Enhanced Adaptive Surrogate Models With Applications in Uncertainty Quantification for Nanoplasmonics

Georg, Niklas; Loukrezis, Dimitrios; Schöps, Sebastian

doi:10.1615/int.j.uncertaintyquantification.2020031727

Cited by 8 publications

(31 citation statements)

References 78 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…as it has already been established in the recent works 8,11,26 and fulfills the intended properties for a substantial range of epsilon neighborhoods, see, for example, Ref., 8 theorem 4 or Ref., 11 Figure 7B. A detailed comparison of different mappings is out of the scope of this paper.…”

Section: Conformally Mapped Generalized Polynomial Chaossupporting

confidence: 57%

“…For further details on this subject, we refer to Refs. 11,14 We start with the time-harmonic curl-curl equation…”

Section: Maxwell's Source Problemmentioning

confidence: 99%

“…where we refer to (Ref., 11 appendix A) for a derivation and definition of the functionals ℱ Á ð Þ, G Á ð Þ. We assume in the following that the complex permittivity ε depends smoothly on a parameter vector y Ξ & ℝ N .…”

Section: Maxwell's Source Problemmentioning

confidence: 99%

“…These parameters can then be used to model variations in the refractive indices or extinction coefficients of the (different) materials in D, as well as changes in the geometry of the material interfaces inside the domain D. Following a standard Galerkin procedure, cf. Ref., 11 we then obtain a FE model in the form find e y ð Þ V s:t:…”

Section: Maxwell's Source Problemmentioning

confidence: 99%

“…8 to derive new numerical quadrature formulas, and have also recently been considered in the context of stochastic collocation methods. 10,11 In this work, we address the combination of conformal maps and polynomial chaos expansions. Based on the assumption that h ≔ Q 1D g has a larger Bernstein ellipse than Q 1D , and is hence better suited to be approximated with polynomials, we propose a new orthogonal basis…”

Section: Conformally Mapped Generalized Polynomial Chaosmentioning

confidence: 99%

See 4 more Smart Citations

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

Georg

2020

Int J Numerical Modelling

Self Cite

View full text Add to dashboard Cite

Generalized Polynomial Chaos (gPC) expansions are well established for forward uncertainty propagation in many application areas. Although the associated computational effort may be reduced in comparison to Monte Carlo techniques, for instance, further convergence acceleration may be important to tackle problems with high parametric sensitivities. In this work, we propose the use of conformal maps to construct a transformed gPC basis, in order to enhance the convergence order. The proposed basis still features orthogonality properties and hence, facilitates the computation of many statistical quantities such as sensitivities and moments. The corresponding surrogate models are computed by pseudo-spectral projection using mapped quadrature rules, which leads to an improved cost accuracy ratio. We apply the methodology to Maxwell's source problem with random input data. In particular, numerical results for a parametric finite element model of an optical grating coupler are given.

show abstract

Section: Conformally Mapped Generalized Polynomial Chaossupporting

confidence: 57%

“…For further details on this subject, we refer to Refs. 11,14 We start with the time-harmonic curl-curl equation…”

Section: Maxwell's Source Problemmentioning

confidence: 99%

Section: Maxwell's Source Problemmentioning

confidence: 99%

Section: Maxwell's Source Problemmentioning

confidence: 99%

Section: Conformally Mapped Generalized Polynomial Chaosmentioning

confidence: 99%

See 3 more Smart Citations

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

Georg

2020

Int J Numerical Modelling

Self Cite

View full text Add to dashboard Cite

show abstract

An adaptive sparse grid rational Arnoldi method for uncertainty quantification of dynamical systems in the frequency domain

Bollhöfer

Sreekumar

Blech

et al. 2021

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

In this paper, we address discrete linear systems in the frequency domain, where both frequency and random parameters are considered. Sampling such a system many times is computationally challenging if the size is too large, which is often the case for a finite element discretization of partial differential equations.We propose an adaptive method, steered by dual error indicators, which combines rational Arnoldi model order reduction and sparse grid interpolation with hierarchical Leja nodes. At each Leja node, a reduced order model (ROM) is constructed such that the ROM-error in the frequency domain is balanced with the sparse grid error in the random parameter domain. Both the ROM basis and the sparse grid set are enlarged in a hierarchical manner to achieve a prescribed accuracy in statistical moments. Moreover, parameter sensitivities over the frequency range can be easily extracted from the combined reduced order-surrogate model. In the numerical tests considered in the paper, the method employs sampling sets, which are reduced by at least an order of magnitude, compared to Monte Carlo simulation. Additionally, for an example from vibroacoustics, building a ROM reduces the system size by roughly a factor of 100, while still providing an acceptable accuracy.

show abstract

An hp‐adaptive multi‐element stochastic collocation method for surrogate modeling with information re‐use

Galetzka

Loukrezis

Georg

et al. 2023

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

This article introduces an hp-adaptive multi-element stochastic collocation method, which additionally allows to re-use existing model evaluations during either h-or p-refinement. The collocation method is based on weighted Leja nodes. After h-refinement, local interpolations are stabilized by adding and sorting Leja nodes on each newly created sub-element in a hierarchical manner.For p-refinement, the local polynomial approximations are based on total-degree or dimension-adaptive bases. The method is applied in the context of forward and inverse uncertainty quantification to handle non-smooth or strongly localized response surfaces. The performance of the proposed method is assessed in several test cases, also in comparison to competing methods.

show abstract

Enhanced Adaptive Surrogate Models With Applications in Uncertainty Quantification for Nanoplasmonics

Cited by 8 publications

References 78 publications

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

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

An adaptive sparse grid rational Arnoldi method for uncertainty quantification of dynamical systems in the frequency domain

An hp‐adaptive multi‐element stochastic collocation method for surrogate modeling with information re‐use

Contact Info

Product

Resources

About