomial chaos expansion. The practical issue here is nonlinearity of high-frequency component outputs, which along with the curse of dimensionality, hinders utilization of this class of techniques for multiparameter components. Physicsbased surrogates (eg, space mapping or various response correction methods) feature improved generalization capability at the expense of being problem specific: rendering the surrogate normally involves an underlying low-fidelity model, for example, equivalent network or coarse-mesh EM simulation. In addition to that, inverse modeling has been recently fostered as a practical alternative to forward models when solving certain types of design tasks, especially dimension scaling or high-frequency structures. The...

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Conformally mapped polynomial chaos expansions for Maxwell's source problem with random input data

Cited by 4 publications

References 32 publications

A New Conformal Map for Polynomial Chaos Applied to Direction-of-Arrival Estimation via UCA Root-MUSIC

A New Conformal Map for Polynomial Chaos Applied to Direction-of-Arrival Estimation via UCA Root-MUSIC

SBOOSP for Massive Devices in 5G WSNs Using Conformable Chaotic Maps

Editorial for the special issue on advances in forward and inverse surrogate modeling for high‐frequency design

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