Mercer's spectral decomposition for the characterization of thermal parameters

Ahusborde, Etienne; Azaïez, Mejdi; Belgacem, Fethi Ben; Barrio, Elena Palomo del

doi:10.1016/j.jcp.2015.03.037

Cited by 1 publication

(6 citation statements)

References 15 publications

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“…The Karhunen-Loève expansion then allows us to keep the equations with the most information. This issue was handled in the continuous case in [5,[7][8][9].…”

Section: Identification Problemmentioning

confidence: 99%

“…The next step is to use the Karhunen-Love's expansion of (T n ) n and set u = v l (v l belongs to H 1 (Ω) by [5,Proposion 3.1] ). By the orthogonality of (v k ) k we get where Φ and V are the singular vectors defined in (4.6), and Σ the diagonal matrix of the singular values.…”

Section: Time-space Equationmentioning

confidence: 99%

“…In order to avoid this variation, the result will be an average of several computations. We take α,β = exp(1),3π ≈ 2.72,9.42 as shown in [5]. The results are presented in Table 1.…”

Section: Time-space Equationmentioning

confidence: 99%

“…For our simulation, we add a noise on the temperature field and perform the Karhunen-Loève expansion on the disturbed field. In [5], the noise is introduced in the Gram matrix. The result depicted in Table 1 seems to be less sensitive to the noise than in [5].…”

Section: Time-space Equationmentioning

confidence: 99%

“…In [28], they explicit this decay by using the smoothness of the solution. Nevertheless, in [1] for bi-variate functions, and in [5] for the heat transfer equation, by using some algebraic properties satisfied by the spatial correlation matrix, they obtain an exponential decay.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Karhunen-Loève Expansion for the Discrete Transient Heat Transfer Equation

Fahlaoui¹

2018

JMS

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In this paper we perform and analyze a Karhunen-Loève expansion on the solution of a discrete heat equation. Unlike the continuous case, several choices can be made from the numerical scheme to the numerical time integration. We analyze some of these choices and compare them. In literature, it is shown that the KL-expansion's error depends on the singular values of the matrix (or the operator) which we attempt to compress, but there is few results on the decay of these singular values. The core of this article is to prove the exponential decay of the singular values. To achieve this result, the analysis is conducted in a classical way by considering the spatial correlation of the temperature. And then, we analyze the problem in a more general view by using the Krylov matrices with Hermitian argument, which are a generalization of the well-known Vandermonde matrices. Some computations are made using MATLAB to ensure the performance of the Karhunen-Loève expansion. This article presents an application of this work to an identification problem where the data are disturbed by a Gaussian white noise.

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“…The Karhunen-Loève expansion then allows us to keep the equations with the most information. This issue was handled in the continuous case in [5,[7][8][9].…”

Section: Identification Problemmentioning

confidence: 99%

Section: Time-space Equationmentioning

confidence: 99%

“…In order to avoid this variation, the result will be an average of several computations. We take α,β = exp(1),3π ≈ 2.72,9.42 as shown in [5]. The results are presented in Table 1.…”

Section: Time-space Equationmentioning

confidence: 99%

Section: Time-space Equationmentioning

confidence: 99%